Fundamentals of Financial Management 14th Edition by Eugene F. Brigham - Test Bank

Fundamentals of Financial Management 14th Edition by Eugene F. Brigham – Test Bank

 

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Sample Questions Are Posted Below

 

Note that there is an overlap between the T/F and multiple-choice questions, as some of the T/F statements are used in multiple-choice questions.   Multiple Choice:  True/False

 

1. Starting to invest early for retirement increases the benefits of compound interest.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Compounding KEYWORDS:   Bloom’s: Knowledge

 

2. Starting to invest early for retirement reduces the benefits of compound interest.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Compounding KEYWORDS:   Bloom’s: Knowledge

 

3. A time line is meaningful even if all cash flows do not occur annually.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Compounding KEYWORDS:   Bloom’s: Knowledge

 

4. A time line is not meaningful unless all cash flows occur annually.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Compounding KEYWORDS:   Bloom’s: Knowledge

 

5. Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Compounding KEYWORDS:   Bloom’s: Knowledge

 

6. Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Compounding KEYWORDS:   Bloom’s: Knowledge

 

7. Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Compounding KEYWORDS:   Bloom’s: Knowledge

 

8. Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Compounding KEYWORDS:   Bloom’s: Knowledge

 

9. Some of the cash flows shown on a time line can be in the form of annuity payments while others can be uneven amounts.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Compounding KEYWORDS:   Bloom’s: Knowledge

 

10. Some of the cash flows shown on a time line can be in the form of annuity payments but none can be uneven amounts.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Compounding KEYWORDS:   Bloom’s: Knowledge

 

11. If the discount (or interest) rate is positive, the present value of an expected series of payments will always exceed the future value of the same series.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-3 Present Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.03 – Present Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV versus FV KEYWORDS:   Bloom’s: Comprehension

 

12. If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-3 Present Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.03 – Present Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV versus FV KEYWORDS:   Bloom’s: Comprehension

 

13. Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future value.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-3 Present Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.03 – Present Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV versus FV KEYWORDS:   Bloom’s: Comprehension

 

14. Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-3 Present Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.03 – Present Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV versus FV KEYWORDS:   Bloom’s: Comprehension

 

15. If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Effective annual rate KEYWORDS:   Bloom’s: Comprehension

 

16. If a bank compounds savings accounts quarterly, the effective annual rate will exceed the nominal rate.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Effective annual rate KEYWORDS:   Bloom’s: Comprehension

 

17. The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the greater the present value of a given lump sum to be received at some future date.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Compounding KEYWORDS:   Bloom’s: Comprehension

 

18. The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the smaller the present value of a given lump sum to be received at some future date.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Compounding KEYWORDS:   Bloom’s: Comprehension

 

19. Suppose Sally Smith plans to invest $1,000. She can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be more than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)   a. True   b. False   ANSWER:   True RATIONALE:   Work out the numbers with a calculator: PV 1000 FVA = $1,710.34 Rate on A 5% 2 × FVA = $3,420.68 Rate on B 12% FVB = $3,478.55 Years 11 FVB > 2 × FVA, so TRUE POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Comparative compounding KEYWORDS:   Bloom’s: Evaluation

 

20. Suppose Randy Jones plans to invest $1,000. He can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be somewhat less than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)   a. True   b. False   ANSWER:   False RATIONALE:   Work out the numbers with a calculator: PV 1000 FVA = $1,710.34 Rate on A 5% 2 × FVA = $3,420.68 Rate on B 12% FVB = $3,478.55 Years 11 FVB > 2 × FVA, so FALSE POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Comparative compounding KEYWORDS:   Bloom’s: Evaluation

 

21. The present value of a future sum decreases as either the discount rate or the number of periods per year increases, other things held constant.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-3 Present Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.03 – Present Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of a sum KEYWORDS:   Bloom’s: Comprehension

 

22. The present value of a future sum increases as either the discount rate or the number of periods per year increases, other things held constant.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-3 Present Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.03 – Present Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of a sum KEYWORDS:   Bloom’s: Comprehension

 

23. All other things held constant, the present value of a given annual annuity decreases as the number of periods per year increases.   a. True   b. False   ANSWER:   True RATIONALE:   One could make up an example and see that the statement is true. Alternatively, one could simply recognize that the PV of an annuity declines as the discount rate increases and recognize that more frequent compounding increases the effective rate. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-9 Present Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.09 – Present Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of an annuity KEYWORDS:   Bloom’s: Comprehension

 

24. All other things held constant, the present value of a given annual annuity increases as the number of periods per year increases.   a. True   b. False   ANSWER:   False RATIONALE:   One could make up an example and see that the statement is false. Alternatively, one could simply recognize that the PV of an annuity declines as the discount rate increases and recognize that more frequent compounding increases the effective rate. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-9 Present Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.09 – Present Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of an annuity KEYWORDS:   Bloom’s: Comprehension

 

25. If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-15 Semiannual and Other Compounding Periods LEARNING OBJECTIVES:   FOFM.BRIG.16.05.15 – Semiannual and Other Compounding Periods NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Periodic and nominal rates KEYWORDS:   Bloom’s: Knowledge

 

26. If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-15 Semiannual and Other Compounding Periods LEARNING OBJECTIVES:   FOFM.BRIG.16.05.15 – Semiannual and Other Compounding Periods NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Periodic and nominal rates KEYWORDS:   Bloom’s: Knowledge

 

27. As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or greater than the nominal rate on the deposit (or loan).   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Effective and nominal rates KEYWORDS:   Bloom’s: Comprehension

 

28. As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or less than the nominal rate on the deposit (or loan).   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Effective and nominal rates KEYWORDS:   Bloom’s: Comprehension

 

29. When a loan is amortized, a relatively high percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment’s percentage declines in the loan’s later years.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization KEYWORDS:   Bloom’s: Comprehension

 

30. When a loan is amortized, a relatively low percentage of the payment goes to reduce the outstanding principal in the early years, and the principal repayment’s percentage increases in the loan’s later years.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FFMC.BRIG.15.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization KEYWORDS:   Bloom’s: Comprehension

 

31. The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan’s life, the greater the percentage of the payment that will be a repayment of principal.   a. True   b. False   ANSWER:   True POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization KEYWORDS:   Bloom’s: Comprehension

 

32. The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan’s life, the smaller the percentage of the payment that will be a repayment of principal.   a. True   b. False   ANSWER:   False POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization KEYWORDS:   Bloom’s: Comprehension

 

33. Midway through the life of an amortized loan, the percentage of the payment that represents interest must be equal to the percentage that represents repayment of principal. This is true regardless of the original life of the loan or the interest rate on the loan.   a. True   b. False   ANSWER:   False RATIONALE:   There is no reason to think that this statement would always be true. The portion of the payment representing interest declines, while the portion representing principal repayment increases. Therefore, the statement is false. We could also work out some numbers to prove this point. Here’s an example for a 3-year loan at a 10% and a 41.45% annual interest rate. The interest component is not equal to the principal repayment component except at the high interest rate. Original loan $1,000   Original loan $1,000 Rate 10%   Rate 41.45% Life 3   Life 3 Payment $402.11   Payment $640.98     Beg.     End.   Beg.     End.   Balance Interest Principal Bal.   Balance Interest Principal Bal. 1 $1,000.00 $100.00 $302.11 $697.89 1 $1,000.00 $414.50 $226.48 $773.52 2 $ 697.89 $ 69.79 $332.33 $365.56 2 $ 773.52 $320.62 $320.36 $453.15 3 $ 365.56 $ 36.56 $365.56 $ 0.00 3 $ 453.15 $187.83 $453.15 $ 0.00 POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization KEYWORDS:   Bloom’s: Comprehension

 

34. Midway through the life of an amortized loan, the percentage of the payment that represents interest could be equal to, less than, or greater than to the percentage that represents repayment of principal. The proportions depend on the original life of the loan and the interest rate.   a. True   b. False   ANSWER:   True RATIONALE:   This statement is true. The portion of the payment representing interest declines, while the portion representing principal repayment increases. The interest portion could be equal to, greater than, or less than the principal portion. We can work out some numbers to prove this point. Here’s an example for a 3-year loan at a 10% and a 41.45% annual interest rate. The interest component is less than the principal at 10%, equal at about 41.45%, and greater at rates above 41.45%. Original loan $1,000   Original loan $1,000 Rate 10%   Rate 41.45% Life 3   Life 3 Payment $402.11   Payment $640.98     Beg.     End.   Beg.     End.   Balance Interest Principal Bal.   Balance Interest Principal Bal. 1 $1,000.00 $100.00 $302.11 $697.89 1 $1,000.00 $414.50 $226.48 $773.52 2 $ 697.89 $ 69.79 $332.33 $365.56 2 $ 773.52 $320.62 $320.36 $453.15 3 $ 365.56 $ 36.56 $365.56 $ 0.00 3 $ 453.15 $187.83 $453.15 $ 0.00 POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization KEYWORDS:   Bloom’s: Comprehension

 

Multiple Choice:  Conceptual   Please note that some of the answer choices, or answers that are very close, are used in different questions.  This has caused us no difficulties, but please take this into account when you make up exams.

 

35. Which of the following statements is CORRECT?   a. A time line is not meaningful unless all cash flows occur annually.   b. Time lines are useful for visualizing complex problems prior to doing actual calculations.   c. Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly.   d. Time lines cannot be constructed for annuities where the payments occur at the beginning of the periods.   e. Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven amounts.   ANSWER:   b POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-1 Time Lines LEARNING OBJECTIVES:   FOFM.BRIG.16.05.01 – Time Lines NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Time lines KEYWORDS:   Bloom’s: Knowledge OTHER:   Multiple Choice: Conceptual

 

36. Which of the following statements is CORRECT?   a. A time line is not meaningful unless all cash flows occur annually.   b. Time lines are not useful for visualizing complex problems prior to doing actual calculations.   c. Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly.   d. Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.   e. Some of the cash flows shown on a time line can be in the form of annuity payments, but none can be uneven amounts.   ANSWER:   d POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-1 Time Lines LEARNING OBJECTIVES:   FOFM.BRIG.16.05.01 – Time Lines NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Time lines KEYWORDS:   Bloom’s: Knowledge OTHER:   Multiple Choice: Conceptual

 

37. Which of the following statements is CORRECT?   a. A time line is not meaningful unless all cash flows occur annually.   b. Time lines are not useful for visualizing complex problems prior to doing actual calculations.   c. Time lines can be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly.   d. Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities.   e. Time lines cannot be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity.   ANSWER:   c POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-1 Time Lines LEARNING OBJECTIVES:   FOFM.BRIG.16.05.01 – Time Lines NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Time lines KEYWORDS:   Bloom’s: Knowledge OTHER:   Multiple Choice: Conceptual

 

38. Which of the following statements is CORRECT?   a. A time line is not meaningful unless all cash flows occur annually.   b. Time lines are not useful for visualizing complex problems prior to doing actual calculations.   c. Time lines cannot be constructed to deal with situations where some of the cash flows occur annually but others occur quarterly.   d. Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for ordinary annuities.   e. Time lines can be constructed where some of the payments constitute an annuity but others are unequal and thus are not part of the annuity.   ANSWER:   e POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-1 Time Lines LEARNING OBJECTIVES:   FOFM.BRIG.16.05.01 – Time Lines NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Time lines KEYWORDS:   Bloom’s: Knowledge OTHER:   Multiple Choice: Conceptual

 

39. You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would lower the calculated value of the investment?   a. The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for only 5 rather than 10 years, hence that each payment is for $20,000 rather than for $10,000.   b. The discount rate increases.   c. The riskiness of the investment’s cash flows decreases.   d. The total amount of cash flows remains the same, but more of the cash flows are received in the earlier years and less are received in the later years.   e. The discount rate decreases.   ANSWER:   b POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-3 Present Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.03 – Present Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Effects of factors on PVs KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

40. You plan to analyze the value of a potential investment by calculating the sum of the present values of its expected cash flows. Which of the following would increase the calculated value of the investment?   a. The cash flows are in the form of a deferred annuity, and they total to $100,000. You learn that the annuity lasts for 10 years rather than 5 years, hence that each payment is for $10,000 rather than for $20,000.   b. The discount rate decreases.   c. The riskiness of the investment’s cash flows increases.   d. The total amount of cash flows remains the same, but more of the cash flows are received in the later years and less are received in the earlier years.   e. The discount rate increases.   ANSWER:   b POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-3 Present Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.03 – Present Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Effects of factors on PVs KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

41. Which of the following statements is CORRECT?   a. The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.   b. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity.   c. The cash flows for an annuity due must all occur at the ends of the periods.   d. The cash flows for an annuity must all be equal, and they must occur at regular intervals, such as once a year or once a month.   e. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity.   ANSWER:   d POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-6 Annuities LEARNING OBJECTIVES:   FOFM.BRIG.16.05.06 – Annuities NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Annuities KEYWORDS:   Bloom’s: Knowledge OTHER:   Multiple Choice: Conceptual

 

42. Which of the following statements is CORRECT?   a. The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.   b. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity.   c. The cash flows for an annuity due must all occur at the beginning of the periods.   d. The cash flows for an annuity may vary from period to period, but they must occur at regular intervals, such as once a year or once a month.   e. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity.   ANSWER:   c POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-6 Annuities LEARNING OBJECTIVES:   FOFM.BRIG.16.05.06 – Annuities NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.06 – Reflective thinking STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Annuities KEYWORDS:   Bloom’s: Knowledge OTHER:   Multiple Choice: Conceptual

 

43. Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?   a. The periodic rate of interest is 1.5% and the effective rate of interest is 3%.   b. The periodic rate of interest is 6% and the effective rate of interest is greater than 6%.   c. The periodic rate of interest is 1.5% and the effective rate of interest is greater than 6%.   d. The periodic rate of interest is 3% and the effective rate of interest is 6%.   e. The periodic rate of interest is 6% and the effective rate of interest is also 6%.   ANSWER:   c POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Quarterly compounding KEYWORDS:   Bloom’s: Application OTHER:   Multiple Choice: Conceptual

 

44. Your bank account pays an 8% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?   a. The periodic rate of interest is 2% and the effective rate of interest is 4%.   b. The periodic rate of interest is 8% and the effective rate of interest is greater than 8%.   c. The periodic rate of interest is 4% and the effective rate of interest is less than 8%.   d. The periodic rate of interest is 2% and the effective rate of interest is greater than 8%.   e. The periodic rate of interest is 8% and the effective rate of interest is also 8%.   ANSWER:   d POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Quarterly compounding KEYWORDS:   Bloom’s: Application OTHER:   Multiple Choice: Conceptual

 

45. A $50,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT?   a. The annual payments would be larger if the interest rate were lower.   b. If the loan were amortized over 10 years rather than 7 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 7-year amortization plan.   c. The proportion of each payment that represents interest as opposed to repayment of principal would be lower if the interest rate were lower.   d. The last payment would have a higher proportion of interest than the first payment.   e. The proportion of interest versus principal repayment would be the same for each of the 7 payments.   ANSWER:   c RATIONALE:   a, d, and e can be ruled out as incorrect by simple reasoning. b is also incorrect because interest in the first year would be loan amount × interest rate regardless of the life of the loan, so the interest payment would be identical for the first payment. Think about the situation where r = 0%, statement c is the “most logical guess.” One could also set up an amortization schedule and change the numbers to confirm that only c is correct. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

46. A $150,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT?   a. The annual payments would be larger if the interest rate were lower.   b. If the loan were amortized over 10 years rather than 7 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 7-year amortization plan.   c. The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were lower.   d. The proportion of each payment that represents interest versus repayment of principal would be higher if the interest rate were higher.   e. The proportion of interest versus principal repayment would be the same for each of the 7 payments.   ANSWER:   d RATIONALE:   a, c, and e are obviously incorrect. b is also incorrect because interest in the first year would be loan amount × interest rate regardless of the life of the loan. That makes d the “most logical guess.” One could also set up an amortization schedule and change the numbers to confirm that only d is correct. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

47. Which of the following statements regarding a 15-year (180-month) $125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)   a. The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years.   b. Because it is a fixed-rate mortgage, the monthly loan payments (which include both interest and principal payments) are constant.   c. Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant.   d. The proportion of the monthly payment that goes towards repayment of principal will be lower 10 years from now than it will be the first year.   e. The outstanding balance declines at a slower rate in the later years of the loan’s life.   ANSWER:   b RATIONALE:   b is the correct answer. Thinking through the question, the other answers can all be eliminated. One could also set up an amortization schedule to prove that only statement b is correct. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

48. Which of the following statements regarding a 15-year (180-month) $125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)   a. The remaining balance after three years will be $125,000 less one third of the interest paid during the first three years.   b. Because the outstanding balance declines over time, the monthly payments will also decline over time.   c. Interest payments on the mortgage will increase steadily over time, but the total amount of each payment will remain constant.   d. The proportion of the monthly payment that goes towards repayment of principal will be lower 10 years from now than it will be the first year.   e. The outstanding balance declines at a faster rate in the later years of the loan’s life.   ANSWER:   e RATIONALE:   e is the correct answer. Thinking through the question, the other answers can all be eliminated. One could also set up an amortization schedule to prove that only statement e is correct. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization KEYWORDS:   Bloom’s Analysis OTHER:   Multiple Choice: Conceptual

 

49. Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT?   a. The monthly payments will decline over time.   b. A smaller proportion of the last monthly payment will be interest, and a larger proportion will be principal, than for the first monthly payment.   c. The total dollar amount of principal being paid off each month gets smaller as the loan approaches maturity.   d. The amount representing interest in the first payment would be higher if the nominal interest rate were 7% rather than 10%.   e. Exactly 10% of the first monthly payment represents interest.   ANSWER:   b RATIONALE:   b is correct. a is clearly wrong, as are c and d. It is not obvious whether e is correct or not, but we could set up an example to see: Loan 100000   Term 30 Rate 10%   Periods/Year 12 Periodic rate 0.008333333   Total periods 360           Payment −$877.57   Interest, Month 1 $833.33 Interest as % of total #360 payment: 1%   Interest, Month 360 $7.25 Principal as % of total #360 payment 99%   Principal, Month 360 $870.32 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

50. Which of the following statements regarding a 30-year monthly payment amortized mortgage with a nominal interest rate of 10% is CORRECT?   a. The monthly payments will increase over time.   b. A larger proportion of the first monthly payment will be interest, and a smaller proportion will be principal, than for the last monthly payment.   c. The total dollar amount of interest being paid off each month gets larger as the loan approaches maturity.   d. The amount representing interest in the first payment would be higher if the nominal interest rate were 7% rather than 10%.   e. Exactly 10% of the first monthly payment represents interest.   ANSWER:   b RATIONALE:   b is correct. a is clearly wrong, as are c and d. It is not obvious whether e is correct or not, but we could set up an example to see: Loan 100000   Term 30 Rate 10%   Periods/Year 12 Periodic rate 0.00833333   Total periods 360           Payment −$877.57   Interest Month 1 $833.33 Interest as % of total payment: 95%,  which is much larger than 10%. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

51. Which of the following investments would have the highest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero.   a. Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).   b. Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).   c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).   d. Investment D pays $2,500 at the end of 10 years (just one payment).   e. Investment E pays $250 at the end of every year for the next 10 years (a total of 10 payments).   ANSWER:   a RATIONALE:   A dominates B because it provides the same total amount, but it comes faster, hence it can earn more interest over the 10 years. A also dominates C and E for the same reason, and it dominates D because with D no interest whatever is earned. We could also do these calculations to answer the question: A $4,382.79 Largest EFF% 10.00% 10 250 B $4,081.59   NOM%   9.76%   125 C $4,280.81         125 D $2,500.00         2500 E $3,984.36         250 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Time value concepts KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

52. Which of the following investments would have the lowest present value? Assume that the effective annual rate for all investments is the same and is greater than zero.   a. Investment A pays $250 at the end of every year for the next 10 years (a total of 10 payments).   b. Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).   c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).   d. Investment D pays $2,500 at the end of 10 years (just one payment).   e. Investment E pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).   ANSWER:   d RATIONALE:   A is smaller than E and B is smaller than C because the money comes in later. A is smaller than B because a larger annuity is received later. So, now the choice comes down to either A or D. Since all of D is received at the end, this is the logical choice. We could also do these calculations to answer the question: A $1,536.14   EFF% 10.00% 10 250 B $1,573.63   NOM%   9.76%   125 C $1,650.44         125 D $ 963.86 Smallest       2500 E $1,689.76         250 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Time value concepts KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

53. A U.S. Treasury bond will pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%, semiannual compounding. Which of the following statements is CORRECT?   a. The periodic interest rate is greater than 3%.   b. The periodic rate is less than 3%.   c. The present value would be greater if the lump sum were discounted back for more periods.   d. The present value of the $1,000 would be smaller if interest were compounded monthly rather than semiannually.   e. The PV of the $1,000 lump sum has a higher present value than the PV of a 3-year, $333.33 ordinary annuity.   ANSWER:   d POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Time value concepts KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

54. A U.S. Treasury bond will pay a lump sum of $1,000 exactly 3 years from today. The nominal interest rate is 6%, semiannual compounding. Which of the following statements is CORRECT?   a. The periodic interest rate is greater than 3%.   b. The periodic rate is less than 3%.   c. The present value would be greater if the lump sum were discounted back for more periods.   d. The present value of the $1,000 would be larger if interest were compounded monthly rather than semiannually.   e. The PV of the $1,000 lump sum has a smaller present value than the PV of a 3-year, $333.33 ordinary annuity.   ANSWER:   e POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Time value concepts KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

55. Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant?   a. The present value of a 5-year, $250 annuity due will be lower than the PV of a similar ordinary annuity.   b. A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage.   c. A bank loan’s nominal interest rate will always be equal to or less than its effective annual rate.   d. If an investment pays 10% interest, compounded annually, its effective annual rate will be less than 10%.   e. Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays semiannually. Deposits in Bank B will provide the higher future value if you leave your funds on deposit.   ANSWER:   c POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Time value concepts KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

56. Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant?   a. The present value of a 5-year, $250 annuity due will be lower than the PV of a similar ordinary annuity.   b. A 30-year, $150,000 amortized mortgage will have larger monthly payments than an otherwise similar 20-year mortgage.   c. A bank loan’s nominal interest rate will always be equal to or greater than its effective annual rate.   d. If an investment pays 10% interest, compounded quarterly, its effective annual rate will be greater than 10%.   e. Banks A and B offer the same nominal annual rate of interest, but A pays interest quarterly and B pays semiannually. Deposits in Bank B will provide the higher future value if you leave your funds on deposit.   ANSWER:   d POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Time value concepts KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

57. Which of the following statements is CORRECT?   a. The present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity.   b. If a loan has a nominal annual rate of 8%, then the effective rate can never be greater than 8%.   c. If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different.   d. The proportion of the payment that goes toward interest on a fully amortized loan increases over time.   e. An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%.   ANSWER:   a POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Time value concepts KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

58. Which of the following statements is CORRECT?   a. The present value of a 3-year, $150 ordinary annuity will exceed the present value of a 3-year, $150 annuity due.   b. If a loan has a nominal annual rate of 8%, then the effective rate will never be less than 8%.   c. If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be different.   d. The proportion of the payment that goes toward interest on a fully amortized loan increases over time.   e. An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is smaller than 6%.   ANSWER:   b POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Time value concepts KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

59. You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?   a. The present value of ORD must exceed the present value of DUE, but the future value of ORD may be less than the future value of DUE.   b. The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD.   c. The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE.   d. The present value of DUE exceeds the present value of ORD, and the future value of DUE also exceeds the future value of ORD.   e. If the going rate of interest decreases from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant.   ANSWER:   d POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Annuities KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

60. You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?   a. A rational investor would be willing to pay more for DUE than for ORD, so their market prices should differ.   b. The present value of DUE exceeds the present value of ORD, while the future value of DUE is less than the future value of ORD.   c. The present value of ORD exceeds the present value of DUE, and the future value of ORD also exceeds the future value of DUE.   d. The present value of ORD exceeds the present value of DUE, while the future value of DUE exceeds the future value of ORD.   e. If the going rate of interest decreases from 10% to 0%, the difference between the present value of ORD and the present value of DUE would remain constant.   ANSWER:   a POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Annuities KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

61. Which of the following statements is CORRECT?   a. If you have a series of cash flows, each of which is positive, you can solve for I, where the solution value of I causes the PV of the cash flows to equal the cash flow at Time 0.   b. If you have a series of cash flows, and CF0 is negative but each of the following CFs is positive, you can solve for I, but only if the sum of the undiscounted cash flows exceeds the cost.   c. To solve for I, one must identify the value of I that causes the PV of the positive CFs to equal the absolute value of the PV of the negative CFs. This is, essentially, a trial-and-error procedure that is easy with a computer or financial calculator but quite difficult otherwise.   d. If you solve for I and get a negative number, then you must have made a mistake.   e. If CF0 is positive and all the other CFs are negative, then you cannot solve for I.   ANSWER:   c POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   5-14 Solving for I with Uneven Cash Flows LEARNING OBJECTIVES:   FOFM.BRIG.16.05.14 – Solving for I with Uneven Cash Flows NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Solving for I: uneven CFs KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Conceptual

 

62. Which of the following statements is CORRECT?   a. If you have a series of cash flows, each of which is positive, you can solve for I, where the solution value of I causes the PV of the cash flows to equal the cash flow at Time 0.   b. If you have a series of cash flows, and CF0 is negative but each of the following CFs is positive, you can solve for I, but only if the sum of the undiscounted cash flows exceeds the cost.   c. To solve for I, one must identify the value of I that causes the PV of the positive CFs to equal the absolute value of the FV of the negative CFs. It is impossible to find the value of I without a computer or financial calculator.   d. If you solve for I and get a negative number, then you must have made a mistake.   e. If CF0 is positive and all the other CFs are negative, then you can still solve for I.   ANSWER:   e POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   5-14 Solving for I with Uneven Cash Flows LEARNING OBJECTIVES:   FOFM.BRIG.16.05.14 – Solving for I with Uneven Cash Flows NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Solving for I: uneven CFs KEYWORDS:   Bloom’s: Analysis

 

63. Which of the following bank accounts has the highest effective annual return?   a. An account that pays 8% nominal interest with monthly compounding.   b. An account that pays 8% nominal interest with annual compounding.   c. An account that pays 7% nominal interest with daily (365-day) compounding.   d. An account that pays 7% nominal interest with monthly compounding.   e. An account that pays 8% nominal interest with daily (365-day) compounding.   ANSWER:   e RATIONALE:   By inspection, we can see that e dominates a and b, and that c dominates d because, with the same interest rate, the account with the most frequent compounding has the highest EFF%. Thus, the correct answer must be either e or c. Moreover, we can see by inspection that since c and e have the same compounding frequency yet e has the higher nominal rate, e must have the higher EFF%. You could also prove that e is the correct choice by calculating the EFF%s: a. 8.300% = (1 + 0.08/12)12 − 1 b. 8.000% = (1 + 0.08/1)1 − 1 c. 7.250% = (1 + 0.07/365)365 − 1 d. 7.229% = (1 + 0.07/12)12 − 1 e. 8.328% = (1 + 0.08/365)365 − 1 POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Effective annual rate KEYWORDS:   Bloom’s: Evaluation

 

64. Which of the following bank accounts has the lowest effective annual return?   a. An account that pays 8% nominal interest with monthly compounding.   b. An account that pays 8% nominal interest with annual compounding.   c. An account that pays 7% nominal interest with daily (365-day) compounding.   d. An account that pays 7% nominal interest with monthly compounding.   e. An account that pays 8% nominal interest with daily (365-day) compounding.   ANSWER:   d RATIONALE:   By inspection, we can see that b must have a lower EFF% than either a or e because they all pay the same nominal rate but b is compounded least frequently. Similarly, c and d pay the same rate, but d is compounded less frequently, hence d must have the lower EFF%. So, the correct answer must be either b or d. It is not obvious which of these two has the lower EFF%, so we must do a quick calculation to determine the correct response. As the following calculations show, d is the correct answer. a. 8.300% = (1 + 0.08/12)12 − 1 b. 8.000% = (1 + 0.08/1)1 − 1 c. 7.250% = (1 + 0.07/365)365 − 1 d. 7.229% = (1 + 0.07/12)12 − 1 e. 8.328% = (1 + 0.08/365)365 − 1 POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Effective annual rate KEYWORDS:   Bloom’s: Evaluation

 

65. You plan to invest some money in a bank account. Which of the following banks provides you with the highest effective rate of interest?   a. Bank 1; 6.1% with annual compounding.   b. Bank 2; 6.0% with monthly compounding.   c. Bank 3; 6.0% with annual compounding.   d. Bank 4; 6.0% with quarterly compounding.   e. Bank 5; 6.0% with daily (365-day) compounding.   ANSWER:   e RATIONALE:   By inspection, we can see that e dominates b, c, and d because, with the same interest rate, the account with the most frequent compounding has the highest EFF%. Thus, the correct answer must be either a or e. However, we cannot tell by inspection whether a or e provides the higher EFF%. We know that with one compounding period a’s EFF% is 6.1%, so we can calculate e’s EFF%. It is 6.183%, so e is the correct answer. a. = (1 + 0.061/12)12 − 1 = 6.100% e. = (1 + 0.06/365)365 − 1 = 6.183% POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Effective annual rate KEYWORDS:   Bloom’s: Evaluation

 

Multiple Choice: Problems

 

66. Sue now has $125. How much would she have after 8 years if she leaves it invested at 8.5% with annual compounding?   a. $205.83   b. $216.67   c. $228.07   d. $240.08   e. $252.08   ANSWER:   d RATIONALE:   N 8 I/YR 8.5% PV $125 PMT $0 FV $240.08 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of a lump sum KEYWORDS:   Bloom’s: Application

 

67. Jose now has $500. How much would he have after 6 years if he leaves it invested at 5.5% with annual compounding?   a. $591.09   b. $622.20   c. $654.95   d. $689.42   e. $723.89   ANSWER:   d RATIONALE:   N 6 I/YR 5.5% PV $500 PMT $0 FV $689.42 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of a lump sum KEYWORDS:   Bloom’s: Application

 

68. Suppose you have $1,500 and plan to purchase a 5-year certificate of deposit (CD) that pays 3.5% interest, compounded annually. How much will you have when the CD matures?   a. $1,781.53   b. $1,870.61   c. $1,964.14   d. $2,062.34   e. $2,165.46   ANSWER:   a RATIONALE:   N 5 I/YR 3.5% PV $1,500 PMT $0 FV $1,781.53 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of a lump sum KEYWORDS:   Bloom’s: Application

 

69. Suppose you have $2,000 and plan to purchase a 10-year certificate of deposit (CD) that pays 6.5% interest, compounded annually. How much will you have when the CD matures?   a. $3,754.27   b. $3,941.99   c. $4,139.09   d. $4,346.04   e. $4,563.34   ANSWER:   a RATIONALE:   N 10 I/YR 6.5% PV $2,000 PMT $0 FV $3,754.27 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of a lump sum KEYWORDS:   Bloom’s: Application

 

70. Last year Rocco Corporation’s sales were $225 million. If sales grow at 6% per year, how large (in millions) will they be 5 years later?   a. $271.74   b. $286.05   c. $301.10   d. $316.16   e. $331.96   ANSWER:   c RATIONALE:   N 5 I/YR 6.0% PV $225.00 PMT $0.00 FV $301.10 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of a lump sum KEYWORDS:   Bloom’s: Application

 

71. Last year Dania Corporation’s sales were $525 million. If sales grow at 7.5% per year, how large (in millions) will they be 8 years later?   a. $ 845.03   b. $ 889.51   c. $ 936.33   d. $ 983.14   e. $1,032.30   ANSWER:   c RATIONALE:   N 8 I/YR 7.5% PV $525.00 PMT $0.00 FV $936.33 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of a lump sum KEYWORDS:   Bloom’s: Application

 

72. How much would $1, growing at 3.5% per year, be worth after 75 years?   a. $12.54   b. $13.20   c. $13.86   d. $14.55   e. $15.28   ANSWER:   b RATIONALE:   N 75 I/YR 3.5% PV $1.00 PMT $0.00 FV $13.20 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of a lump sum KEYWORDS:   Bloom’s: Application

 

73. How much would $100, growing at 5% per year, be worth after 75 years?   a. $3,689.11   b. $3,883.27   c. $4,077.43   d. $4,281.30   e. $4,495.37   ANSWER:   b RATIONALE:   N 75 I/YR 5.0% PV $100.00 PMT $0.00 FV $3,883.27 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of a lump sum KEYWORDS:   Bloom’s: Application

 

74. You deposit $1,000 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years?   a. $2,245.08   b. $2,363.24   c. $2,481.41   d. $2,605.48   e. $2,735.75   ANSWER:   b RATIONALE:   N 25 I/YR 3.5% PV $1,000 PMT $0 FV $2,363.24 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of a lump sum KEYWORDS:   Bloom’s: Application

 

75. You deposit $500 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years?   a. $1,122.54   b. $1,181.62   c. $1,240.70   d. $1,302.74   e. $1,367.88   ANSWER:   b RATIONALE:   N 25 I/YR 3.5% PV $500 PMT $0 FV $1,181.62 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-2 Future Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.02 – Future Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of a lump sum KEYWORDS:   Bloom’s: Application

 

76. Suppose a State of New York bond will pay $1,000 ten years from now. If the going interest rate on these 10-year bonds is 5.5%, how much is the bond worth today?   a. $585.43   b. $614.70   c. $645.44   d. $677.71   e. $711.59   ANSWER:   a RATIONALE:   N 10 I/YR 5.5% PMT $0 FV $1,000.00 PV $585.43 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-3 Present Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.03 – Present Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of a lump sum KEYWORDS:   Bloom’s: Application

 

77. Suppose a State of California bond will pay $1,000 eight years from now. If the going interest rate on these 8-year bonds is 5.5%, how much is the bond worth today?   a. $651.60   b. $684.18   c. $718.39   d. $754.31   e. $792.02   ANSWER:   a RATIONALE:   N 8 I/YR 5.5% PMT $0 FV $1,000.00 PV $651.60 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-3 Present Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.03 – Present Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of a lump sum KEYWORDS:   Bloom’s: Application

 

78. How much would $20,000 due in 50 years be worth today if the discount rate were 7.5%?   a. $438.03   b. $461.08   c. $485.35   d. $510.89   e. $537.78   ANSWER:   e RATIONALE:   N 50 I/YR 7.5% PMT $0 FV $20,000 PV $537.78 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-3 Present Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.03 – Present Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of a lump sum KEYWORDS:   Bloom’s: Application

 

79. How much would $5,000 due in 25 years be worth today if the discount rate were 5.5%?   a. $1,067.95   b. $1,124.16   c. $1,183.33   d. $1,245.61   e. $1,311.17   ANSWER:   e RATIONALE:   N 25 I/YR 5.5% PMT $0 FV $5,000 PV $1,311.17 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-3 Present Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.03 – Present Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of a lump sum KEYWORDS:   Bloom’s: Application

 

80. Suppose a U.S. treasury bond will pay $2,500 five years from now. If the going interest rate on 5-year treasury bonds is 4.25%, how much is the bond worth today?   a. $1,928.78   b. $2,030.30   c. $2,131.81   d. $2,238.40   e. $2,350.32   ANSWER:   b RATIONALE:   N 5 I/YR 4.25% PMT $0 FV $2,500.00 PV $2,030.30 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-3 Present Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.03 – Present Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of a lump sum KEYWORDS:   Bloom’s: Application

 

81. Suppose an Exxon Corporation bond will pay $4,500 ten years from now. If the going interest rate on safe 10-year bonds is 4.25%, how much is the bond worth today?   a. $2,819.52   b. $2,967.92   c. $3,116.31   d. $3,272.13   e. $3,435.74   ANSWER:   b RATIONALE:   N 10 I/YR 4.25% PMT $0 FV $4,500.00 PV $2,967.92 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-3 Present Values LEARNING OBJECTIVES:   FOFM.BRIG.16.05.03 – Present Values NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of a lump sum KEYWORDS:   Bloom’s: Application

 

82. Suppose the U.S. Treasury offers to sell you a bond for $747.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price?   a. 4.37%   b. 4.86%   c. 5.40%   d. 6.00%   e. 6.60%   ANSWER:   d RATIONALE:   N 5 PV $747.25 PMT $0 FV $1,000.00 I/YR 6.00% POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-4 Finding the Interest Rate, I LEARNING OBJECTIVES:   FOFM.BRIG.16.05.04 – Finding the Interest Rate, I NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Finding I KEYWORDS:   Bloom’s: Application

 

83. Suppose the U.S. Treasury offers to sell you a bond for $3,000. No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $5,000. What interest rate would you earn if you bought this bond at the offer price?   a. 3.82%   b. 4.25%   c. 4.72%   d. 5.24%   e. 5.77%   ANSWER:   d RATIONALE:   N 10 PV $3,000.00 PMT $0 FV $5,000.00 I/YR 5.24% POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-4 Finding the Interest Rate, I LEARNING OBJECTIVES:   FOFM.BRIG.16.05.04 – Finding the Interest Rate, I NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Finding I KEYWORDS:   Bloom’s: Application

 

84. Ten years ago, Lucas Inc. earned $0.50 per share. Its earnings this year were $2.20. What was the growth rate in earnings per share (EPS) over the 10-year period?   a. 15.17%   b. 15.97%   c. 16.77%   d. 17.61%   e. 18.49%   ANSWER:   b RATIONALE:   N 10 PV $0.50 PMT $0 FV $2.20 I/YR 15.97% POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-4 Finding the Interest Rate, I LEARNING OBJECTIVES:   FOFM.BRIG.16.05.04 – Finding the Interest Rate, I NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Growth rate KEYWORDS:   Bloom’s: Application

 

85. Five years ago, Weed Go Inc. earned $1.50 per share. Its earnings this year were $3.20. What was the growth rate in earnings per share (EPS) over the 5-year period?   a. 15.54%   b. 16.36%   c. 17.18%   d. 18.04%   e. 18.94%   ANSWER:   b RATIONALE:   N 5 PV $1.50 PMT $0 FV $3.20 I/YR 16.36% POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-4 Finding the Interest Rate, I LEARNING OBJECTIVES:   FOFM.BRIG.16.05.04 – Finding the Interest Rate, I STATE STANDARDS:   United States – OH – DISC.FFMC.BRIG.15.04 – Time value of money TOPICS:   Growth rate KEYWORDS:   Bloom’s: Application

 

86. Janice has $5,000 invested in a bank that pays 3.8% annually. How long will it take for her funds to triple?   a. 23.99   b. 25.26   c. 26.58   d. 27.98   e. 29.46   ANSWER:   e RATIONALE:   I/YR 3.8% PV $5,000.00 PMT $0 FV $15,000.00 N 29.46 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-5 Finding the Number of Years, N LEARNING OBJECTIVES:   FOFM.BRIG.16.05.05 – Finding the Number of Years, N NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Finding N KEYWORDS:   Bloom’s: Application

 

87. Bob has $2,500 invested in a bank that pays 4% annually. How long will it take for his funds to double?   a. 14.39   b. 15.15   c. 15.95   d. 16.79   e. 17.67   ANSWER:   e RATIONALE:   I/YR 4.0% PV $2,500.00 PMT $0 FV $5,000.00 N 17.67 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-5 Finding the Number of Years, N LEARNING OBJECTIVES:   FOFM.BRIG.16.05.05 – Finding the Number of Years, N NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Finding N KEYWORDS:   Bloom’s: Application

 

88. Last year Thomson Inc’s earnings per share were $3.50, and its growth rate during the prior 5 years was 9.0% per year. If that growth rate were maintained, how many years would it take for Thomson’s EPS to triple?   a. 9.29   b. 10.33   c. 11.47   d. 12.75   e. 14.02   ANSWER:   d RATIONALE:   I/YR 9.0% PV $3.50 PMT $0 FV $10.50 N 12.75 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-5 Finding the Number of Years, N LEARNING OBJECTIVES:   FOFM.BRIG.16.05.05 – Finding the Number of Years, N NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Finding N KEYWORDS:   Bloom’s: Application

 

89. You plan to invest in securities that pay 8.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?   a. 5.14   b. 5.71   c. 6.35   d. 7.05   e. 7.84   ANSWER:   e RATIONALE:   I/YR 8.0% PV $5,000.00 PMT $0 FV $9,140.20 N 7.84 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-5 Finding the Number of Years, N LEARNING OBJECTIVES:   FOFM.BRIG.16.05.05 – Finding the Number of Years, N NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Finding N KEYWORDS:   Bloom’s: Application

 

90. You plan to invest in bonds that pay 6.0%, compounded annually. If you invest $10,000 today, how many years will it take for your investment to grow to $30,000?   a. 12.37   b. 13.74   c. 15.27   d. 16.97   e. 18.85   ANSWER:   e RATIONALE:   I/YR 6.0% PV $10,000.00 PMT $0 FV $30,000.00 N 18.85 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-5 Finding the Number of Years, N LEARNING OBJECTIVES:   FOFM.BRIG.16.05.05 – Finding the Number of Years, N NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Finding N KEYWORDS:   Bloom’s: Application

 

91. You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the 3rd deposit, 3 years from now?   a. $11,973   b. $12,603   c. $13,267   d. $13,930   e. $14,626   ANSWER:   c RATIONALE:   N 3 I/YR 5.2% PV $0.00 PMT $4,200 FV $13,266.56 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-7 Future Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.07 – Future Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of ordinary annuity KEYWORDS:   Bloom’s: Application

 

92. You want to buy a new ski boat 2 years from now, and you plan to save $8,200 per year, beginning one year from today. You will deposit your savings in an account that pays 6.2% interest. How much will you have just after you make the 2nd deposit, 2 years from now?   a. $15,260   b. $16,063   c. $16,908   d. $17,754   e. $18,642   ANSWER:   c RATIONALE:   N 2 I/YR 6.2% PV $0.00 PMT $8,200 FV $16,908 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-7 Future Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.07 – Future Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of ordinary annuity KEYWORDS:   Bloom’s: Application

 

93. You want to go to Europe 5 years from now, and you can save $3,100 per year, beginning one year from today. You plan to deposit the funds in a mutual fund that you think will return 8.5% per year. Under these conditions, how much would you have just after you make the 5th deposit, 5 years from now?   a. $18,369   b. $19,287   c. $20,251   d. $21,264   e. $22,327   ANSWER:   a RATIONALE:   N 5 I/YR 8.5% PV $0.00 PMT $3,100 FV $18,369 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-7 Future Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.07 – Future Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of ordinary annuity KEYWORDS:   Bloom’s: Application

 

94. You want to quit your job and go back to school for a law degree 4 years from now, and you plan to save $3,500 per year, beginning immediately. You will make 4 deposits in an account that pays 5.7% interest. Under these assumptions, how much will you have 4 years from today?   a. $16,112   b. $16,918   c. $17,763   d. $18,652   e. $19,584   ANSWER:   a RATIONALE:   BEGIN Mode N 4 I/YR 5.7% PV $0.00 PMT $3,500 FV $16,112   Alternative setup:     0 1 2 3 4 $3,500 $3,500 $3,500 $3,500           FV = $16,112 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-8 Future Value of an Annuity Due LEARNING OBJECTIVES:   FOFM.BRIG.16.05.08 – Future Value of an Annuity Due NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of annuity due KEYWORDS:   Bloom’s: Application

 

95. You want to quit your job and return to school for an MBA degree 3 years from now, and you plan to save $7,000 per year, beginning immediately. You will make 3 deposits in an account that pays 5.2% interest. Under these assumptions, how much will you have 3 years from today?   a. $20,993   b. $22,098   c. $23,261   d. $24,424   e. $25,645   ANSWER:   c RATIONALE:   BEGIN Mode N 3 I/YR 5.2% PV $0.00 PMT $7,000 FV $23,261   Alternative setup:   0 1 2 3 $7,000 $7,000 $7,000 $7,000       FV = $23,261 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-8 Future Value of an Annuity Due LEARNING OBJECTIVES:   FOFM.BRIG.16.05.08 – Future Value of an Annuity Due NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of annuity due KEYWORDS:   Bloom’s: Application

 

96. What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5%?   a. $16,576   b. $17,449   c. $18,367   d. $19,334   e. $20,352   ANSWER:   e RATIONALE:   N 10 I/YR 5.5% PMT $2,700 FV $0.00 PV $20,352 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-9 Present Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.09 – Present Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of ordinary annuity KEYWORDS:   Bloom’s: Application

 

97. What is the PV of an ordinary annuity with 5 payments of $4,700 if the appropriate interest rate is 4.5%?   a. $16,806   b. $17,690   c. $18,621   d. $19,601   e. $20,633   ANSWER:   e RATIONALE:   N 5 I/YR 4.5% PMT $4,700 FV $0.00 PV $20,633 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-9 Present Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.09 – Present Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of ordinary annuity KEYWORDS:   Bloom’s: Application

 

98. You have a chance to buy an annuity that pays $2,500 at the end of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?   a. $5,493.71   b. $5,782.85   c. $6,087.21   d. $6,407.59   e. $6,744.83   ANSWER:   e RATIONALE:   N 3 I/YR 5.5% PMT $2,500 FV $0.00 PV $6,744.83 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-9 Present Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.09 – Present Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of ordinary annuity KEYWORDS:   Bloom’s: Application

 

99. You just inherited some money, and a broker offers to sell you an annuity that pays $5,000 at the end of each year for 20 years. You could earn 5% on your money in other investments with equal risk. What is the most you should pay for the annuity?   a. $50,753   b. $53,424   c. $56,236   d. $59,195   e. $62,311   ANSWER:   e RATIONALE:   N 20 I/YR 5.0% PMT $5,000 FV $0.00 PV $62,311 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-9 Present Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.09 – Present Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of ordinary annuity KEYWORDS:   Bloom’s: Application

 

100. Your aunt is about to retire, and she wants to sell some of her stock and buy an annuity that will provide her with income of $50,000 per year for 30 years, beginning a year from today. The going rate on such annuities is 7.25%. How much would it cost her to buy such an annuity today?   a. $574,924   b. $605,183   c. $635,442   d. $667,214   e. $700,575   ANSWER:   b RATIONALE:   N 30 I/YR 7.25% PMT $50,000 FV $0.00 PV $605,183 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-9 Present Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.09 – Present Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of ordinary annuity KEYWORDS:   Bloom’s: Application

 

101. What is the PV of an annuity due with 5 payments of $2,500 at an interest rate of 5.5%?   a. $11,262.88   b. $11,826.02   c. $12,417.32   d. $13,038.19   e. $13,690.10   ANSWER:   a RATIONALE:   BEGIN Mode N 5 I/YR 5.5% PMT $2,500 FV $0.00 PV $11,262.88 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-9 Present Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.09 – Present Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of annuity due KEYWORDS:   Bloom’s: Application

 

102. What’s the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%?   a. $4,750   b. $5,000   c. $5,250   d. $5,513   e. $5,788   ANSWER:   b RATIONALE:   I/YR 5.0% PMT $250 PV $5,000 POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-11 Perpetuities LEARNING OBJECTIVES:   FOFM.BRIG.16.05.11 – Perpetuities NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of a perpetuity KEYWORDS:   Bloom’s: Application

 

103. ​What’s the rate of return you would earn if you paid $950 for a perpetuity that pays $85 per year?   a. ​8.95%   b. ​9.39%   c. ​9.86%   d. ​10.36%   e. ​10.88%   ANSWER:   a RATIONALE:   Cost (PV) $950 PMT $85 I/YR 8.95% POINTS:   1 DIFFICULTY:   EASY REFERENCES:   5-11 Perpetuities LEARNING OBJECTIVES:   FOFM.BRIG.16.05.11 – Perpetuities NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Return on a perpetuity KEYWORDS:   Bloom’s: Application

 

104. You have a chance to buy an annuity that pays $550 at the beginning of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?   a. $1,412.84   b. $1,487.20   c. $1,565.48   d. $1,643.75   e. $1,725.94   ANSWER:   c RATIONALE:   BEGIN Mode N 3 I/YR 5.5% PMT $550 FV $0.00 PV $1,565.48 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-9 Present Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.09 – Present Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of annuity due KEYWORDS:   Bloom’s: Application

 

105. You have a chance to buy an annuity that pays $5,000 at the beginning of each year for 5 years. You could earn 4.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?   a. $20,701   b. $21,791   c. $22,938   d. $24,085   e. $25,289   ANSWER:   c RATIONALE:   BEGIN Mode N 5 I/YR 4.5% PMT $5,000 FV $0.00 PV $22,938 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-9 Present Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.09 – Present Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of annuity due KEYWORDS:   Bloom’s: Application

 

106. Your uncle is about to retire, and he wants to buy an annuity that will provide him with $75,000 of income a year for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much would it cost him to buy the annuity today?   a. $ 825,835   b. $ 869,300   c. $ 915,052   d. $ 963,213   e. $1,011,374   ANSWER:   d RATIONALE:   BEGIN Mode N 20 I/YR 5.25% PMT $75,000 FV $0.00 PV $963,213 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-9 Present Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.09 – Present Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of annuity due KEYWORDS:   Bloom’s: Application

 

107. Your father is about to retire, and he wants to buy an annuity that will provide him with $85,000 of income a year for 25 years, with the first payment coming immediately. The going rate on such annuities is 5.15%. How much would it cost him to buy the annuity today?   a. $1,063,968   b. $1,119,966   c. $1,178,912   d. $1,240,960   e. $1,303,008   ANSWER:   d RATIONALE:   BEGIN Mode N 25 I/YR 5.15% PMT $85,000 FV $0.00 PV $1,240,960 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-9 Present Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.09 – Present Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of annuity due KEYWORDS:   Bloom’s: Application

 

108. You inherited an oil well that will pay you $25,000 per year for 25 years, with the first payment being made today. If you think a fair return on the well is 7.5%, how much should you ask for it if you decide to sell it?   a. $284,595   b. $299,574   c. $314,553   d. $330,281   e. $346,795   ANSWER:   b RATIONALE:   BEGIN Mode N 25 I/YR 7.5% PMT $25,000 FV $0.00 PV $299,574 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-9 Present Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.09 – Present Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of annuity due KEYWORDS:   Bloom’s: Application

 

109. Sam was injured in an accident, and the insurance company has offered him the choice of $25,000 per year for 15 years, with the first payment being made today, or a lump sum. If a fair return is 7.5%, how large must the lump sum be to leave him as well off financially as with the annuity?   a. $225,367   b. $237,229   c. $249,090   d. $261,545   e. $274,622   ANSWER:   b RATIONALE:   BEGIN Mode N 15 I/YR 7.5% PMT $25,000 FV $0.00 PV $237,229 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-9 Present Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.09 – Present Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of annuity due KEYWORDS:   Bloom’s: Application

 

110. What’s the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%?   a. $ 8,509   b. $ 8,957   c. $ 9,428   d. $ 9,924   e. $10,446   ANSWER:   e RATIONALE:   N 4 I/YR 5.0% PMT $2,250 FV $3,000 PV $10,446   Alternative setup:     0 1 2 3 4   $2,250 $2,250 $2,250 $2,250         $3,000   $2,250 $2,250 $2,250 $5,250 PV = $10,446.50     POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-9 Present Value of an Ordinary Annuity LEARNING OBJECTIVES:   FOFM.BRIG.16.05.09 – Present Value of an Ordinary Annuity NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of ord. ann. and end. pmt. KEYWORDS:   Bloom’s: Application

 

111. Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the end of each of the next 20 years?   a. $28,532   b. $29,959   c. $31,457   d. $33,030   e. $34,681   ANSWER:   a RATIONALE:   N 20 I/YR 8.25% PV $275,000 FV $0.00 PMT $28,532 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-10 Finding Annuity Payments, Periods, and Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.10 – Finding Annuity Payments, Periods, and Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Ord. annuity payments KEYWORDS:   Bloom’s: Application

 

112. Your uncle has $375,000 and wants to retire. He expects to live for another 25 years and to earn 7.5% on his invested funds. How much could he withdraw at the end of each of the next 25 years and end up with zero in the account?   a. $28,843.38   b. $30,361.46   c. $31,959.43   d. $33,641.50   e. $35,323.58   ANSWER:   d RATIONALE:   N 25 I/YR 7.5% PV $375,000 FV $0.00 PMT $33,641.50 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-10 Finding Annuity Payments, Periods, and Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.10 – Finding Annuity Payments, Periods, and Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Ord. annuity payments KEYWORDS:   Bloom’s: Application

 

113. Your uncle has $375,000 and wants to retire. He expects to live for another 25 years, and he also expects to earn 7.5% on his invested funds. How much could he withdraw at the beginning of each of the next 25 years and end up with zero in the account?   a. $28,243.21   b. $29,729.70   c. $31,294.42   d. $32,859.14   e. $34,502.10   ANSWER:   c RATIONALE:   BEGIN Mode N 25 I/YR 7.5% PV $375,000 FV $0.00 PMT $31,294.42 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-10 Finding Annuity Payments, Periods, and Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.10 – Finding Annuity Payments, Periods, and Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Annuity due payments KEYWORDS:   Bloom’s: Application

 

114. Your grandmother just died and left you $100,000 in a trust fund that pays 6.5% interest. You must spend the money on your college education, and you must withdraw the money in 4 equal installments, beginning immediately. How much could you withdraw today and at the beginning of each of the next 3 years and end up with zero in the account?   a. $24,736   b. $26,038   c. $27,409   d. $28,779   e. $30,218   ANSWER:   c RATIONALE:   BEGIN Mode N 4 I/YR 6.5% PV $100,000 FV $0.00 PMT $27,409 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-10 Finding Annuity Payments, Periods, and Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.10 – Finding Annuity Payments, Periods, and Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Annuity due payments KEYWORDS:   Bloom’s: Application

 

115. Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the beginning of each of the next 20 years?   a. $22,598.63   b. $23,788.03   c. $25,040.03   d. $26,357.92   e. $27,675.82   ANSWER:   d RATIONALE:   BEGIN Mode N 20 I/YR 8.25% PV $275,000 FV $0.00 PMT $26,357.92 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-10 Finding Annuity Payments, Periods, and Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.10 – Finding Annuity Payments, Periods, and Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Annuity due payments KEYWORDS:   Bloom’s: Application

 

116. Your father’s employer was just acquired, and he was given a severance payment of $375,000, which he invested at a 7.5% annual rate. He now plans to retire, and he wants to withdraw $35,000 at the end of each year, starting at the end of this year. How many years will it take to exhaust his funds, i.e., run the account down to zero?   a. 22.50   b. 23.63   c. 24.81   d. 26.05   e. 27.35   ANSWER:   a RATIONALE:   I/YR 7.5% PV $375,000 PMT $35,000 FV $0.00 N 22.50 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-10 Finding Annuity Payments, Periods, and Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.10 – Finding Annuity Payments, Periods, and Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Finding annuity periods KEYWORDS:   Bloom’s: Application

 

117. Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, starting at the end of this year. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?   a. 14.21   b. 14.96   c. 15.71   d. 16.49   e. 17.32   ANSWER:   b RATIONALE:   I/YR 7.50% PV $300,000 PMT $35,000 FV $25,000 N 14.96 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-10 Finding Annuity Payments, Periods, and Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.10 – Finding Annuity Payments, Periods, and Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Finding annuity periods KEYWORDS:   Bloom’s: Application

 

118. Your Aunt Ruth has $500,000 invested at 6.5%, and she plans to retire. She wants to withdraw $40,000 at the beginning of each year, starting immediately. How many years will it take to exhaust her funds, i.e., run the account down to zero?   a. 18.62   b. 19.60   c. 20.63   d. 21.71   e. 22.86   ANSWER:   e RATIONALE:   BEGIN Mode I/YR 6.5% PV $500,000 PMT $40,000 FV $0.00 N 22.86 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-10 Finding Annuity Payments, Periods, and Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.10 – Finding Annuity Payments, Periods, and Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Finding annuity due periods KEYWORDS:   Bloom’s: Application

 

119. Your aunt has $500,000 invested at 5.5%, and she now wants to retire. She wants to withdraw $45,000 at the beginning of each year, beginning immediately. She also wants to have $50,000 left to give you when she ceases to withdraw funds from the account. For how many years can she make the $45,000 withdrawals and still have $50,000 left in the end?   a. 15.54   b. 16.36   c. 17.22   d. 18.08   e. 18.99   ANSWER:   c RATIONALE:   BEGIN Mode I/YR 5.5% PV $500,000 PMT $45,000 FV $50,000 N 17.22 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   FFMC.BRIG.15.05.10 LEARNING OBJECTIVES:   FOFM.BRIG.16.05.10 – Finding Annuity Payments, Periods, and Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Finding annuity due periods KEYWORDS:   Bloom’s: Application

 

120. Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes.   a. 7.12%   b. 7.49%   c. 7.87%   d. 8.26%   e. 8.67%   ANSWER:   b RATIONALE:   N 20 PV $2,550,000 PMT $250,000 FV $0.00 I/YR 7.49% POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-10 Finding Annuity Payments, Periods, and Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.10 – Finding Annuity Payments, Periods, and Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Finding I: annuity KEYWORDS:   Bloom’s: Application

 

121. Your girlfriend just won the Florida lottery. She has the choice of $15,000,000 today or a 20-year annuity of $1,050,000, with the first payment coming one year from today. What rate of return is built into the annuity?   a. 3.44%   b. 3.79%   c. 4.17%   d. 4.58%   e. 5.04%   ANSWER:   a RATIONALE:   N 20 PV $15,000,000 PMT $1,050,000 FV $0.00 I/YR 3.44% POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-10 Finding Annuity Payments, Periods, and Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.10 – Finding Annuity Payments, Periods, and Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Finding I: annuity KEYWORDS:   Bloom’s: Application

 

122. Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today. You need money today to start a new business, and your uncle offers to give you $120,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment?   a. 6.85%   b. 7.21%   c. 7.59%   d. 7.99%   e. 8.41%   ANSWER:   e RATIONALE:   BEGIN Mode N 12 PV $120,000 PMT $15,000 FV $0.00 I/YR 8.41% POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-10 Finding Annuity Payments, Periods, and Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.10 – Finding Annuity Payments, Periods, and Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Finding I: annuity due KEYWORDS:   Bloom’s: Application

 

123. What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,250?   a. $77.19   b. $81.25   c. $85.31   d. $89.58   e. $94.06   ANSWER:   b RATIONALE:   Cost (PV) $1,250   I/YR 6.5%   PMT $81.25    Multiply Cost by I/YR. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-11 Perpetuities LEARNING OBJECTIVES:   FOFM.BRIG.16.05.11 – Perpetuities NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Payments on a perpetuity KEYWORDS:   Bloom’s: Application

 

124. What is the present value of the following cash flow stream at a rate of 6.25%? ​ ​ ​​   a. $411.57   b. $433.23   c. $456.03   d. $480.03   e. $505.30   ANSWER:   e RATIONALE:   I/YR = 6.25%   0 1 2 3 4 CFs: $0 $75 $225 $0 $300 PV of CFs: $0 $71 $199 $0 $235   PV = $505.30 Found using the Excel NPV function. PV = $505.30 Found by summing individual PVs. You can find the individual PVs and sum them. Alternately, you can automate the process using Excel or a calculator, by inputting the data into the cash flow register and pressing the NPV key. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-12 Uneven Cash Flows LEARNING OBJECTIVES:   FOFM.BRIG.16.05.12 – Uneven Cash Flows NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of uneven cash flows KEYWORDS:   Bloom’s: Application

 

125. What is the present value of the following cash flow stream at a rate of 12.0%? ​ ​ ​   a. $ 9,699   b. $10,210   c. $10,747   d. $11,284   e. $11,849   ANSWER:   c RATIONALE:   I/YR = 12.0%   0 1 2 3 4 CFs: $0 $1,500 $3,000 $4,500 $6,000 PV of CFs: $0 $1,339 $2,392 $3,203 $3,813   PV = $10,747 Found using the Excel NPV function. PV = $10,747 Found by summing individual PVs. PV = $10,747 Found using the calculator NPV key. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-12 Uneven Cash Flows LEARNING OBJECTIVES:   FOFM.BRIG.16.05.12 – Uneven Cash Flows NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of uneven cash flows KEYWORDS:   Bloom’s: Application

 

126. What is the present value of the following cash flow stream at a rate of 8.0%? ​   a. $7,917   b. $8,333   c. $8,772   d. $9,233   e. $9,695   ANSWER:   d RATIONALE:   I/YR = 8.0%   0 1 2 3 CFs: $750 $2,450 $3,175 $4,400 PV of CFs: $750 $2,269 $2,722 $3,493   PV = $9,233 Found by summing individual PVs. PV = $9,233 Found with a calculator or Excel to automate the process. With a calculator, input the cash flows and I into the cash flow register, then press the NPV key. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-12 Uneven Cash Flows LEARNING OBJECTIVES:   FOFM.BRIG.16.05.12 – Uneven Cash Flows NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of uneven cash flows KEYWORDS:   Bloom’s: Application

 

127. You sold a car and accepted a note with the following cash flow stream as your payment. What was the effective price you received for the car assuming an interest rate of 6.0%? ​ ​ ​   a. $5,987   b. $6,286   c. $6,600   d. $6,930   e. $7,277   ANSWER:   a RATIONALE:   I/YR = 6.0%   0 1 2 3 4 CFs: $0 $1,000 $2,000 $2,000 $2,000 PV of CFs: $0 $ 943 $1,780 $1,679 $1,584   PV = $5,987 Found using the Excel NPV function. PV = $5,987 Found by summing individual PVs. PV = $5,987 Found using the calculator NPV key. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-12 Uneven Cash Flows LEARNING OBJECTIVES:   FOFM.BRIG.16.05.12 – Uneven Cash Flows NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV of uneven cash flows KEYWORDS:   Bloom’s: Application

 

128. At a rate of 6.5%, what is the future value of the following cash flow stream? ​ ​ ​​   a. $526.01   b. $553.69   c. $582.83   d. $613.51   e. $645.80   ANSWER:   e RATIONALE:   I/YR = 6.5%   0 1 2 3 4 CFs: $0 $75 $225 $0 $300 FV of CFs: $0 $91 $255 $0 $300   FV = $645.80 Found by summing individual FVs. FV = $645.80 Found with the NFV key in some calculators. FV = $645.80 Found with a calculator by first finding the PV of the stream, then finding the FV of that PV.     PV of the stream: $501.99 FV of the PV: $645.80 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-13 Future Value of an Uneven Cash Flow Stream LEARNING OBJECTIVES:   FOFM.BRIG.16.05.13 – Future Value of an Uneven Cash Flow Stream NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV of uneven cash flows KEYWORDS:   Bloom’s: Application

 

129. Your father paid $10,000 (CF at t = 0) for an investment that promises to pay $750 at the end of each of the next 5 years, then an additional lump sum payment of $10,000 at the end of the 5th year. What is the expected rate of return on this investment?   a. 6.77%   b. 7.13%   c. 7.50%   d. 7.88%   e. 8.27%   ANSWER:   c RATIONALE:     0 1 2 3 4 5 CFs: −$10,000 $750 $750 $750 $750 $ 750             $10,000   −$10,000 $750 $750 $750 $750 $10,750   ​ I/YR ​ 7.50% ​ I is the discount rate that causes the PV of the inflows to equal the initial negative CF, and is found with Excel’s IRR function or by inputting the CFs into a calculator and pressing the IRR key. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-14 Solving for I with Uneven Cash Flows LEARNING OBJECTIVES:   FOFM.BRIG.16.05.14 – Solving for I with Uneven Cash Flows NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Rate in uneven cash flows KEYWORDS:   Bloom’s: Application

 

130. You are offered a chance to buy an asset for $7,250 that is expected to produce cash flows of $750 at the end of Year 1, $1,000 at the end of Year 2, $850 at the end of Year 3, and $6,250 at the end of Year 4. What rate of return would you earn if you bought this asset?   a. 4.93%   b. 5.19%   c. 5.46%   d. 5.75%   e. 6.05%   ANSWER:   e RATIONALE:     0 1 2 3 4 CFs: −$7,250 $750 $1,000 $850 $6,250   ​ I/YR ​ 6.05% ​ I is the discount rate that causes the PV of the positive inflows to equal the initial negative CF. I can be found using Excel’s IRR function or by inputting the CFs into a calculator and pressing the IRR key. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-14 Solving for I with Uneven Cash Flows LEARNING OBJECTIVES:   FOFM.BRIG.16.05.14 – Solving for I with Uneven Cash Flows NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Rate in uneven cash flows KEYWORDS:   Bloom’s: Application

 

131. What’s the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded semiannually?   a. $1,819   b. $1,915   c. $2,016   d. $2,117   e. $2,223   ANSWER:   c RATIONALE:   Years 5     Periods/Yr 2     Nom. I/YR 6.0%             N = Periods 10     PMT $0     I = I/Period 3.0%     PV $1,500   Could be found using a calculator, an equation, or Excel. FV = $2,016   Note that we must first convert to periods and rate per period. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-15 Semiannual and Other Compounding Periods LEARNING OBJECTIVES:   FOFM.BRIG.16.05.15 – Semiannual and Other Compounding Periods NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV, semiannual compounding KEYWORDS:   Bloom’s: Application

 

132. What’s the present value of $4,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?   a. $3,089   b. $3,251   c. $3,422   d. $3,602   e. $3,782   ANSWER:   d RATIONALE:   Years 5     Periods/Yr 2     Nom. I/YR 4.5%             FV $4,500     N = Periods 10     PMT $0     I = I/Period 2.25%   Could be found using a calculator, the equation, or Excel. PV = $3,602   Note that we must first convert to periods and rate per period. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-15 Semiannual and Other Compounding Periods LEARNING OBJECTIVES:   FOFM.BRIG.16.05.15 – Semiannual and Other Compounding Periods NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV, semiannual compounding KEYWORDS:   Bloom’s: Application

 

133.   a. ​   b. ​   c. ​   d. ​   e. ​   ANSWER:   b RATIONALE:   Years 5     Periods/Yr 12     Nom. I/YR 6.0%             N = Periods 60     PMT $0     I/Period 0.5%     PV $1,200   Could be found using a calculator, the equation, or Excel. FV $1,618.62   Note that we must first convert to periods and rate per period. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-15 Semiannual and Other Compounding Periods LEARNING OBJECTIVES:   FOFM.BRIG.16.05.15 – Semiannual and Other Compounding Periods NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV, monthly compounding KEYWORDS:   Bloom’s: Application

 

134. What’s the present value of $1,525 discounted back 5 years if the appropriate interest rate is 6%, compounded monthly?   a. $ 969   b. $1,020   c. $1,074   d. $1,131   e. $1,187   ANSWER:   d RATIONALE:   Years 5   Periods/Yr 12   Nom. I/YR 6.0%         N = Periods 60   PMT $0   I/Period 0.5%   FV $1,525   PV = $1,131 = FV/(1 + rPer)N   PV = $1,131 Found using a calculator or Excel POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-15 Semiannual and Other Compounding Periods LEARNING OBJECTIVES:   FOFM.BRIG.16.05.15 – Semiannual and Other Compounding Periods NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   PV, monthly compounding KEYWORDS:   Bloom’s: Application

 

135. Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements. If the APR is stated to be 18.00%, with interest paid monthly, what is the card’s EFF%?   a. 18.58%   b. 19.56%   c. 20.54%   d. 21.57%   e. 22.65%   ANSWER:   b RATIONALE:   APR = Nominal rate 18.00% Periods/yr 12 EFF% = (1 + (rNOM/N))N − 1 = 19.56% POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   APR vs. EFF% KEYWORDS:   Bloom’s: Application

 

136. Riverside Bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly. The loan (principal plus interest) must be repaid at the end of the year. Midwest Bank also offers to lend you the $50,000, but it will charge an annual rate of 7.0%, with no interest due until the end of the year. How much higher or lower is the effective annual rate charged by Midwest versus the rate charged by Riverside?   a. 0.52%   b. 0.44%   c. 0.36%   d. 0.30%   e. 0.24%   ANSWER:   d RATIONALE:   This problem can be worked using the interest conversion feature of a calculator or Excel. It could also be worked using the conversion formula. We used the conversion formula. Nominal rate, Riverside 6.5% Nominal rate, Midwest 7.0% Periods/yr, Riverside 12 Periods/yr, Midwest 1 EFF% Riverside = (1 + (rNOM/N))N − 1 = 6.70% EFF% Midwest 7.00% Difference 0.30% POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Comparing EFF% KEYWORDS:   Bloom’s: Analysis

 

137. Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual rate of 8.00%, but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year. What is the effective annual rate on the loan?   a. 8.24%   b. 8.45%   c. 8.66%   d. 8.88%   e. 9.10%   ANSWER:   a RATIONALE:   Nominal I/YR 8.00% Periods/yr 4 EFF% = (1 + (rNOM/N))N − 1 = 8.24% You could also find the EFF% as follows: Interest paid each quarter = Loan × Rate/4 = Qtrly PMT = $200.00 Then find the IRR as a quarterly rate and convert to an annual rate. This procedure is obviously longer.   0 1 2 3 4 CFs: 10,000.00 −200.00 −200.00 −200.00 −200.00           −10,000.00   10,000.00 −200.00 −200.00 −200.00 −10,200.00 ​ IRR (quarterly) = 2.00% Annual effective rate = 8.24% vs. nominal rate = 8.00% POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Nominal rate vs. EFF% KEYWORDS:   Bloom’s: Application

 

138. Suppose a bank offers to lend you $10,000 for 1 year on a loan contract that calls for you to make interest payments of $250.00 at the end of each quarter and then pay off the principal amount at the end of the year. What is the effective annual rate on the loan?   a. 8.46%   b. 8.90%   c. 9.37%   d. 9.86%   e. 10.38%   ANSWER:   e RATIONALE:   Interest payment: $250.00   0 1 2 3 4 CFs: 10,000 −250 −250 −250 −250           −10,000   10,000 −250 −250 −250 −10,250 ​ IRR (quarterly) = 2.50% Annual effective rate = 10.38% vs. nominal rate = 10.00% POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Nominal rate vs. EFF% KEYWORDS:   Bloom’s: Application

 

139. Charter Bank pays a 4.50% nominal rate on deposits, with monthly compounding. What effective annual rate (EFF%) does the bank pay?   a. 3.72%   b. 4.13%   c. 4.59%   d. 5.05%   e. 5.56%   ANSWER:   c RATIONALE:   Nominal I/YR 4.50% Periods/yr 12 Periodic rate 0.38% EFF% = (1 + (rNOM/N))N − 1 = 4.59% POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Nominal rate vs. EFF% KEYWORDS:   Bloom’s: Application

 

140. Suppose your credit card issuer states that it charges a 15.00% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding. What is the effective annual rate?   a. 15.27%   b. 16.08%   c. 16.88%   d. 17.72%   e. 18.61%   ANSWER:   b RATIONALE:   Nominal I/YR = APR 15.00% Periods/yr 12 EFF% = (1 + (rNOM/N))N − 1 = 16.08% POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Nominal rate vs. EFF% KEYWORDS:   Bloom’s: Application

 

141. Pace Co. borrowed $20,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would Pace have to pay in a 30-day month?   a. $120.83   b. $126.88   c. $133.22   d. $139.88   e. $146.87   ANSWER:   a RATIONALE:   Nominal I/YR 7.25%   Days in month 30 Days/yr 360   Daily rate 0.020139% Amount borrowed $20,000   Interest per day $4.02778 Interest per month = Interest/day × 30 = $120.83       POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-17 Fractional Time Periods LEARNING OBJECTIVES:   FOFM.BRIG.16.05.17 – Fractional Time Periods NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Simple interest KEYWORDS:   Bloom’s: Application

 

142. Suppose you deposited $5,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year. How much would be in the account after 8 months, assuming each month has 30 days?   a. $5,178.09   b. $5,436.99   c. $5,708.84   d. $5,994.28   e. $6,294.00   ANSWER:   a RATIONALE:   Nominal I/YR 5.25%   Rate/day = rNOM/360 = 0.0146% Number of months 8   Days = Months × 30 = 240 Days in year 360       Days in month 30       Amount deposited $5,000       Ending amount $5,178.09       POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-17 Fractional Time Periods LEARNING OBJECTIVES:   FOFM.BRIG.16.05.17 – Fractional Time Periods NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Fractional time periods KEYWORDS:   Bloom’s: Application

 

143. Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be?   a. $3,704.02   b. $3,889.23   c. $4,083.69   d. $4,287.87   e. $4,502.26   ANSWER:   a RATIONALE:   Years = N 4   I/YR 9.0%   FV $0   Amount borrowed = PV $12,000   Payments = PMT $3,704.02    Found with a calculator, as the PMT. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization: payment KEYWORDS:   Bloom’s: Application

 

144. Suppose you are buying your first condo for $145,000, and you will make a $15,000 down payment. You have arranged to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate, with the first payment due in one month. What will your monthly payments be?   a. $741.57   b. $780.60   c. $821.69   d. $862.77   e. $905.91   ANSWER:   c RATIONALE:   Years 30   N 360 Payments/year 12   Periodic rate 0.54% Nominal rate 6.50%   PV $130,000 Purchase price $145,000   FV $0.00 Down payment $15,000   PMT $821.69 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization: payment KEYWORDS:   Bloom’s: Application

 

145. Your uncle will sell you his bicycle shop for $250,000, with “seller financing,” at a 6.0% nominal annual rate. The terms of the loan would require you to make 12 equal end-of-month payments per year for 4 years, and then make an additional final (balloon) payment of $50,000 at the end of the last month. What would your equal monthly payments be?   a. $4,029.37   b. $4,241.44   c. $4,464.67   d. $4,699.66   e. $4,947.01   ANSWER:   e RATIONALE:   Monthly annuity, so interest must be calculated on a monthly basis. Years 4   Payments/year 12 N 48   Nominal rate 6.0% PV $250,000   I/period 0.5% FV $50,000   PMT $4,947.01 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization: payment KEYWORDS:   Bloom’s: Application

 

146. Suppose you borrowed $14,000 at a rate of 10.0% and must repay it in 5 equal installments at the end of each of the next 5 years. How much interest would you have to pay in the first year?   a. $1,200.33   b. $1,263.50   c. $1,330.00   d. $1,400.00   e. $1,470.00   ANSWER:   d RATIONALE:   I/YR 10.0%     Years 5     Amount borrowed $14,000     Interest in Year 1 $1,400.00   Simply multiply the rate times the amount borrowed. POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization: interest KEYWORDS:   Bloom’s: Application

 

147. You plan to borrow $35,000 at a 7.5% annual interest rate. The terms require you to amortize the loan with 7 equal end-of-year payments. How much interest would you be paying in Year 2?   a. $1,994.49   b. $2,099.46   c. $2,209.96   d. $2,326.27   e. $2,442.59   ANSWER:   d RATIONALE:   Find the required payment: N 7   I 7.5%   PV $35,000   FV $0   PMT $6,608.01   Found with a calculator or Excel. Amortization schedule (first 2 years) Year Beg. Balance Payment Interest Principal End. Balance 1 35,000.00 6,608.01 2,625.00 3,983.01 31,016.99 2 31,016.99 6,608.01 2,326.27 4,281.74 26,735.25 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization: interest KEYWORDS:   Bloom’s: Application

 

148. Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business. The terms require you to amortize the loan with 10 equal end-of-year payments. How much interest would you be paying in Year 2?   a. $7,531   b. $7,927   c. $8,323   d. $8,740   e. $9,177   ANSWER:   b RATIONALE:   Find the required payment: N 10   I 8.5%   PV $100,000   FV $0   PMT $15,241   Found with a calculator or Excel. Amortization schedule (first 2 years) Year Beg. Balance Payment Interest Principal End. Balance 1 100,000 15,241 8,500 6,741 93,259 2 93,259 15,241 7,927 7,314 85,945 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization: interest KEYWORDS:   Bloom’s: Application

 

149. You are considering an investment in a Third World bank account that pays a nominal annual rate of 18%, compounded monthly. If you invest $5,000 at the beginning of each month, how many months would it take for your account to grow to $250,000? Round fractional months up.   a. 23   b. 27   c. 32   d. 38   e. 44   ANSWER:   d RATIONALE:   BEGIN Mode I/YR 18.0%     I/MO 1.5%   Monthly annuity due, so interest must be calculated on monthly basis. rNOM/12. PV $0     PMT $5,000     FV $250,000     N 37.16   Rounded up: 38 POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   N, ann. due, monthly comp. KEYWORDS:   Bloom’s: Application

 

150. You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $150,000?   a. 39.60   b. 44.00   c. 48.40   d. 53.24   e. 58.57   ANSWER:   b RATIONALE:   I/YR 7.0%     I/MO 0.583333%   Monthly annuity, so interest must be calculated on monthly basis PV $0     PMT $3,000     FV $150,000     N 44.0021     POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   N, ann. due, monthly comp. KEYWORDS:   Bloom’s: Application

 

151. Your child’s orthodontist offers you two alternative payment plans. The first plan requires a $4,000 immediate up-front payment. The second plan requires you to make monthly payments of $137.41, payable at the end of each month for 3 years. What nominal annual interest rate is built into the monthly payment plan?   a. 12.31%   b. 12.96%   c. 13.64%   d. 14.36%   e. 15.08%   ANSWER:   d RATIONALE:   N 36     PV $4,000     PMT $137.41     FV $0     I/MO 1.20%   Monthly annuity, so interest must be calculated on monthly basis I/YR = I/MO × 12 = 14.36% POINTS:   1 DIFFICULTY:   MODERATE REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Rate, ord. ann., monthly comp. KEYWORDS:   Bloom’s: Application

 

152. Your subscription to Investing Wisely Weekly is about to expire. You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $850, also payable immediately. Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy?   a. 7.48   b. 8.80   c. 10.35   d. 12.18   e. 14.33   ANSWER:   e RATIONALE:   Find N for an annuity due with the indicated terms to determine how long you must live to make the lifetime subscription worthwhile. BEGIN Mode   Interest rate (I/YR) 6.0% Annual cost (PMT) $85 Lifetime subscription cost (PV) $850 Number of payments made (N) 14.33 POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   5-10 Finding Annuity Payments, Periods, and Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.10 – Finding Annuity Payments, Periods, and Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   N, lifetime vs. yearly KEYWORDS:   Bloom’s: Analysis

 

153. You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning?   a. 7.62%   b. 8.00%   c. 8.40%   d. 8.82%   e. 9.26%   ANSWER:   a RATIONALE:   BEGIN Mode N 24 PV $0 PMT $500 FV $13,000 I/MO 0.63% I/YR 7.62% POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   5-10 Finding Annuity Payments, Periods, and Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.10 – Finding Annuity Payments, Periods, and Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Finding I: annuity due KEYWORDS:   Bloom’s: Application

 

154. You just deposited $2,500 in a bank account that pays a 4.0% nominal interest rate, compounded quarterly. If you also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account two years (8 quarters) from now, how much will be in the account three years (12 quarters) from now?   a. $15,234.08   b. $16,035.87   c. $16,837.67   d. $17,679.55   e. $18,563.53   ANSWER:   b RATIONALE:   Interest rate 4.0%       Periods/year 4 Years on Quarters Ending Quarterly rate 1.0% Deposit on Deposit Amount 1st deposit $2,500 3 12 $  2,817.06 2nd deposit $5,000 2 8 5,414.28 3rd deposit $7,500 1 4     7,804.53       Total ​ $16,035.87 POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   5-15 Semiannual and Other Compounding Periods LEARNING OBJECTIVES:   FOFM.BRIG.16.05.15 – Semiannual and Other Compounding Periods NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Non-annual compounding KEYWORDS:   Bloom’s: Application

 

155. Farmers Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid quarterly. Merchants Bank offers to lend you the $50,000, but it will charge 6.0%, simple interest, with interest paid at the end of the year. What’s the difference in the effective annual rates charged by the two banks?   a. 1.56%   b. 1.30%   c. 1.09%   d. 0.91%   e. 0.72%   ANSWER:   d RATIONALE:   Students must understand that “simple interest with interest paid quarterly” means that the bank gets the interest at the end of each quarter, hence it can invest it, presumably at the same nominal rate. This results in the same effective rate as if it were stated as “6%, quarterly compounding.” Nominal rate, Farmers 5.0% Periods/yr, Farmers 4 Nominal rate, Merchants 6.0% Periods/yr, Merchants 1 EFF% Farmers 5.09% EFF% Merchants 6.00% Difference 0.91% POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   5-16 Comparing Interest Rates LEARNING OBJECTIVES:   FOFM.BRIG.16.05.16 – Comparing Interest Rates NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Comparing EFF% KEYWORDS:   Bloom’s: Analysis

 

156. Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year?   a. $2,404.91   b. $2,531.49   c. $2,658.06   d. $2,790.96   e. $2,930.51   ANSWER:   b RATIONALE:   Interest rate 8.5% Years 5 Amount borrowed $15,000   Step 1: Find the PMT 3,806.49 Step 2: Find the 1st year’s interest 1,275.00 Step 3: Subtract the interest from the payment; this is repayment of principal 2,531.49 POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization: princ. repymt. KEYWORDS:   Bloom’s: Application

 

157. Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. How much would you still owe at the end of the first year, after you have made the first payment?   a. $10,155.68   b. $10,690.19   c. $11,252.83   d. $11,845.09   e. $12,468.51   ANSWER:   e RATIONALE:   Interest rate 8.5% Years 5 Amount borrowed $15,000   Step 1: Find the PMT $3,806.49 Step 2: Find the 1st year’s interest $1,275.00 Step 3: Subtract the interest from the payment; this is repayment of principal $2,531.49 Step 4: Subtract the repayment of principal from the beginning amount owed $12,468.51 POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization: ending bal. KEYWORDS:   Bloom’s: Application

 

158. Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal?   a. 73.67%   b. 77.55%   c. 81.63%   d. 85.93%   e. 90.45%   ANSWER:   e RATIONALE:   N 12   rNOM 11.0%   Per. r 0.9167%   PV $72,500   PMT $6,407.67   FV $0    % prin. = Prin2/PMT = 90.45% Amortization schedule (first 4 months) Month Beg. Balance Payment Interest Principal Ending Balance 1 72,500.00 6,407.67 664.58 5,743.09 66,756.91 2 66,756.91 6,407.67 611.94 5,795.73 60,961.18 3 60,961.18 6,407.67 558.81 5,848.86 55,112.32 4 55,112.32 6,407.67 505.20 5,902.47 49,209.85 POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization KEYWORDS:   Bloom’s: Application

 

159. Your brother’s business obtained a 30-year amortized mortgage loan for $250,000 at a nominal annual rate of 7.0%, with 360 end-of-month payments. The firm can deduct the interest paid for tax purposes. What will the interest tax deduction be for Year 1?   a. $17,419.55   b. $17,593.75   c. $17,769.68   d. $17,947.38   e. $18,126.85   ANSWER:   a RATIONALE:   Years 30   Nominal r 7.00% Periods/yr 12   I/period 0.5833% N (12 mo.) 360   PMT $1,663.26 PV = Loan $250,000   Interest, Year 1 $17,419.55 FV $0       Amortization schedule (first 12 months) Months Beg. Balance Payment Interest Principal End. Balance 1 250,000.00   1,663.26   1,458.33    204.92 249,795.08 2 249,795.08   1,663.26   1,457.14    206.12 249,588.96 3 249,588.96   1,663.26   1,455.94    207.32 249,381.64 4 249,381.64   1,663.26   1,454.73    208.53 249,173.11 5 249,173.11   1,663.26   1,453.51    209.75 248,963.36 6 248,963.36   1,663.26   1,452.29    210.97 248,752.39 7 248,752.39   1,663.26   1,451.06    212.20 248,540.19 8 248,540.19   1,663.26   1,449.82    213.44 248,326.75 9 248,326.75   1,663.26   1,448.57    214.68 248,112.07 10 248,112.07   1,663.26   1,447.32    215.94 247,896.13 11 247,896.13   1,663.26   1,446.06    217.20 247,678.94 12 247,678.94   1,663.26   1,444.79    218.46 247,460.48     19,959.07 17,419.55 2,539.52   POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   5-18 Amortized Loans LEARNING OBJECTIVES:   FOFM.BRIG.16.05.18 – Amortized Loans NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Amortization: interest KEYWORDS:   Bloom’s: Application

 

160. Your sister turned 35 today, and she is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that’s expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year.   a. $58,601   b. $61,686   c. $64,932   d. $68,179   e. $71,588   ANSWER:   c RATIONALE:   Interest rate 7.5% Years to retirement 30 Years in retirement 25 Amount saved per year $7,000   Step 1: Find the amount at age 65; use the FV function 723,796 Step 2: Find the PMT for a 25-year ordinary annuity using the FV you just found as the PV. 64,932 POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Retirement planning KEYWORDS:   Bloom’s: Application

 

161. Steve and Ed are cousins who were both born on the same day, and both turned 25 today. Their grandfather began putting $2,500 per year into a trust fund for Steve on his 20th birthday, and he just made a 6th payment into the fund. The grandfather (or his estate’s trustee) will make 40 more $2,500 payments until a 46th and final payment is made on Steve’s 65th birthday. The grandfather set things up this way because he wants Steve to work, not be a “trust fund baby,” but he also wants to ensure that Steve is provided for in his old age. ​ Until now, the grandfather has been disappointed with Ed, hence has not given him anything. However, they recently reconciled, and the grandfather decided to make an equivalent provision for Ed. He will make the first payment to a trust for Ed today, and he has instructed his trustee to make 40 additional equal annual payments until Ed turns 65, when the 41st and final payment will be made. If both trusts earn an annual return of 8%, how much must the grandfather put into Ed’s trust today and each subsequent year to enable him to have the same retirement nest egg as Steve after the last payment is made on their 65th birthday?   a. $3,726   b. $3,912   c. $4,107   d. $4,313   e. $4,528   ANSWER:   a RATIONALE:   Steve’s retirement account     Ed’s retirement account No. of payments thus far, including today’s payment 6   Payment today 1 Number of remaining payments 40     40 N = total payments 46   N 41 I/YR 8.0%   I/YR 8.0% PV $0   PV $0 PMT $2,500   FV = Ed’s FV = $1,046,065 FV Steve’s FV = $1,046,065   PMT $3,726 POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Retirement planning KEYWORDS:   Bloom’s: Analysis OTHER:   Multiple Choice: Problem

 

162. After graduation, you plan to work for Dynamo Corporation for 12 years and then start your own business. You expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6) and $15,000 annually for the following 6 years (t = 7 through t = 12). The first deposit will be made a year from today. In addition, your grandfather just gave you a $25,000 graduation gift which you will deposit immediately (t = 0). If the account earns 9% compounded annually, how much will you have when you start your business 12 years from now?   a. $238,176   b. $250,712   c. $263,907   d. $277,797   e. $291,687   ANSWER:   d RATIONALE:   There are 3 cash flow streams: the gift and the two annuities. The gift will grow for 12 years. Then there is a 6-year annuity whose FV at the end of Year 6 will compound for an additional 6 years. Finally, there is a second 6-year annuity. The sum of the compounded values of those three sets of cash flows is the final amount.       Amount Amount       at end of at end of       Year 6 Year 12 Interest rate 9.0%       1st annuity $  7,500   $56,425 Compound @ 9% $  94,630 2nd annuity $15,000   NA $112,850 Gift $25,000   NA $  70,317 Total years 12       Annuity years 6   Final amt: $277,797 POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   FV comb. CF lump sum and ann. KEYWORDS:   Bloom’s: Application OTHER:   Multiple Choice: Problem

 

163. You are negotiating to make a 7-year loan of $25,000 to Breck Inc. To repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from Year 4 through Year 7. Breck is essentially riskless, so you are confident the payments will be made. You regard 8% as an appropriate rate of return on a low risk but illiquid 7-year loan. What cash flow must the investment provide at the end of each of the final 4 years, that is, what is X?   a. $4,271.67   b. $4,496.49   c. $4,733.15   d. $4,969.81   e. $5,218.30   ANSWER:   c RATIONALE:   This is a relatively difficult problem for an efficient calculator solution or classroom exam, but it is appropriate for a challenging take-home or online exam. I/YR = 8%   0 1 2 3 4 5 6 7 −$25,000 $2,500 $5,000 $7,500 X X X X ​ Calculator solution: Step 1. Use the CF register to find the NPV of the 4 known cash flows, CF0 to CF3: −$12,444.75 Step 2. Find the FV of this NPV at the end of period 3, i.e., compound the NPV you found for 3 years. −$15,676.80 Step 3. Now find the PMT for a 4-year annuity with this PV. $ 4,733.15 POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   CF for given return KEYWORDS:   Bloom’s: Application OTHER:   Multiple Choice: Problem

 

164. John and Daphne are saving for their daughter Ellen’s college education. Ellen just turned 10 (at t = 0), and she will be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently $14,500 a year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years⎯if she takes longer or wants to go to graduate school, she will be on her own. Tuition and other costs will be due at the beginning of each school year (at t = 8, 9, 10, and 11). ​ So far, John and Daphne have accumulated $15,000 in their college savings account (at t = 0). Their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). Then they plan to make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their investment account to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Ellen’s anticipated college costs?   a. $1,965.21   b. $2,068.64   c. $2,177.51   d. $2,292.12   e. $2,412.76   ANSWER:   e RATIONALE:   This is a very difficult problem. It should only be used as a take-home assignment. Current college cost/year $14,500 College cost inflation 3.5% Return on investment account 9.0% Payments at t = 1, 2, 3, and 4 $5,000 Account balance at t = 0 $15,000   ​ 1. ​ Determine the cost of each year during college and its PV at t = 8, discounted at the return on investment.         Cost PV at t = 8 Year 1 (t = 8) = Current cost × (1 + infl)8 = −19,093.73 −19,093.73 Year 2 (t = 9) = Prior year × (1 + infl) = −19,762.01 −18,130.29 Year 3 (t = 10) = Prior year × (1 + infl) = −20,453.68 −17,215.45 Year 4 (t = 11) = Prior year × (1 + infl) = −21,169.56 −16,346.79 Find PV (at t = 8) of all college costs = amount needed at t = 8:   −70,786.26   ​ 2. ​ Create a time line with those cash flows, plus the known initial CFs, as shown below. Put X in for the unknown values for t = 5-7. We show the time line on three sets of rows. Ours now has the solution value, but it didn’t originally.     0 1 2 3 > Known values; X for unknown: $15,000.00 $5,000.00 $5,000.00 $5,000.00 > Solution value for X:         > Cash flows: $15,000.00 $5,000.00 $5,000.00 $5,000.00 > ​ <   4 5 6 7 > < Known values; X for unknown: $5,000.00 X X X > < Solution value for X:   $2,412.76 $2,412.76 $2,412.76 > < Cash flows: $5,000.00 $2,412.76 $2,412.76 $2,412.76 > ​ <   8 9 10 11   < Known values; X for unknown: −$19,093.73 −$19,762.01 −$20,453.68 −$21,169.56   < Solution value for X:           < Cash flows: −$19,093.73 −$19,762.01 −$20,453.68 −$21,169.56     ​ 3. ​ We found the PV of the college costs (t = 8-11) at t = 8 above.         Their sum is shown to the right. −70,786.26               4. Find the FV of t = 0 & 4 positive CFs at t = 8 0 $15,000.00 $29,888.44     1 $ 5,000.00 $  9,140.20     2 $ 5,000.00 $  8,385.50     3 $ 5,000.00 $  7,693.12     4 $ 5,000.00 $  7,057.91         ​ $62,165.16           5. Find the difference between the positive and negative t = 8 values: −$8,621.09               6. Find PMT for a 3-year annuity due whose FV is equal to this difference: $2,412.76     POINTS:   1 DIFFICULTY:   CHALLENGING REFERENCES:   Comprehensive LEARNING OBJECTIVES:   FOFM.BRIG.16.05.00 – Comprehensive NATIONAL STANDARDS:   United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills STATE STANDARDS:   United States – OH – DISC.FOFM.BRIG.16.04 – Time value of money TOPICS:   Saving for college KEYWORDS:   Bloom’s: Application OTHER:   Multiple Choice: Problem