Finance Applications and Theory Marcia Cornett 5e - Test Bank

Finance Applications and Theory Marcia Cornett 5e – Test Bank

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Sample Questions Are Posted Below

Finance, 5e (Cornett)

Chapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows

1) When saving for future expenditures, we can add the ________ of contributions over time to see what the total will be worth at some point in time.

A) present value
B) future value
C) time value to money
D) payment

Answer: B

Difficulty: 1 Easy

Topic: Future value – multiple cash flows

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-01 Compound multiple cash flows to the future.

2) When moving from the left to the right of a time line, we are using

A) compound interest to calculate future values.
B) discounted cash flows to calculate present values.
C) only payments to calculate future values.
D) simple interest to calculate future values.

Answer: A

Difficulty: 1 Easy

Topic: Time value of money

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-01 Compound multiple cash flows to the future.

3) Level sets of frequent, consistent cash flows are called

A) loans.
B) budgets.
C) annuities.
D) bills.

Answer: C

Difficulty: 1 Easy

Topic: Annuities

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

4) The length of time of the annuity is very important in accumulating wealth within an annuity. What other factor also has this effect?

A) the time line
B) interest rate for compounding
C) the present value
D) the future value

Answer: B

Difficulty: 1 Easy

Topic: Annuities

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

5) In order to discount multiple cash flows to the present, one would use

A) the appropriate compound rate.
B) the appropriate discount rate.
C) the appropriate simple rate.
D) the appropriate tax rate.

Answer: B

Difficulty: 1 Easy

Topic: Time value of money

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-03 Discount multiple cash flows to the present.

6) An annuity due:

A) is an annuity in which the cash flows occur at the beginning of each period.
B) makes the cash flow in the beginning of year 1 look like it’s a cash flow of today.
C) moves the cash flow from the end of the year to the beginning, which looks like the end of the previous year.
D) the appropriate tax rate.

Answer: A

Difficulty: 1 Easy

Topic: Time value of money

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-03 Discount multiple cash flows to the present.

7) Your credit rating and current economic conditions will determine

A) whether you get simple or compound interest.
B) how long compounding will affect you.
C) how long discounting will affect you.
D) the interest rate that a lender will offer.

Answer: D

Difficulty: 1 Easy

Topic: Loan interest and rates

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

8) When interest rates are lower, borrowers can

A) get loans more easily.
B) cannot get loans as easily.
C) borrow more money.
D) afford higher payments.

Answer: C

Difficulty: 2 Medium

Topic: Loan interest and rates

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

9) The present value of annuity payments made far into the future is

A) worth very little today.
B) worth much more today.
C) valued as having no time value of money.
D) valued as worthless as their value is not determinable.

Answer: A

Difficulty: 2 Medium

Topic: Present value – annuity

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

10) Which of the following statements about compound frequency is not true?

A) Compounding frequency can only be annual, semi-annual or quarterly.
B) The higher the compound frequency, the higher the future value will be.
C) The relative increase in value from increasing compounding frequency seems to diminish with increasing frequencies.
D) None of the above are untrue statements.

Answer: A

Difficulty: 2 Medium

Topic: Compound frequency

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

11) Which of the following statements about annual percentage rate (APR) and effective annual rate (EAR) are not true?

A) The annual percentage rate (APR) is considered a more accurate measurement of what you will actually pay.
B) Lenders are legally required to show potential borrowers the effective annual rate (EAR) on any loan offered.
C) The difference between APR and EAR is not that large.
D) None of the above are untrue statements.

Answer: A

Difficulty: 2 Medium

Topic: APR and EAR

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

12) A perpetuity, a special form of annuity, pays cash flows

A) and is not effected by interest rate changes.
B) that do not have time value of money implications.
C) continuously for one year.
D) periodically forever.

Answer: D

Difficulty: 1 Easy

Topic: Perpetuities

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-05 Figure cash flows and present value of a perpetuity.

13) Many people who want to start investing for their future want to start today, which implies an annuity stream that is paid at the beginning of the period. Beginning-of-period cash flows are referred to as

A) ordinary annuities.
B) annuities due.
C) perpetuities.
D) present values.

Answer: B

Difficulty: 1 Easy

Topic: Annuities

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-06 Adjust values for beginning-of-period annuity payments.

14) To compute the present or future value of an annuity due, one computes the value of an ordinary annuity and then

A) multiplies it by (1 + i).
B) divides it by (1 + i).
C) multiplies it by (1 − i).
D) divides it by (1 − i).

Answer: A

Difficulty: 2 Medium

Topic: Annuities

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-06 Adjust values for beginning-of-period annuity payments.

15) When computing the future value of an annuity, the higher the compound frequency

A) the lower the future value will be.
B) the higher the future value will be.
C) the less likely the future value can be calculated.
D) the more likely the future value can be calculated.

Answer: B

Difficulty: 2 Medium

Topic: Future value – annuity

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

16) Compounding monthly versus annually causes the interest rate to be effectively higher, and thus the future value

A) grows.
B) decreases.
C) is independent of the monthly compounding.
D) is affected only if the calculation involves an annuity due.

Answer: A

Difficulty: 1 Easy

Topic: Simple and compound interest

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

17) The simple form of an annualized interest rate is called the annual percentage rate (APR). The effective annual rate (EAR) is a

A) less accurate measure of the interest rate paid for monthly compounding.
B) more accurate measure of the interest rate paid for monthly compounding.
C) concept that is only used because the law requires it, and is of no use to a borrower.
D) measure that only applies to mortgages.

Answer: B

Difficulty: 1 Easy

Topic: Simple and compound interest

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

18) People refinance their home mortgages

A) when rates fall.
B) when rates rise.
C) when rates fall and rise.
D) whenever they need to, independent of rates.

Answer: A

Difficulty: 1 Easy

Topic: Loan interest and rates

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

19) Loan amortization schedules show

A) the principal balance paid per period only.
B) the interest paid per period only.
C) both the principal balance and interest paid per period.
D) the present value of the payments due.

Answer: C

Difficulty: 1 Easy

Topic: Amortization

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

20) When you get your credit card bill, it will offer a minimum payment, which

A) usually only pays the accrued interest and a small amount of principal.
B) usually only pays the principal and a small amount of accrued interest.
C) usually only pays the principal and no accrued interest.
D) usually only pays the accrued interest and no principal.

Answer: A

Difficulty: 1 Easy

Topic: Amortization

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-10 Calculate the number of payments on a loan.

21) When you get your credit card bill, if you make a payment larger than the minimum payment

A) you are wasting your current consumption and making TVM not work for you.
B) you will reduce the payoff time.
C) you will increase the payoff time.
D) you will not affect the payoff time.

Answer: B

Difficulty: 1 Easy

Topic: Amortization

Bloom’s: Remember

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-10 Calculate the number of payments on a loan.

22) Compute the future value in year 10 of a $1,000 deposit in year 1, and another $1,500 deposit at the end of year 4 using an 8 percent interest rate.

A) $3,120.73
B) $4,379.31
C) $4,500.00
D) $5,397.31

Answer: B

Explanation:

N	=	10 − 1 = 9	N	=	10 − 4 = 6
I	=	8	I	=	8
PV	=	1000	PV	=	1500
PMT	=	0	PMT	=	0
CPT FV	=	1999.00	CPT FV	=	2380.31
1999.00 + 2380.31	=	4379.31

Difficulty: 1 Easy

Topic: Future value – multiple cash flows

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-01 Compound multiple cash flows to the future.

23) Compute the future value in year 4 of a $500 deposit in year 1, and another $1,000 deposit at the end of year 3 using a 5 percent interest rate.

A) $1,625.00
B) $1,628.81
C) $1,800.00
D) $1,823.26

Answer: B

Explanation:

N	=	4 − 1 = 3	N	=	4 − 3 = 1
I	=	5	I	=	5
PV	=	500	PV	=	1000
PMT	=	0	PMT	=	0
CPT FV	=	578.81	CPT FV	=	1050.00
578.81 + 1050.00	=	1628.81

Difficulty: 1 Easy

Topic: Future value – multiple cash flows

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-01 Compound multiple cash flows to the future.

24) What is the future value of an $800 annuity payment over 15 years if the interest rates are 6 percent?

A) $1,917.25
B) $7,002.99
C) $12,720.00
D) $18,620.78

Answer: D

Explanation: N = 15

I = 6

PV = 0

PMT = 800

CPT FV = 18620.78

Difficulty: 1 Easy

Topic: Future value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

25) What is the future value of a $1,000 annuity payment over 4 years if the interest rates are 8 percent?

A) $3,312.10
B) $4,320.00
C) $4,506.11
D) $9,214.20

Answer: C

Explanation: N = 4

I = 8

PV = 0

PMT = 1000

CPT FV = 4506.11

Difficulty: 1 Easy

Topic: Future value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

26) What is the present value of a $500 deposit in year 1, and another $100 deposit at the end of year 4 if interest rates are 5 percent?

A) $480.00
B) $493.62
C) $558.46
D) $582.27

Answer: C

Explanation: 0 = CFO

500 = C01, 1 F01

0 = C02, 2 F02

400 = C03, 1 F03

I = 5

NPV = 558.46

Difficulty: 1 Easy

Topic: Present value – multiple cash flows

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-03 Discount multiple cash flows to the present.

27) What is the present value of a $250 deposit in year 1, and another $50 deposit at the end of year 6 if interest rates are 10 percent?

A) $120.00
B) $169.34
C) $255.50
D) $278.22

Answer: C

Explanation: 0 = CFO

250 = C01, 1 F01

0 = C02, 4 F02

50 = C03, 1 F03

I = 10

NPV = 255.50

Difficulty: 1 Easy

Topic: Present value – multiple cash flows

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-03 Discount multiple cash flows to the present.

28) What is the present value of a $300 annuity payment over 5 years if interest rates are 8 percent?

A) $204.17
B) $440.80
C) $1,197.81
D) $1,938.96

Answer: C

Explanation: FV = 0

PMT = 300

I = 8

N = 5

CPT PV = 1197.81

Difficulty: 1 Easy

Topic: Present value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

29) What is the present value of a $600 annuity payment over 4 years if interest rates are 6 percent?

A) $475.26
B) $757.49
C) $2,079.06
D) $3,145.28

Answer: C

Explanation: FV = 0

PMT = 600

I = 6

N = 4

CPT PV = 2079.06

Difficulty: 1 Easy

Topic: Present value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

30) What is the present value, when interest rates are 6.5 percent, of a $100 payment made every year forever?

A) $6.50
B) $650.00
C) $1,000.00
D) $1,538.46

Answer: D

Explanation: $100/0.065 = $1538.46.

Difficulty: 1 Easy

Topic: Perpetuities

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-05 Figure cash flows and present value of a perpetuity.

31) What is the present value, when interest rates are 10 percent, of a $75 payment made every year forever?

A) $6.75
B) $675.00
C) $750.00
D) $1,000.00

Answer: C

Explanation: $75/0.10 = $750.

Difficulty: 1 Easy

Topic: Perpetuities

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-05 Figure cash flows and present value of a perpetuity.

32) If the present value of an ordinary, 4-year annuity is $1,000 and interest rates are 6 percent, what is the present value of the same annuity due?

A) $943.40
B) $1,000.00
C) $1,040.00
D) $1,060.00

Answer: D

Explanation: END MODE

PV = 1000

FV = 0

I = 6

N = 4

CPT PMT = 288.59149

BGN MODE

FV = 0

PMT = 288.59149

I = 6

N = 4

CPT PV = 1060.00

Difficulty: 1 Easy

Topic: Present value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-06 Adjust values for beginning-of-period annuity payments.

33) If the future value of an ordinary, 7-year annuity is $10,000 and interest rates are 4 percent, what is the future value of the same annuity due?

A) $9,615.38
B) $10,000.00
C) $10,400.00
D) $10,700.00

Answer: C

Explanation: END MODE

FV = 10000

PV = 0

I = 4

N = 7

CPT PMT = 1266.09612

BGN MODE

PV = 0

PMT = 1266.09612

I = 4

N = 7

CPT FV = 10400.00

Difficulty: 1 Easy

Topic: Future value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-06 Adjust values for beginning-of-period annuity payments.

34) If the future value of an ordinary, 4-year annuity is $1,000 and interest rates are 6 percent, what is the future value of the same annuity due?

A) $943.40
B) $1,000.00
C) $1,040.00
D) $1,060.00

Answer: D

Explanation: END MODE

FV = 1000

PV = 0

I = 6

N = 4

CPT PMT = 228.59149

BGN MODE

PV = 0

PMT = 228.59149

I = 6

N = 4

CPT FV = 1060.00

Difficulty: 1 Easy

Topic: Future value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-06 Adjust values for beginning-of-period annuity payments.

35) A loan is offered with monthly payments and a 10 percent APR. What is the loan’s effective annual rate (EAR)?

A) 10.00 percent
B) 10.47 percent
C) 11.20 percent
D) 12.67 percent

Answer: B

Explanation: (1 + 0.10/12)^12 − 1 = 0.1047 = 10.47 percent.

Difficulty: 1 Easy

Topic: Simple and compound interest

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

36) A loan is offered with monthly payments and a 6.5 percent APR. What is the loan’s effective annual rate (EAR)?

A) 5.69 percent
B) 6.697 percent
C) 7.28 percent
D) 12.63 percent

Answer: B

Explanation: (1 + 0.065/12)^12 − 1 = 0.06697 = 6.697 percent.

Difficulty: 1 Easy

Topic: Simple and compound interest

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

37) Given a 4 percent interest rate, compute the year 6 future value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,200, and $1,400.

A) $4,334.53
B) $5,070.78
C) $5,191.68
D) $5,484.56

Answer: D

Explanation: N = 5, I = 4, PV = 1000, PMT = 0, CPT FV = 1216.65

N = 4, I = 4, PV = 1200, PMT = 0, CPT FV = 1403.83

N = 3, I = 4, PV = 1200, PMT = 0, CPT FV = 1349.8368

N = 2, I = 4, PV = 1400, PMT = 0, CPT FV = 1514.24

sum of FV = 5484.56.

Difficulty: 2 Medium

Topic: Future value – multiple cash flows

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-01 Compound multiple cash flows to the future.

38) Given a 6 percent interest rate, compute the year 6 future value of deposits made in years 1, 2, 3, and 4 of $1,200, $1,400, $1,400, and $1,500.

A) $4,741.68
B) $5,986.26
C) $6,179.80
D) $6,726.16

Answer: D

Explanation: N = 5, I = 6, PV = 1200, PMT = 0, CPT FV = 1605.8707

N = 4, I = 6, PV = 1400, PMT = 0, CPT FV = 1767.4677

N = 3, I = 6, PV = 1400, PMT = 0, CPT FV = 1667.4224

N = 2, I = 6, PV = 1500, PMT = 0, CPT FV = 1685.40

sum of FV = 6726.16.

Difficulty: 2 Medium

Topic: Future value – multiple cash flows

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-01 Compound multiple cash flows to the future.

39) Assume that you contribute $100 per month to a retirement plan for 20 years. Then you are able to increase the contribution to $200 per month for another 20 years. Given a 6 percent interest rate, what is the value of your retirement plan after 40 years?

A) $225,353
B) $19,155
C) $245,353
D) $199,359

Answer: C

Explanation: N = 40 × 12 = 480, I = 6/12 = 0.5, PV = 0, PMT = 100, CPT FV = 199149

N = 20 × 12 = 240, I = 6/12 = 0.5, PV = 0, PMT = 100 (200 − 100), CPT FV = 46204

sum of FV = 245353.

Difficulty: 2 Medium

Topic: Future value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

40) Assume that you contribute $200 per month to a retirement plan for 15 years. Then you are able to increase the contribution to $400 per month for another 25 years. Given a 5 percent interest rate, what is the value of your retirement plan after 40 years?

A) $424,305.97
B) $24,159.95
C) $28,475.66
D) $72,479.86

Answer: A

Explanation: N = 40 × 12 = 480, I = 5/12 = 0.4167, PV = 0, PMT = 200, CPT FV = 305,204.03

N = 25 × 12 = 300, I = 5/12 = 0.4167, PV = 0, PMT = 200 (400 − 200), CPT FV = 119,101.94

sum of FV = 424305.97.

Difficulty: 2 Medium

Topic: Future value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

41) Given a 5 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,400, $1,400, and $1,500.

A) $4,360.32
B) $4,665.65
C) $5,047.62
D) $5,305.00

Answer: B

Explanation: 0 = CF0

1000 = C01, 1 F01

1400 = C02, 2 F02

1500 = C03, 1 F03

I = 5

NPV = 4665.65

Difficulty: 2 Medium

Topic: Present value – multiple cash flows

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-03 Discount multiple cash flows to the present.

42) Given a 7 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,500, and $1,500.

A) $3,967.06
B) $4,351.50
C) $4,859.81
D) $5,207.00

Answer: B

Explanation: 0 = CF0

1000 = CO1, 1 F01

1200 = C02, 1 F02

1500 = C03, 2 F03

I = 7

NPV = 4351.50

Difficulty: 2 Medium

Topic: Present value – multiple cash flows

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-03 Discount multiple cash flows to the present.

43) Given a 4 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,200, and $1,400.

A) $4,103.06
B) $4,334.53
C) $4,615.38
D) $4,804.00

Answer: B

Explanation: 0 = CF0

1000 = CO1, 1 F01

1200 = C02, 2 F02

1400 = C03, 1 F03

I = 4

NPV = 4334.53

Difficulty: 2 Medium

Topic: Present value – multiple cash flows

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-03 Discount multiple cash flows to the present.

44) Given a 6 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,200, $1,400, $1,400, and $1,500.

A) $4,356.52
B) $4,741.68
C) $5,188.68
D) $5,506.00

Answer: B

Explanation: 0 = CF0

1200 = CO1, 1 F01

1400 = C02, 2 F02

1500 = C03, 1 F03

I = 6

NPV = 4741.68

Difficulty: 2 Medium

Topic: Present value – multiple cash flows

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-03 Discount multiple cash flows to the present.

45) A small business owner visits his bank to ask for a loan. The owner states that he can repay a loan at $1,500 per month for the next three years and then $500 per month for the two years after that. If the bank is charging customers 5.5 percent APR, how much would it be willing to lend the business owner?

A) $4,046.90
B) $59,293.50
C) $24,261.00
D) $66,000.00

Answer: B

Explanation: N = 5 × 12 = 60, I = 5.5/12 = 0.4583, FV = 0, PMT = 500, CPT PV = 26176.42

N = 3 × 12 = 36, I = 5.5/12 = 0.4583, FV = 0, PMT = 1000 (1500 − 500), CPT PV = 33117.08

sum of PV = 59293.50.

Difficulty: 2 Medium

Topic: Present value – multiple cash flows

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

46) A small business owner visits his bank to ask for a loan. The owner states that he can repay a loan at $2,000 per month for the next three years and then $1,000 per month for the two years after that. If the bank is charging customers 8.5 percent APR, how much would it be willing to lend the business owner?

A) $80,419.29
B) $6,494.66
C) $21,780.74
D) $96,000.00

Answer: A

Explanation: N = 5 × 12 = 60, I = 8.5/12 = 0.7083, FV = 0, PMT = 1000, CPT PV = 48741.18

N = 3 × 12 = 36, I = 8.5/12 = 0.7083, FV = 0, PMT = 1000 (2000 − 1000), CPT PV = 31678.11

sum of PV = 80419.29.

Difficulty: 2 Medium

Topic: Present value – multiple cash flows

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

47) A perpetuity pays $100 per year and interest rates are 6.5 percent. How much would its value change if interest rates increased to 9 percent?

A) $250.00 increase
B) $250.00 decrease
C) $427.35 increase
D) $427.35 decrease

Answer: D

Explanation: $100/0.065 = $1538.46, $100/0.09 = $1111.11.

change = 1538.46 − 1111.11 = 427.35 decrease.

Difficulty: 2 Medium

Topic: Perpetuities

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-05 Figure cash flows and present value of a perpetuity.

48) A perpetuity pays $50 per year and interest rates are 9 percent. How much would its value change if interest rates decreased to 6 percent?

A) $150.00 increase
B) $150.00 decrease
C) $277.78 increase
D) $277.78 decrease

Answer: C

Explanation: $50/0.09 = $555.55, $50/0.06 = $833.33.

change = 555.55 − 833.33 = 277.78 increase.

Difficulty: 2 Medium

Topic: Perpetuities

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-05 Figure cash flows and present value of a perpetuity.

49) If you start making $100 monthly contributions today and continue them for five years, what is their future value if the compounding rate is 10 percent APR? What is the present value of this annuity?

A) $508.14, $487.74
B) $512.64, $491.80
C) $7,743.71, $4,706.53
D) $7,808.24, $4,745.76

Answer: D

Explanation: N = 5 × 12 = 60, I = 10/12 = 0.83, PV = 0, PMT = 100, CPT FV = 7808.24

N = 5 × 12 = 60, I = 10/12 = 0.83, FV = 0, PMT = 100, CPT PV = 4745.76

Difficulty: 2 Medium

Topic: Future value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-06 Adjust values for beginning-of-period annuity payments.

50) If you start making $25 monthly contributions today and continue them for four years, what is their future value if the compounding rate is 6 percent APR? What is the present value of this annuity?

A) $101.26, $99.26
B) $1,352.45, $1,064.51
C) $1,359.21, $1,069.83
D) $2,171.02, $1,516.03

Answer: C

Explanation: N = 4 × 12 = 48, I = 6/12 = 0.5, PV = 0, PMT = 25, CPT FV = 1359.21

N = 4 × 12 = 48, I = 6/12 = 0.5, FV = 0, PMT = 25, CPT PV = 1069.83

Difficulty: 2 Medium

Topic: Future value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-06 Adjust values for beginning-of-period annuity payments.

51) Payday loans are very short-term loans that charge very high interest rates. You can borrow $500 today and repay $550 in two weeks. What is the compound annual rate implied by this 10 percent rate charged for only two weeks?

A) 10.50 percent
B) 12.00 percent
C) 1091.82 percent
D) 110.50 percent

Answer: C

Explanation: (1 + 0.10)^26 − 1 = 1091.82 percent.

Difficulty: 2 Medium

Topic: Simple and compound interest

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

52) Payday loans are very short-term loans that charge very high interest rates. You can borrow $600 today and repay $675 in two weeks. What is the compound annual rate implied by this 12.5 percent rate charged for only two weeks?

A) 12.89 percent
B) 13.28 percent
C) 2037.79 percent
D) 113.28 percent

Answer: C

Explanation: ((1 + 0.125)^26) − 1 = 2037.79 percent.

Difficulty: 2 Medium

Topic: Simple and compound interest

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

53) Payday loans are very short-term loans that charge very high interest rates. You can borrow $200 today and repay $250 in two weeks. What is the compound annual rate implied by this 25 percent rate charged for only two weeks?

A) 26.60 percent
B) 32,987.22 percent
C) 30.00 percent
D) 128.25 percent

Answer: B

Explanation: ((1 + 0.25)^26) − 1 = 32,987.22 percent.

Difficulty: 2 Medium

Topic: Simple and compound interest

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

54) What is the interest rate of a 4-year, annual $1,000 annuity with present value of $3,500?

A) 3.85 percent
B) 5.56 percent
C) 8.84 percent
D) 9.70 percent

Answer: B

Explanation: N = 4, PV = −3500, PMT = 1000, FV = 0, CPT I = 5.56

Difficulty: 2 Medium

Topic: Interest rates

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-08 Compute the interest rate of annuity payments.

55) What is the interest rate of a 6-year, annual $3,000 annuity with present value of $14,000?

A) 5.64 percent
B) 7.69 percent
C) 10.17 percent
D) 11.32 percent

Answer: B

Explanation: N = 6, PV = −14000, PMT = 3000, FV = 0, CPT I = 7.69

Difficulty: 2 Medium

Topic: Interest rates

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-08 Compute the interest rate of annuity payments.

56) What annual interest rate would you need to earn if you wanted a $200 per month contribution to grow to $14,700 in five years?

A) 6.47 percent
B) 7.76 percent
C) 8.01 percent
D) 14.70 percent

Answer: C

Explanation: N = 5 × 12 = 60, PV = 0, PMT = −200, FV = 14700, CPT I = .6676 × 12 = 8.01

Difficulty: 2 Medium

Topic: Interest rates

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-08 Compute the interest rate of annuity payments.

57) What annual interest rate would you need to earn if you wanted a $500 per month contribution to grow to $27,050 in four years?

A) 2.37 percent
B) 5.77 percent
C) 6.00 percent
D) 13.53 percent

Answer: C

Explanation: N = 4 × 12 = 48, PV = 0, PMT = −500, FV = 27050, CPT I = .5002 × 12 = 6.00

Difficulty: 2 Medium

Topic: Interest rates

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-08 Compute the interest rate of annuity payments.

58) You wish to buy a $20,000 car. The dealer offers you a 5-year loan with an 8 percent APR. What are the monthly payments?

A) $272.19
B) $333.33
C) $405.53
D) $4,080.35

Answer: C

Explanation: N = 5 × 12 = 60, PV = 20000, I = 8/12 = 0.6667, FV = 0, CPT PMT = −405.53

Difficulty: 2 Medium

Topic: Loan payments

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

59) You wish to buy a $15,000 car. The dealer offers you a 4-year loan with a 9 percent APR. What are the monthly payments?

A) $260.78
B) $312.50
C) $373.28
D) $3,820.56

Answer: C

Explanation: N = 4 × 12 = 48, PV = 15000, I = 9/12 = 0.75, FV = 0, CPT PMT = −373.28

Difficulty: 2 Medium

Topic: Loan payments

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

60) Joey realizes that he has charged too much on his credit card and has racked up $3,000 in debt. If he can pay $150 each month and the card charges 18 percent APR (compounded monthly), how long will it take him to pay off the debt?

A) 13.03 months
B) 14.68 months
C) 20.00 months
D) 23.96 months

Answer: D

Explanation: PV = 3000, I = 18/12 = 1.5, FV = 0, PMT = −150, CPT N = 23.96

Difficulty: 2 Medium

Topic: Number of time periods

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-10 Calculate the number of payments on a loan.

61) Joey realizes that he has charged too much on his credit card and has racked up $4,000 in debt. If he can pay $200 each month and the card charges 20 percent APR (compounded monthly), how long will it take him to pay off the debt?

A) 17.40 months
B) 20.00 months
C) 24.04 months
D) 24.53 months

Answer: D

Explanation: PV = 4000, I = 20/12 = 1.6667, FV = 0, PMT = −200, CPT N = 24.53

Difficulty: 2 Medium

Topic: Number of time periods

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-10 Calculate the number of payments on a loan.

62) Phoebe realizes that she has charged too much on her credit card and has racked up $7,000 in debt. If she can pay $200 each month and the card charges 17 percent APR (compounded monthly), how long will it take her to pay off the debt?

A) 28.63 months
B) 35.00 months
C) 47.71 months
D) 48.68 months

Answer: D

Explanation: PV = 7000, I = 17/12 = 1.416667, FV = 0, PMT = −200, CPT N = 48.68

Difficulty: 2 Medium

Topic: Number of time periods

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-10 Calculate the number of payments on a loan.

63) Phoebe realizes that she has charged too much on her credit card and has racked up $10,000 in debt. If she can pay $300 each month and the card charges 18 percent APR (compounded monthly), how long will it take her to pay off the debt?

A) 27.23 months
B) 33.33 months
C) 46.56 months
D) 69.70 months

Answer: C

Explanation: PV = 10000, I = 18/12 = 1.5, FV = 0, PMT = −300, CPT N = 46.56

Difficulty: 2 Medium

Topic: Number of time periods

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-10 Calculate the number of payments on a loan.

64) Given a 7 percent interest rate, compute the year 6 future value if deposits of $2,500 and $1,500 are made in years 2 and 3, respectively, and a withdrawal of $900 is made in year 4.

A) $2,721.44
B) $4,084.15
C) $4,491.60
D) $7,059.04

Answer: B

Explanation: Step 1:

0 = CFO

0 = C01, 1 F01

2500 = C02, 1 F02

1500 = C03, 1 F03

−900 = C04, 1 F04

7 = I

NPV = 2721.44

Step 2:

PV = 2721.44

N = 6

I = 7

PMT = 0

CPT FV = 4084.15

Difficulty: 3 Hard

Topic: Future value – multiple cash flows

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-01 Compound multiple cash flows to the future.

65) Given an 8 percent interest rate, compute the year 7 future value if deposits of $1,500 and $2,500 are made in years 2 and 3, respectively, and a withdrawal of $2,000 is made in year 5.

A) $1,909.42
B) $3,272.41
C) $3,433.60
D) $5,656.34

Answer: B

Explanation: Step 1:

0 = CFO

0 = C01, 1 F01

1500 = C02, 1 F02

2500 = C03, 1 F03

0 = C04, 1 F04

−2000 = C05, 1 F05

8 = I

NPV = 1909.42

Step 2:

PV = 1909.42

N = 7

I = 8

PMT = 0

CPT FV = 3272.41

Difficulty: 3 Hard

Topic: Future value – multiple cash flows

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-01 Compound multiple cash flows to the future.

66) If you are saving for a plane ticket for a future vacation and you deposit $200 today, followed by $250 at the end of the first year, and a $300 deposit at the end of the second year, what will the future value of your deposits be in 3 years if the interest rates are 5%?

A) $750
B) $822.15
C) $787.5
D) None of the above

Answer: B

Explanation: $200 × (1 × 0.05)3 = $231.525

$250 × (1 × 0.05)2 = $275.625

$300 × (1 × 0.05)1 = $315

FV3 = $200 × (1 × 0.05)3 + $250 × (1 × 0.05)2 + $300 × (1 × 0.05)1 = $822.15

Difficulty: 3 Hard

Topic: Future value – multiple cash flows

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-01 Compound multiple cash flows to the future.

67) A car company is offering a choice of deals. You can receive $2,000 cash back on the purchase, or a 2 percent APR, 3-year loan. The price of the car is $17,000 and you could obtain a 3-year loan from your credit union, at 7 percent APR. Which deal is cheaper?

A) the car company’s 2 percent 3-year loan
B) the rebate with the credit union’s 7 percent 3-year loan

Answer: B

Explanation: Car Company: PV = 17000, I = 2/12 = 0.1667, FV = 0, N = 3 × 12 = 36, PMT = −486.92

Credit Union: PV = (17000 − 2000) = 15,000, N = 3 × 12 = 36, I = 7/12 = 0.5833, FV = 0, CPT PMT = −463.15

Difficulty: 3 Hard

Topic: Loan payments

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.; 05-09 Compute payments and amortization schedules for car and mortgage loans.

68) Monica has decided that she wants to build enough retirement wealth that, if invested at 7 percent per year, will provide her with $3,000 monthly income for 30 years. To date, she has saved nothing, but she still has 20 years until she retires. How much money does she need to contribute per month to reach her goal?

A) $671.78
B) $865.62
C) $3,000.00
D) $7,025.77

Answer: B

Explanation: Step 1: FV = 0, I = 7/12 = 0.5833, PMT = 3000, N = 30 × 12 = 360, CPT PV = 450922.70.

Step 2: FV = 450922.70, I = 7/12 = 0.5833, N = 20 × 12 = 240, PV = 0, CPT PMT = −865.62.

Difficulty: 3 Hard

Topic: Present value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.; 05-09 Compute payments and amortization schedules for car and mortgage loans.

69) Ross has decided that he wants to build enough retirement wealth that, if invested at 6 percent per year, will provide him with $2,500 monthly income for 30 years. To date, he has saved nothing, but he still has 20 years until he retires. How much money does he need to contribute per month to reach his goal?

A) $895.95
B) $902.47
C) $1,947.88
D) $2,500.00

Answer: B

Explanation: Step 1: FV = 0, I = 6/12 = 0.5, PMT = 2500, N = 30 × 12 = 360, CPT PV = 416979.036.

Step 2: FV = 416979.036, I = 6/12 = 0.5, N = 20 × 12 = 240, PV = 0, CPT PMT = −902.47.

Difficulty: 3 Hard

Topic: Present value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.; 05-09 Compute payments and amortization schedules for car and mortgage loans.

70) Hank purchased a $20,000 car two years ago using an 8 percent, 5-year loan. He has decided that he would sell the car now, if he could get a price that would pay off the balance of his loan. What is the minimum price Hank would need to receive for his car?

A) $8,000.00
B) $12,079.65
C) $12,941.12
D) $15,133.64

Answer: C

Explanation: FV = 0, I = 8/12 = 0.6667, N = 5 × 12 = 60, PV = 20000, CPT PMT = −405.53

2nd, Amort, P1 = 1, P2 = (2 × 12) = 24, Bal = 12941.12

Difficulty: 3 Hard

Topic: Amortization

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

71) A mortgage broker is offering a 30-year mortgage with a teaser rate. In the first two years of the mortgage, the borrower makes monthly payments on only a 5 percent APR interest rate. After the second year, the mortgage interest charged increases to 8 percent APR. What is the effective interest rate in the first two years? What is the effective interest rate after the second year?

A) 4.89 percent, 7.72 percent respectively
B) 5.00 percent, 8.00 percent respectively
C) 5.12 percent, 8.30 percent respectively
D) 12.59 percent, 12.65 percent respectively

Answer: C

Explanation: (1 + 0.05/12)^12 − 1 = 0.05116 = 5.12 percent.

(1 + 0.08/12)^12 − 1 = 0.0830 = 8.30 percent.

Difficulty: 3 Hard

Topic: Loan interest and rates

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

72) A mortgage broker is offering a 30-year mortgage with a teaser rate. In the first two years of the mortgage, the borrower makes monthly payments on only a 5.5 percent APR interest rate. After the second year, the mortgage interest charged increases to 8.5 percent APR. What is the effective interest rate in the first two years? What is the effective interest rate after the second year?

A) 5.37 percent, 8.19 percent respectively
B) 5.50 percent, 8.50 percent respectively
C) 5.64 percent, 8.84 percent respectively
D) 12.60 percent, 12.66 percent respectively

Answer: C

Explanation: (1 + 0.055/12)^12 − 1 = 0.0564 = 5.64 percent.

(1 + 0.085/12)^12 − 1 = 0.0884 = 8.84 percent.

Difficulty: 3 Hard

Topic: Loan interest and rates

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

73) Compute the future value in year 12 of a $2,000 deposit in year 3 and another $4,000 deposit at the end of year 5 using a 10 percent interest rate.

A) $12,510.77
B) $12,909.81
C) $13,406.73
D) $15,007.52

Answer: A

Explanation: Step 1: PV = 2000, N = 9, I = 10, => FV = 4715.90.

Step 2: PV = 4000, N = 7, I = 10, => FV = 7794.87.

sum of FV = 12510.77.

Difficulty: 1 Easy

Topic: Future value – multiple cash flows

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-01 Compound multiple cash flows to the future.

74) What is the future value of a $500 annuity payment over eight years if interest rates are 14 percent?

A) $6,241.09
B) $6,616.38
C) $6,750.14
D) $6,809.72

Answer: B

Explanation: PV = 0, PMT= 500, N = 8, I = 14, => FV = 6616.38

Difficulty: 1 Easy

Topic: Future value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

75) Bill makes $100 payments at the end of each year for 5 years. If interest rates are 8%, what is the present value of this annuity stream?

A) $500
B) $399.27
C) $475
D) $455.63

Answer: B

Explanation: PVA5 = $100 × = $100 × 3.9927 = $399.27

Difficulty: 1 Easy

Topic: Future value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

76) Compute the present value of a $2,500 deposit in year 4 and another $10,000 deposit at the end of year 8 if interest rates are 15 percent.

A) $4,211.26
B) $4,572.19
C) $4,698.40
D) $4,901.57

Answer: C

Explanation: Step 1: FV = 2500, N = 4, I = 15, => PV = 1429.38.

Step 2: FV = 10000, N = 8, I = 15, => PV = 3269.02.

sum of the PVs = 4698.40.

Difficulty: 1 Easy

Topic: Present value – multiple cash flows

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-03 Discount multiple cash flows to the present.

77) What is the present value of a $775 annuity payment over six years if interest rates are 11 percent?

A) $3,017.84
B) $3,119.67
C) $3,202.92
D) $3,278.67

Answer: D

Explanation: PMT= 775, FV = 0, N = 6, I = 11, => PV = 3278.67

Difficulty: 1 Easy

Topic: Present value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

78) What is the present value of a $1,100 payment made every year forever when interest rates are 4.5 percent?

A) $11,100
B) $21,089.37
C) $22,963.14
D) $24,444.44

Answer: D

Explanation: 1100/0.045 = 24444.44.

Difficulty: 1 Easy

Topic: Perpetuities

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-05 Figure cash flows and present value of a perpetuity.

79) If the present value of an ordinary, 8-year annuity is $12,500 and interest rates are 9.1 percent, what is the present value of the same annuity due?

A) $13,637.50
B) $13,941.90
C) $14,114.80
D) $14,211.90

Answer: A

Explanation: 12500(1.091) = 13637.50.

Difficulty: 1 Easy

Topic: Present value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-06 Adjust values for beginning-of-period annuity payments.

80) If the future value of an ordinary, 11-year annuity is $5,575 and interest rates are 5.5 percent, what is the future value of the same annuity due?

A) $5,619.52
B) $5,769.06
C) $5,881.63
D) $5,947.88

Answer: C

Explanation: 5575(1.055) = 5881.63.

Difficulty: 1 Easy

Topic: Future value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-06 Adjust values for beginning-of-period annuity payments.

81) A loan is offered with monthly payments and a 14.5 percent APR. What is the loan’s effective annual rate (EAR)?

A) 14.97 percent
B) 15.50 percent
C) 15.13 percent
D) 15.63 percent

Answer: B

Explanation: [(1 + 0.145/12)^12] − 1 = 0.1550.

Difficulty: 1 Easy

Topic: Loan interest and rates

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

82) Given a 7 percent interest rate, compute the year 8 future value of deposits made in years 1, 2, 3, and 4 of $750, $1,200, $500, and $250.

A) $3,801.62
B) $3,899.17
C) $4,034.20
D) $4,167.29

Answer: C

Explanation: Step 1: PV= 750, I = 7, N = 7, => FV= 1204.34.

Step 2: PV= 1200, I = 7, N = 6, => FV = 1800.88.

Step 3: PV = 500, I = 7, N = 5, => FV = 701.28.

Step 4: PV = 250, I = 7, N = 4, => FV = 327.70. sum of FVs = 4034.20.

Difficulty: 2 Medium

Topic: Future value – multiple cash flows

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-01 Compound multiple cash flows to the future.

83) Assume that you contribute $300 per month to a retirement plan for 25 years. Then you are able to increase the contribution to $500 per month for 20 years. Given a 9 percent interest rate, what is the value of your retirement plan after 45 years?

A) $1,743,956.03
B) $1,989,703.51
C) $2,189,194.36
D) $2,355,040.91

Answer: D

Explanation: Step 1: PV = 0, PMT = 300, I = 9/12, N = 300, => FV = 336336.58.

Step 2: PV = 336336.58, PMT = 500, N = 240, I = 9/12; => FV = 2355040.91.

Difficulty: 2 Medium

Topic: Future value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

84) Given an 8 percent interest rate, compute the present value of payments made in years 1, 2, 3, and 4 of $900, $800, $700, and $600.

A) $2,409.33
B) $2,515.90
C) $2,591.72
D) $2,611.38

Answer: B

Explanation: 0 = CF0 900 = C01, 1 F01 800 = C02, 2 F02 700 = C03, 1 F03 600 = C04, 1 F04 I = 8 NPV = 2,515.90

Difficulty: 2 Medium

Topic: Present value – multiple cash flows

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-03 Discount multiple cash flows to the present.

85) A small business owner visits his bank to ask for a loan. The owner states that she can repay a loan at $2,500 per month for the next two years and then $3,000 per month for another two years after that. If the bank is charging customers 6.5 percent APR, how much would it be willing to lend the business owner?

A) $111,712.39
B) $114,009.21
C) $115,278.17
D) $117,809.63

Answer: C

Explanation: Step 1: PMT = 3000, N = 48, I = 6.5/12, FV = 0 => PV = 126502.46.

Step 2: PMT = 500, N = 24, I = 6.5/12, FV = 0; => PV = 11,224.29.

Step 3: 126502.46 − 11,224.29 = 115278.17.

Difficulty: 2 Medium

Topic: Present value – multiple cash flows

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

86) A perpetuity pays $250 per year and interest rates are 8.5 percent. How much would its value change if interest decreased to 5.5 percent? Did the value increase or decrease?

A) $1,604.27; increase
B) $1,604.27; decrease
C) $1,714.20; increase
D) $1,714.20; decrease

Answer: A

Explanation: Step 1: 250/0.085 = 2941.18.

Step 2: 250/0.055 = 4545.45.

Step 3: Difference = 1604.27.

Difficulty: 2 Medium

Topic: Perpetuities

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-05 Figure cash flows and present value of a perpetuity.

87) A perpetuity pays $250 per year and interest rates are 5.5 percent. How much would its value change if interest increased to 8.5 percent? Did the value increase or decrease?

A) $1,604.27; increase
B) $1,604.27; decrease
C) $1,508.29; increase
D) $1,508.29; decrease

Answer: B

Explanation: Step 1: 250/0.055 = 4545.45.

Step 2: 250/0.085 = 2941.18.

Step 3: Difference = −1604.27.

Difficulty: 2 Medium

Topic: Perpetuities

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-05 Figure cash flows and present value of a perpetuity.

88) If you start making $115 monthly contributions today and continue them for six years, what is their present value if the compounding rate is 12 percent APR? What is the present value of this annuity?

A) $5,512.90
B) $5,633.10
C) $5,882.30
D) $5,941.12

Answer: D

Explanation: Set BEG mode. PMT = 115, N = 72, I = 1, FV = 0, => PV = 5941.12

Difficulty: 2 Medium

Topic: Present value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-06 Adjust values for beginning-of-period annuity payments.

89) Payday loans are very short-term loans that charge very high interest rates. You can borrow $550 today and repay $675 in two weeks. What is the compounded annual rate implied by this 22.73 percent rate charged for only two weeks?

A) 25.40 percent
B) 204.45 percent
C) 2,044.56 percent
D) 20,445.61 percent

Answer: D

Explanation: [(1 + 0.2273)^26] − 1 = 204.4561 = 20445.61 percent.

Difficulty: 2 Medium

Topic: Simple and compound interest

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

90) What is the interest rate of a 6-year, annual $10,000 annuity with a present value of $40,000?

A) 11.94 percent
B) 12.24 percent
C) 12.98 percent
D) 13.12 percent

Answer: C

Explanation: PV = 40,000, PMT = 10,000, FV = 0, N = 6, => I = 12.98

Difficulty: 2 Medium

Topic: Interest rates

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-08 Compute the interest rate of annuity payments.

91) What annual interest rate would you need to earn if you wanted a $1,250 per month contribution to grow to $65,000 in three years?

A) 18.59 percent
B) 21.26 percent
C) 24.00 percent
D) 25.19 percent

Answer: C

Explanation: PV = 0; N = 36, PMT = 1250, FV = 65000, => I = 2.00 annual rate = 2 × 12 = 24

Difficulty: 2 Medium

Topic: Interest rates

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-08 Compute the interest rate of annuity payments.

92) You wish to buy a $30,000 car. The dealer offers you a 5-year loan with a 9 percent APR. What are the monthly payments? What is the monthly payment if you paid interest only?

A) $622.75, $225.00
B) $659.41, $291.23
C) $701.23, $291.23
D) $712.03, $271.19

Answer: A

Explanation: Step 1: PV = 30,000, N = 60, I = 9/12, FV = 0, => PMT = 622.75.

Step 2: PV = 30000, N = 60, I = 9/12, FV = −30000, => PMT = 225.00.

Difficulty: 2 Medium

Topic: Loan payments

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

93) Isaac realizes that he charged too much on his credit card and has racked up $5,000 in debt. If he can pay $225 each month and the card charges 17.55 percent APR (compounded monthly), how long will it take him to pay off the credit card?

A) 19.14 months
B) 21.77 months
C) 22.62 months
D) 27.07 months

Answer: D

Explanation: PV = 5000, PMT = 225, FV = 0, I = 17.55/12, => N = 27.07

Difficulty: 2 Medium

Topic: Number of time periods

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-10 Calculate the number of payments on a loan.

94) Isaac realizes that he charged too much on his credit card and has racked up $7,000 in debt. If he can pay $275 each month and the card charges 17.55 percent APR (compounded monthly), how long will it take him to pay off the credit card? How much interest expense will Isaac pay during this time?

A) 32.07 months; $8,819.25
B) 32.07 months; $1,819.25
C) 22.07 months; $8,819.25
D) 22.07 months; $1,819.25

Answer: B

Explanation: Step 1: PV = 7000, PMT = 275, FV = 0, I = 17.55/12, => N = 32.07.

Step 2: (32.07 × 275) − 7000 = $1,819.25.

Difficulty: 3 Hard

Topic: Number of time periods

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

95) Given a 10 percent interest rate, compute the year 9 future value if deposits of $10,000 and $20,000 are made in years 1 and 5 respectively, and a withdrawal of $5,000 is made in year 7.

A) $44,667.89
B) $45,103.47
C) $46,585.66
D) $47,002.89

Answer: A

Explanation: Step 1: PV= 10,000, N = 8, I = 10, PMT= 0, => FV = 21435.89.

Step 2: PV = 20000, N = 4, I = 10, PMT = 0, => FV = 29282.00.

Step 3: PV = −5000, PMT = 0, N = 2, I = 10, => FV = −6050.00. sum of FVs = 44,667.89

Difficulty: 3 Hard

Topic: Future value – multiple cash flows

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

96) A car company is offering a choice of deals. You can receive $600 cash back on the purchase, or a 2 percent APR, 4-year loan. The price of the car is $18,900 and you could obtain a 4-year loan from your credit union at 6 percent APR. What is the monthly payment of each deal?

A) cash back: PMT = $429.78, 2 percent APR: PMT = $410.04
B) cash back: PMT = $438.24, 2 percent APR: PMT = $424.09
C) cash back: PMT = $458.12, 2 percent APR: PMT = $414.09
D) cash back: PMT = $408.33, 2 percent APR: PMT = $410.04

Answer: A

Explanation: Step 1: PV= 18300, FV = 0, I = 6/12, N = 48, => PMT = 429.78.

Step 2: PV = 18900, FV = 0, I = 2/12, N = 48, => PMT = 410.04.

Difficulty: 3 Hard

Topic: Loan payments

Bloom’s: Apply; Evaluate

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.; 05-09 Compute payments and amortization schedules for car and mortgage loans.

97) A furniture company is offering a choice of deals. You can receive $100 cash back on the purchase, or a 2 percent APR, 2-year loan. The price of the dining room set is $3,750 and you could obtain a 2-year loan from your credit union at 6 percent APR. What is the cost per month of each deal?

A) Cash back: $161.77, 2 percent APR: $159.53
B) Cash back: $171.29, 2 percent APR: $179.02
C) Cash back: $153.96, 2 percent APR: $181.09
D) Cash back: $180.03, 2 percent APR: $166.17

Answer: A

Explanation: Step 1: Cash back: PV = 3650, N = 24, I = 6/12; FV = 0, => PMT = 161.77.

Step 2: 2 percent APR: PV = 3750, N = 24, I = 2/12, FV = 0, PMT = 159.53.

Difficulty: 3 Hard

Topic: Loan payments

Bloom’s: Apply; Evaluate

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.; 05-09 Compute payments and amortization schedules for car and mortgage loans.

98) What is the amount of interest and repayment of principal balance in month 2 for a loan of $10,000, paid monthly over five years at a 7 percent APR?

A) Interest = $101.32, Principal repayment = $57.51
B) Interest = $57.52, Principal repayment = $140.49
C) Interest = $157.52, Principal repayment = $40.49
D) Interest = $107.52, Principal repayment = $40.49

Answer: B

Explanation: Step 1: PV = 10000, N = 60, I = 7/12, FV = 0, => PMT = 198.01.

Step 2: N = 1, PV = 10000, PMT = −198.01, I = 7/12, => FV = 9860.32.

Step 3: Int = 9860.32 × 0.07/12 = 57.52.

Step 4: 198.01 − 57.52 = Repayment = 140.49.

Difficulty: 3 Hard

Topic: Amortization

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

99) Jasmine has decided that she wants to build enough retirement wealth that, if invested at 6 percent per year, will provide her with $3,000 of monthly income for 30 years. To date, she has saved nothing but she still has 25 years until she retires. Jasmine believes that she can earn 6 percent on her investments until she retires. How much money does she need to contribute per month to reach her goal?

A) $512.93
B) $616.27
C) $722.05
D) $863.49

Answer: C

Explanation: Step 1: FV = 0, PMT = 3000, N = 360, I = 6/12, PV = 500374.84.

Step 2: PV = 0, FV = 500374.84, N = 300, I = 6/12, => PMT = 722.05.

Difficulty: 3 Hard

Topic: Present value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.; 05-09 Compute payments and amortization schedules for car and mortgage loans.

100) Jasmine has decided that she wants to build enough retirement wealth that, if invested at 6 percent per year, will provide her with $3,000 of monthly income for 30 years. To date, she has saved nothing but she still has 25 years until she retires. Jasmine believes that she can earn 9 percent on her investments until she retires. How much money does she need to contribute per month to reach her goal?

A) $446.32
B) $521.84
C) $667.13
D) $722.05

Answer: A

Explanation: Step 1: FV = 0, PMT = 3000, N = 360, I = 6/12, PV = 500374.84.

Step 2: PV = 0, FV = 500374.84, N = 300, I = 9/12, => PMT = 446.32.

Difficulty: 3 Hard

Topic: Present value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.; 05-09 Compute payments and amortization schedules for car and mortgage loans.

101) Chase purchased a $23,000 car three years ago using a 14 percent, 6-year car loan. He has decided that he would sell the car now if he could get a price that would pay off the balance of his loan. What is the minimum price Chase would need to receive for his car? (Assume monthly payments.)

A) $12,592.41
B) $13,866.82
C) $14,136.72
D) $14,809.48

Answer: B

Explanation: Step 1: PV = 23000, FV = 0, N = 72, I = 14/12, => PMT = 473.93.

Step 2: PV = 23000, N = 36, I = 14/12, PMT = −473.93, => FV = 13866.82.

Difficulty: 3 Hard

Topic: Amortization

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

102) Chase purchased a $30,000 car three years ago using a 10 percent, 5-year car loan. He has decided that he would sell the car now if he could get a price that would pay off the balance of his loan. What is the minimum price Chase would need to receive for his car? (Assume monthly payments.)

A) $12,000.00
B) $13,813.25
C) $21,500.75
D) $23,739.05

Answer: B

Explanation: Step 1: PV = 30000, FV = 0, N = 60, I = 10/12, => PMT = 637.4113.

Step 2: PV = 30000, N = 36, I = 10/12, PMT = −637.4113, => FV = 13813.2487.

Difficulty: 3 Hard

Topic: Amortization

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

103) A mortgage broker is offering a $225,000 30-year mortgage with a teaser rate. In the first two years of the mortgage, the borrower makes monthly payments on only a 2.5 percent APR interest rate. After the second year, the mortgage interest rate charged increases to 8.5 percent APR. What are the mortgage payments in the first two years? What are the mortgage payments after the second year?

A) $790.25; $1,512.93
B) $790.25; $1,309.13
C) $889.02; $1,650.61
D) $889.02; $1,677.09

Answer: D

Explanation: Step 1: N = 360, I = 2.5/12, PV = 225000, FV = 0, PMT = 889.02.

Step 2: N = 24, I = 2.5/12, PMT = 889.02, PV = 225000, => FV = 214668.13.

Step 3: PV = 214668.13, N = 336, I = 8.5/12, FV = 0, => PMT = 1677.09.

Difficulty: 3 Hard

Topic: Loan payments

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

104) Consider that you are 30 years old and have just changed to a new job. You have $91,000 in the retirement plan from your former employer. You can roll that money into the retirement plan of the new employer. You will also contribute $4,800 each year into your new employer’s plan. If the rolled-over money and the new contributions both earn a 7 percent return, how much should you expect to have when you retire in 38 years?

A) $2,012,560.60
B) $2,018,506.60
C) $2,106,718.60
D) $2,216,781.60

Answer: B

Explanation: PV = 91000, I = 7, PMT = 4800, N = 38, => FV = 2018506.60

Difficulty: 3 Hard

Topic: Future value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

105) Consider that you are 30 years old and have just changed to a new job. You have $91,000 in the retirement plan from your former employer. You can roll that money into the retirement plan of the new employer. You will also contribute $400 each month into your new employer’s plan. If the rolled-over money and the new contributions both earn a 7 percent annual return, how much should you expect to have when you retire in 38 years?

A) $2,019,095.26
B) $2,195,145.40
C) $2,298,025.12
D) $2,301,116.92

Answer: B

Explanation: PV = 91000, N = 456, I = 7/12, PMT = 400, => FV = 2195145.40

Difficulty: 3 Hard

Topic: Future value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

106) Your client has been given a trust fund valued at $1 million. She cannot access the money until she turns 68 years old, which is in 12 years. At that time, she can withdraw $30,000 per month. If the trust fund is invested at a 7 percent interest rate, how many months will it last your client once she starts to withdraw the money?

A) 77.05 months
B) 81.05 months
C) 99.05 months
D) 119.05 months

Answer: C

Explanation: Step 1: PV = 1000000, N = 12, I = 7, FV = 2252191.59.

Step 2: PV = 2252161.59, PMT = −30000, FV = 0, I = 7/12, => N = 99.05 months.

Difficulty: 3 Hard

Topic: Number of time periods

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.; 05-10 Calculate the number of payments on a loan.

107) A local furniture store is advertising a deal in which you buy a $3,500 living room set with three years before you need to make payments (no interest is incurred). How much would you have to deposit each month in a savings account earning 3.5 percent APR, compounded monthly, to be able to pay the $3,500 bill in three years?

A) $92.35
B) $108.13
C) $112.86
D) $121.97

Answer: A

Explanation: PV = 0, N = 36, I = 3.5/12, FV = 3500, => PMT = 92.35

Difficulty: 3 Hard

Topic: Time value payments

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

108) A local furniture store is advertising a deal in which you buy a $3,500 living room set with three years before you need to make payments (no interest is incurred). How much money would you have to deposit now in a savings account earning 3.5 percent APR, compounded monthly, to pay the $3,500 bill in three years?

A) $2,981.17
B) $3,151.62
C) $3,200.61
D) $3,886.89

Answer: B

Explanation: FV = 3500, I = 3.5/12, N = 36, PMT = 0, => PV = 3151.62

Difficulty: 3 Hard

Topic: Present value – single cash flow

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

109) You have secured a loan from your bank for two years to build your home. The terms of the loan are that you will borrow $120,000 now and an additional $52,000 in one year. Interest of 9 percent APR will be charged on the balance monthly. Since no payments will be made during the 2-year loan, the balance will grow. At the end of the two years, the balance will be converted to a traditional 30-year mortgage at a 6.5 percent interest rate. What will you pay as monthly mortgage payments (principal and interest only)?

A) $998.49
B) $1,063.27
C) $1,190.14
D) $1,266.97

Answer: D

Explanation: Step 1: PV = 120000, PMT = 0, N = 12, I = 9/12, => FV = 131256.83.

Step 2: PV = 183256.83, PMT = 0, I = 9/12, N = 12, FV = 200447.58.

Step 3: PV = 200447.58, N = 360, I = 6.5/12, FV = 0, => PMT = 1266.97.

Difficulty: 3 Hard

Topic: Loan payments

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

110) Say that you purchase a house for $150,000 by getting a mortgage for $135,000 and paying a $15,000 down payment. If you get a 15-year mortgage with a 6 percent interest rate, what are the monthly payments?

A) $997.28
B) $1,072.51
C) $1,139.21
D) $1,238.93

Answer: C

Explanation: PV = 135000, N = 180, I = 6/12, FV = 0, => PMT = 1139.21

Difficulty: 2 Medium

Topic: Loan payments

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

111) Say that you purchase a house for $150,000 by getting a mortgage for $135,000 and paying a $15,000 down payment. If you get a 15-year mortgage with a 6 percent interest rate, what would the loan balance be in seven years?

A) $74,778.16
B) $79,091.72
C) $84,223.16
D) $86,687.84

Answer: D

Explanation: Step 1: PV = 135000, N = 180, I = 6/12, FV = 0, => PMT = 1139.21.

Step 2: PV = −135000, PMT = 1139.21, N = 84, I = 6/12, FV = 86687.84.

Difficulty: 3 Hard

Topic: Amortization

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

112) Say that you purchase a house for $150,000 by getting a mortgage for $135,000 and paying a $15,000 down payment. Assume you get a 15-year mortgage with a 6 percent interest rate. If the house appreciates at a 2 percent rate per year, what will be the value of the house in seven years? How much of this value is equity?

A) $172,302.85; $65,101.91
B) $172,302.85; $85,615.01
C) $185,612.09; $79,662.83
D) $185,612.09; $81,038.72

Answer: B

Explanation: Step 1: PV = 150000, N = 7, I = 2, PMT = 0, => FV = 172302.85.

Step 2: PV = 135000, N = 180, I = 6/12, FV = 0, => PMT = 1139.21.

Step 3: PV = −135000, PMT = 1139.21, N = 84, I = 6/12, FV = 86687.84.

Step 4: 172302.85 − 86687.84 = 85615.01.

Difficulty: 3 Hard

Topic: Amortization

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

113) A small business owner visits his bank to ask for a loan. The owner states that she can repay a loan at $1,250 per month for the next three years and then $500 per month for two years after that. If the bank is charging customers 12 percent APR, how much would it be willing to lend the business owner?

A) $45,058.15
B) $45,911.64
C) $46,055.21
D) $46,813.94

Answer: A

Explanation: Step 1: PMT = 500, N = 60, I = 1, => PV = 22477.52.

Step 2: PMT = 750, N = 36, I = 1, => PV = 22580.63.

Step 3: 22477.52 + 22580.63 = 45058.15.

Difficulty: 3 Hard

Topic: Present value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

114) A small business owner visits his bank to ask for a loan. The owner states that she can repay a loan at $1,500 per month for the next 3 years and then $500 per month for three years after that. If the bank is charging customers 10 percent APR, how much would it be willing to lend the business owner?

A) $32,019.95
B) $57,980.57
C) $61,982.47
D) $192,119.70

Answer: B

Explanation: Step 1: PMT = 500, N = 72, I = 10/12, => PV = 26989.33.

Step 2: PMT = 1000, N = 36, I = 10/12, => PV = 30991.24.

Step 3: 26989.33 + 30991.24 = 57980.57.

Difficulty: 3 Hard

Topic: Present value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

115) You win $1,000 today, which happens to be your 20th birthday. You decide to deposit this money in an account and plan to add $1,000 to it each year on your birthday beginning one year from today. If you earn 10 percent per year in the account, how long will it take to grow to $750,000?

A) 23.17 years
B) 32.87 years
C) 44.44 years
D) 51.38 years

Answer: C

Explanation: PV = 1000, PMT = 1000, I = 10, FV = −750000, => N = 44.44

Difficulty: 3 Hard

Topic: Number of time periods

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

116) Your 30-year $95,000 mortgage calls for payments to be made at the end of each month. The loan has a 5.85 percent annual interest rate. What is the remaining balance after five years?

A) $68,194.73
B) $76,903.26
C) $81,072.85
D) $88,236.44

Answer: D

Explanation: Step 1: PV = 95000, N = 360, I = 5.85/12, FV = 0, => PMT = 560.44.

Step 2: PV = 95000, N = 60, I = 5.85/12, PMT = −560.44, => FV = 88236.44.

Difficulty: 3 Hard

Topic: Amortization

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

117) Due to poor spending habits, Ricky has accumulated $10,000 in credit card debt. He has missed several payments and now the annual interest rate on the card is 18.95 percent! If he pays $175 per month on the card, how long will it take Ricky to pay off the card?

A) 121.5 months
B) 148.50 months
C) 162.5 months
D) Ricky never pays off the card.

Answer: B

Explanation: PV = 10000, PMT = −175, I = 18.95/12, FV = 0, => N = 148.50

Difficulty: 2 Medium

Topic: Number of time periods

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-10 Calculate the number of payments on a loan.

118) Due to poor spending habits, Ricky has accumulated $10,000 in credit card debt. He has missed several payments and now the annual interest rate on the card is 18.95 percent! If he pays $175 per month on the card, in total, how much interest expense does Ricky pay to the credit card company?

A) $15,987.50
B) $17,008.52
C) $12,905.13
D) $8,714.62

Answer: A

Explanation: Step 1: PV = 10000, PMT = −175, I = 18.95/12, FV = 0, => N = 148.50.

Step 2: 148.5 × 175 = 25987.5 − 10000 = 15987.5.

Difficulty: 3 Hard

Topic: Number of time periods

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.; 05-10 Calculate the number of payments on a loan.

119) Due to poor spending habits, Ricky has accumulated $5,000 in credit card debt. He has missed several payments and now the annual interest rate on the card is 16.75 percent! If he pays $200 per month on the card, in total, how much interest expense does Ricky pay to the credit card company?

A) $847.50
B) $1,192.00
C) $2,118.75
D) $6,192.00

Answer: B

Explanation: Step 1: PV = 5000, PMT = −200, I = 16.75/12, FV = 0, => N = 30.96.

Step 2: 30.96 × 200 = 6192 − 5000 = 1192.

Difficulty: 3 Hard

Topic: Number of time periods

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.; 05-10 Calculate the number of payments on a loan.

120) You deposit $1,000 today and want to save $100 each month beginning one month from today. Your account earns a 5 percent annual interest rate. How long will it take you to accumulate $5,000?

A) 29.3 months
B) 35.7 months
C) 42.6 months
D) 52.1 months

Answer: B

Explanation: PV = 1000, PMT = 100, FV = −5000, I = 5/12, => N = 35.7 months

Difficulty: 2 Medium

Topic: Number of time periods

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

121) You are deciding among several different bank accounts. Which of the following will generate the highest effective annual rate (EAR)?

A) a 6 percent rate with monthly compounding
B) a 6 percent rate with annual compounding
C) a 6.08 percent rate with annual compounding
D) a 6 percent rate with quarterly compounding

Answer: A

Explanation: [(1 + 0.06/12)^12] − 1 = 6.17 percent.

Difficulty: 2 Medium

Topic: Simple and compound interest

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

122) You are deciding among several different bank accounts. Which of the following will generate the highest effective annual rate (EAR)?

A) a 10 percent rate with monthly compounding
B) a 10 percent rate with annual compounding
C) a 10.5 percent rate with annual compounding
D) a 10 percent rate with quarterly compounding

Answer: C

Explanation: [(1 + 0.1/12)^12] − 1 = 10.47 percent.

Difficulty: 2 Medium

Topic: Simple and compound interest

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

123) Which of the following will increase the present value of an annuity?

A) The discount rate increases.
B) The discount rate decreases.
C) The number of periods the annuity is received decreases.
D) The final payment diminishes.

Answer: B

Difficulty: 2 Medium

Topic: Present value – annuity

Bloom’s: Apply; Evaluate

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

124) Which of the following will decrease the present value of an annuity?

A) The discount rate increases.
B) The discount rate decreases.
C) The number of periods the annuity is received increases.
D) The final payment increases.

Answer: A

Difficulty: 2 Medium

Topic: Present value – annuity

Bloom’s: Analyze

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

125) Which of the following statements is correct?

A) A 15-year mortgage will have larger monthly payments than a 30-year mortgage.
B) If an account earns 3 percent per year compounded annually, then it also has an effective annual rate (EAR) of 3 percent.
C) The present value of a $500 perpetuity is greater if the interest rate is higher.
D) The first, second, and third statements above are correct.
E) Only the first and second, statements above are correct.

Answer: E

Difficulty: 3 Hard

Topic: Simple and compound interest

Bloom’s: Apply; Evaluate

AACSB: Reflective Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.; 05-09 Compute payments and amortization schedules for car and mortgage loans.

126) You just bought a new home and have a 30-year mortgage with monthly payments. Which statement regarding your mortgage is correct?

A) Your monthly payments will decrease over time.
B) The dollar amount of interest expense you pay each year will remain the same each year.
C) The dollar amount of principal paid increases each month.
D) All of these choices are correct.

Answer: C

Difficulty: 2 Medium

Topic: Amortization

Bloom’s: Remember; Understand

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

127) Bank A charges a 7.75 percent annual percentage rate and interest is due at the end of the year. Bank B charges a 7 percent annual percentage rate and interest must be paid monthly. What is the effective annual rate charged by each bank?

A) Bank A: 7.75 percent, Bank B: 7.23 percent
B) Bank A: 7.85 percent, Bank B: 7.23 percent
C) Bank A: 7.25 percent, Bank B: 7.5 percent
D) Bank A: 7.85 percent, Bank B: 8.15 percent

Answer: A

Explanation: EAR for Bank B: [(1 + 0.07/12)^12] − 1 = 7.23; EAR for Bank A = 7.75 percent.

Difficulty: 2 Medium

Topic: Simple and compound interest

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

128) Bank A charges a 7.50 percent annual percentage rate and interest is due at the end of the year. Bank B charges a 6.95 percent annual percentage rate and interest must be paid monthly. What is the effective annual rate charged by each bank?

A) Bank A: 7.5 percent, Bank B: 6.95 percent
B) Bank A: 7.76 percent, Bank B: 6.95 percent
C) Bank A: 7.5 percent, Bank B: 7.18 percent
D) Bank A: 7.76 percent, Bank B: 7.18 percent

Answer: C

Explanation: EAR for Bank B: [(1 + 0.0695/12)^12] − 1 = 7.1757 percent; EAR for Bank A = 7.5 percent.

Difficulty: 2 Medium

Topic: Simple and compound interest

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

129) Your company borrows $55,000 today to fund its growth initiatives. It must repay the bank in four annual payments of $17,100 at the end of each year. What annual interest rate is your firm paying?

A) 7.76 percent
B) 8.26 percent
C) 9.33 percent
D) 10.26 percent

Answer: C

Explanation: PV = 55000, PMT = −17100, N = 4, FV = 0, => I = 9.33

Difficulty: 2 Medium

Topic: Interest rates

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-08 Compute the interest rate of annuity payments.

130) Your company borrows $75,000 today to fund its growth initiatives. It must repay the bank in four annual payments of $26,600 at the end of each year. What annual interest rate is your firm paying?

A) 15.62 percent
B) 17.18 percent
C) 14.74 percent
D) 16.97 percent

Answer: A

Explanation: PV = 75000, N = 4, PMT = −26600, FV = 0, => I = 15.62

Difficulty: 2 Medium

Topic: Interest rates

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-08 Compute the interest rate of annuity payments.

131) Your company borrows $275,000 today to fund its growth initiatives. It must repay the bank in five annual payments of $76,300 at the end of each year. What annual interest rate is your firm paying?

A) 10.85 percent
B) 12.01 percent
C) 17.75 percent
D) 18.02 percent

Answer: B

Explanation: PV = 275000, N = 5, PMT = −76,300, FV = 0, => I = 12.0065

Difficulty: 2 Medium

Topic: Interest rates

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-08 Compute the interest rate of annuity payments.

132) As a college student, you probably receive many credit card offers in the mail. Consider these two offers. The first card charges a 17 percent APR. An examination of the footnotes reveals that this card compounds monthly. The second credit card charges 16.25 percent APR and compounds weekly. What is the effective annual rate of the cheaper card?

A) 17.00 percent
B) 17.62 percent
C) 16.25 percent
D) 18.39 percent

Answer: B

Explanation: Step 1: EAR of card 1: [(1 + 0.17/12)^12] − 1 = 18.39 percent.

Step 2: EAR of card 2: [(1 + 0.1625/52)^52] − 1 = 17.62 percent.

Difficulty: 2 Medium

Topic: Simple and compound interest

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

133) As a college student, you probably receive many credit card offers in the mail. Consider these two offers. The first card charges a 17 percent APR. An examination of the footnotes reveals that this card compounds daily (365 day year). The second credit card charges 18 percent APR and compounds semiannually. What is the effective annual rate of the cheaper card?

A) 18.00 percent
B) 17.00 percent
C) 18.81 percent
D) 18.53 percent

Answer: D

Explanation: Step 1: EAR of card 1: [(1 + 0.17/365)^365] − 1 = 18.53 percent.

Step 2: EAR of card 2: [(1 + 0.18/2)^2] − 1 = 18.81 percent.

Difficulty: 2 Medium

Topic: Simple and compound interest

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

134) You have reviewed your budget and determine that the most you can afford on a car loan is $375 per month. What is the most you can borrow if interest rates are 8 percent and you can pay the loan over five years?

A) $20,591.86
B) $16,779.02
C) $18,494.41
D) $21,147.83

Answer: C

Explanation: FV = 0, PMT = −375, N = 60, I = 8/12, => PV = 18494.41

Difficulty: 2 Medium

Topic: Present value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

135) You have reviewed your budget and determine that the most you can afford on a car loan is $455 per month. What is the most you can borrow if interest rates are 7 percent and you can pay the loan over four years?

A) $19,000.89
B) $19,741.29
C) $20,074.82
D) $21,671.53

Answer: A

Explanation: FV = 0, N = 48, I = 7/12, PMT = −455, => PV = 19000.89

Difficulty: 2 Medium

Topic: Present value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

136) You have reviewed your budget and determine that the most you can afford on a car loan is $550 per month. What is the most you can borrow if interest rates are 6 percent and you can pay the loan over three years?

A) $1,470.16
B) $15,639.28
C) $17,641.92
D) $18,079.06

Answer: D

Explanation: FV = 0, N = 36, I = 6/12, PMT = −550, => PV = 18079.0589

Difficulty: 2 Medium

Topic: Present value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

137) Your firm needs to buy additional physical therapy equipment that costs $27,000. The equipment manufacturer will give you the equipment now if you will pay $7,000 per year for the next five years. Assume your firm can borrow at a 13 percent interest rate. You need to analyze if your firm should pay the manufacturer the $27,000 now or accept the five-year annuity offer of $7,000. Which of the following statements is correct?

A) You decide to pay $27,000 today because paying in cash is always cheaper.
B) You decide to pay for the equipment over time because it only costs $24,620.62.
C) You decide to pay for the equipment over time because it only costs $29,112.86.
D) You decide to pay $27,000 today because it is cheaper than paying for the equipment over time.

Answer: B

Explanation: Cost of Annuity: PMT = 7000, I = 13, N = 5, FV = 0, => PV = 24620.62

Difficulty: 3 Hard

Topic: Present value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

138) Your firm needs to buy additional physical therapy equipment that costs $35,000. The equipment manufacturer will give you the equipment now if you will pay $8,000 per year for the next five years. Assume your firm can borrow at a 3 percent interest rate. You need to analyze if your firm should pay the manufacturer the $35,000 now or accept the five-year annuity offer of $8,000. Which of the following statements is correct?

A) You decide to pay $35,000 today because paying in cash is always cheaper.
B) You decide to pay $35,000 today because paying for the equipment over time costs $36,637.66.
C) You decide to pay for the equipment over time because it only costs $39,112.86.
D) Paying for the equipment over time costs $36,637.66, which is less than paying $35,000 today.

Answer: B

Explanation: Cost of Annuity: FV = 0, PMT = 8000, N = 5, I = 3, => PV = 36637.66

Difficulty: 2 Medium

Topic: Present value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

139) You started your first job after graduating from college. Your company offers a retirement plan for which the company contributes 50 percent of what you contribute each year. You expect to contribute $4,000 per year from your salary. You decide to invest the contributions in assets that you expect to earn 8 percent per year. If you plan to retire in 35 years, how big will you expect that retirement account to be?

A) $689,267.21
B) $823,147.29
C) $1,033,900.82
D) $1,308,427.41

Answer: C

Explanation: PMT = 6000, FV = 0, N = 35, I = 8, => FV = 1,033,900.82

Difficulty: 2 Medium

Topic: Future value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

140) You started your first job after graduating from college. Your company offers a retirement plan for which the company contributes 25 percent of what you contribute each year. You expect to contribute $5,000 per year from your salary. You decide to invest the contributions in assets that you expect to earn 8 percent per year. If you plan to retire in 35 years, how big will you expect that retirement account to be?

A) $861,584.02
B) $921,597.31
C) $972,110.74
D) $1,076,980.02

Answer: D

Explanation: PV = 0, PMT= 6250, I = 8, N = 35, => FV = 1076980.02

Difficulty: 2 Medium

Topic: Future value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

141) You started your first job after graduating from college. Your company offers a retirement plan for which the company contributes 50 percent of what you contribute each year. You expect to contribute $2,000 per year from your salary. You decide to invest the contributions in assets that you expect to earn 10 percent per year. If you plan to retire in 40 years, how big will you expect that retirement account to be?

A) $442,592.56
B) $885,185.11
C) $1,327,777.67
D) $1,527,787.70

Answer: C

Explanation: PV = 0, PMT = 3000, I = 10, N = 40, => FV = 1327777.667

Difficulty: 2 Medium

Topic: Future value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

142) Sally saves $500 per month in her retirement plan. She plans on making monthly contributions for 35 years. If her account earns a 12 percent annual interest rate, how much will she have at the end of 35 years and what percent of the total are her out-of-pocket contributions?

A) $1,113,879.14; 43.72 percent
B) $2,452,905.33; 12.07 percent
C) $3,215,479.74; 6.53 percent
D) $3,691,003.27; 8.28 percent

Answer: C

Explanation: Step 1: PV = 0, PMT = 500, N = 35 × 12, I = 12/12, => FV = 3215479.74.

Step 2: 35 × 12 × 500/3215479.74 = 6.53 percent.

Difficulty: 3 Hard

Topic: Future value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

143) Jane has been saving $500 in her retirement account each month for the last 20 years and plans to continue contributing $500 each month for the next 20 years. Her account has been earning an 8 percent annual interest rate and she expects to earn the same rate for the next 20 years. Her twin brother, Hal, has not saved anything for the last 20 years. Due to sibling rivalry, he wants to have as much as Jane is expected to have at the end of 20 years. If Hal expects to earn the same annual interest rate as Jane, how much must Hal save each month to achieve his goal?

A) $1,043.71
B) $1,517.92
C) $2,007.53
D) $2,963.40

Answer: D

Explanation: Step 1: PV = 0, PMT = 500, N = 40 × 12, I = 8/12, => FV = 1745503.92.

Step 2: PV = 0, N = 20 × 12, I = 8/12, FV = 1745503.92, => PMT = 2963.40.

Difficulty: 3 Hard

Topic: Future value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

144) Jane has been saving $450 in her retirement account each month for the last 20 years and plans to continue contributing $450 each month for the next 20 years. Her account has been earning a 9 percent annual interest rate and she expects to earn the same rate for the next 20 years. Her twin brother, Hal, has not saved anything for the last 20 years. Due to sibling rivalry, he wants to have as much as Jane is expected to have at the end of 20 years. If Hal expects to earn the same annual interest rate as Jane, how much must Hal save each month to achieve his goal?

A) $1,791.34
B) $2,109.28
C) $2,872.91
D) $3,154.12

Answer: D

Explanation: Step 1: PV = 0, PMT = 450, I = 9/12; N = 40 × 12, => FV = 2106594.12

Step 2: PV = 0, FV = 2106594.12, I = 9/12, N = 20 × 12, => PMT = 3154.12

Difficulty: 3 Hard

Topic: Future value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

145) Jane has been saving $200 in her retirement account each month for the last 20 years and plans to continue contributing $200 each month for the next 20 years. Her account has been earning an 8 percent annual interest rate and she expects to earn the same rate for the next 20 years. Her twin brother, Hal, has not saved anything for the last 20 years. Due to sibling rivalry, he wants to have as much as Jane is expected to have at the end of 20 years. If Hal expects to earn the same annual interest rate as Jane, how much must Hal save each month to achieve his goal?

A) $400.00
B) $1,185.36
C) $1,569.85
D) $2,909.17

Answer: B

Explanation: Step 1: PV = 0, PMT = 200, I = 8/12, N = 40 × 12, => FV = 698,201.5663.

Step 2: PV = 0, FV = 698,201.5663, I = 8/12, N = 20 × 12, => PMT = 1185.3606.

Difficulty: 3 Hard

Topic: Future value – annuity

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

146) Your current $95,000 mortgage calls for monthly payments over 30 years at an annual interest rate of 6 percent. If you pay an additional $50 each month beginning with the first payment, how soon do you pay off your mortgage?

A) 329.67 months
B) 311.56 months
C) 291.78 months
D) 288.45 months

Answer: C

Explanation: Step 1: PV = 95000, FV = 0, N = 360, I = 6/12, => PMT = 569.57.

Step 2: PMT = −619.57, FV = 0, I = 6/12, PV = 95000, => N = 291.78.

Difficulty: 3 Hard

Topic: Number of time periods

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.; 05-10 Calculate the number of payments on a loan.

147) Your current $115,000 mortgage calls for monthly payments over 30 years at an annual interest rate of 7 percent. If you pay an additional $50 each month beginning with the first payment, how much interest expense do you save by prepaying?

A) $32,764.43
B) $30,718.29
C) $29,503.14
D) $22,008.73

Answer: A

Explanation: Step 1: PV = 115000, FV = 0, N = 360, I = 7/12, => PMT = 765.10.

Step 2: PV = 115000, PMT = −815.10, I = 7/12, FV = 0, => N = 297.72.

Step 3: 360 × 765.10 − 297.72 × 815.10 = 32,764.43.

Difficulty: 3 Hard

Topic: Number of time periods

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.; 05-10 Calculate the number of payments on a loan.

148) Your current $155,000 mortgage calls for monthly payments over 25 years at an annual interest rate of 6 percent. If you pay an additional $50 each month beginning with the first payment, how much interest expense do you save by pre-paying?

A) $15,981.28
B) $16,009.62
C) $17,152.22
D) $19,001.69

Answer: C

Explanation: Step 1: PV = 155000, FV = 0, N = 25 × 12, I = 6/12, => PMT = 998.67.

Step 2: PV = 155000, PMT = −1048.67, I = 6/12, FV = 0, => N = 269.34.

Step 3: 300 × 998.67 − 269.34 × 1048.67 = 17,152.22.

Difficulty: 3 Hard

Topic: Number of time periods

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.; 05-10 Calculate the number of payments on a loan.

149) After saving diligently your entire career, you and your spouse are ready to retire with a nest egg of $600,000. You need to invest this money in a mix of stocks and bonds that will allow you to earn $5,000 per month for 30 years. What annual interest rate (APR) do you need to earn?

A) 9.40 percent
B) 10.13 percent
C) 8.37 percent
D) 9.61 percent

Answer: A

Explanation: PV = 600,000, N = 360, FV = 0, PMT = −5000, => I = 0.7831, APR = 0.7831 × 12 = 9.40

Difficulty: 2 Medium

Topic: Interest rates

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-08 Compute the interest rate of annuity payments.

150) After saving diligently your entire career, you and your spouse are ready to retire with a nest egg of $500,000. You need to invest this money in a mix of stocks and bonds that will allow you to earn $4,000 per month for 30 years. What annual interest rate (APR) do you need to earn?

A) 6.92 percent
B) 7.45 percent
C) 8.94 percent
D) 9.17 percent

Answer: C

Explanation: PV = 500000, N = 360, FV = 0, PMT = −4000, => I = 0.7446, APR = 0.74 × 12 = 8.94 percent

Difficulty: 2 Medium

Topic: Interest rates

Bloom’s: Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-08 Compute the interest rate of annuity payments.

151) Which of the following will increase the future value of an annuity?

A) The number of periods increases.
B) The amount of the annuity increases.
C) The interest rate increases.
D) All of these choices are correct.

Answer: D

Difficulty: 1 Easy

Topic: Future value – annuity

Bloom’s: Remember

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-02 Compute the future value of frequent, level cash flows.

152) Which of the following will increase the present value of an annuity?

A) The number of periods decreases.
B) The interest rate decreases.
C) The amortization schedule decreases.
D) The effective rate is calculated over fewer years.

Answer: B

Difficulty: 1 Easy

Topic: Present value – annuity

Bloom’s: Remember

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.

153) If the present value of an ordinary, 10-year annuity is $25,000 and interest rates are 7 percent, what is the present value of the same annuity due?

A) $23,644.49
B) $24,997.51
C) $25,000.00
D) $26,750.00

Answer: D

Explanation: END MODE

PV = 25000

FV = 0

I = 7

N = 10

CPT PMT = 3559.4376

BGN MODE

FV = 0

PMT = 3559.4376

I = 7

N = 10

CPT PV = 26750.00

Difficulty: 1 Easy

Topic: Present value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-06 Adjust values for beginning-of-period annuity payments.

154) If the future value of an ordinary, 5-year annuity is $100,000 and interest rates are 5 percent, what is the future value of the same annuity due?

A) $95,238.10
B) $100,000.00
C) $105,000.00
D) $107,000.00

Answer: C

Explanation: END MODE

FV = 100000

PV = 0

I = 5

N = 5

CPT PMT = 18097.4798

BGN MODE

PV = 0

PMT = 18097.4798

I = 5

N = 5

CPT FV = 105000.00

Difficulty: 1 Easy

Topic: Future value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

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Learning Goal: 05-06 Adjust values for beginning-of-period annuity payments.

155) If you start making $90 monthly contributions today and continue them for ten years, what is their future value if the compounding rate is 6 percent APR? What is the present value of this annuity?

A) $14,794.14; $8,106.61
B) $14,794.14; $8,147.14
C) $14,822.89; $8,106.61
D) $14,822.89; $8,147.14

Answer: A

Explanation: N = 10 × 12 = 120, I = 6/12 = 0.50, PV = 0, PMT = 90, CPT FV = 14794.14

N = 10 × 12 = 120, I = 6/12 = 0.50, FV = 0, PMT = 90, CPT PV = 8106.61

Difficulty: 2 Medium

Topic: Future value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

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Learning Goal: 05-06 Adjust values for beginning-of-period annuity payments.

156) Payday loans are very short-term loans that charge very high interest rates. You can borrow $500 today and repay $550 in ten weeks. What is the compound annual rate implied by this 10 percent rate charged for only ten weeks?

A) 5.20 percent
B) 10.41 percent
C) 59.94 percent
D) 64.15 percent

Answer: D

Explanation: [(1 + 0.10)^5.2] − 1 = 64.15 percent.

Difficulty: 2 Medium

Topic: Compound frequency

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

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Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

157) A car company is offering a choice of deals. You can receive $4,000 cash back on the purchase, or a 0 percent APR, 4-year loan. The price of the car is $40,000 and you could obtain a 4-year loan from your credit union, at 6 percent APR. Which deal is cheaper?

A) The car company’s 0 percent 4-year loan.
B) The rebate with the credit union’s 6 percent 4-year loan.
C) There is not enough information given to determine which deal is cheaper.

Answer: A

Explanation: Car Company: PV = 40000, I = 0, FV = 0, N = 4 × 12 = 48, PMT = −833.33

Credit Union: PV = (40000 − 4000) = 36,000, N = 4 × 12 = 48, I = 6/12 = 0.50, FV = 0, CPT PMT = −845.46

Difficulty: 3 Hard

Topic: Loan payments

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.; 05-09 Compute payments and amortization schedules for car and mortgage loans.

158) Paige has decided that she wants to build enough retirement wealth that, if invested at 5 percent per year, will provide her with $2,500 monthly income for 20 years. To date, she has saved nothing, but she still has 40 years until she retires. How much money does she need to contribute per month to reach her goal?

A) $180.02
B) $248.24
C) $460.81
D) $921.61

Answer: B

Explanation: Step 1: FV = 0, I = 5/12 = 0.4167, PMT = 2500, N = 20 × 12 = 240, CPT PV = −378,813.2827.

Step 2: FV = 378,813.2827, I = 5/12 = 0.4167, N = 40 × 12 = 480, PV = 0, CPT PMT = −248.2361.

Difficulty: 3 Hard

Topic: Present value – annuity

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.; 05-09 Compute payments and amortization schedules for car and mortgage loans.

159) Bethany purchased a $35,000 car three years ago using a 6 percent, 5-year loan. She has decided that she would sell the car now, if she could get a price that would pay off the balance of her loan. What is the minimum price Bethany would need to receive for her car?

A) $9,680,67
B) $15,267.12
C) $22,242.11
D) $23,429.19

Answer: B

Explanation: FV = 0, I = 6/12 = 0.50, N = 5 × 12 = 60, PV = 35000, CPT PMT = −676.6481

2nd, Amort, P1 = 1, P2 = (3 × 12) = 36, Bal = 15267.12

Difficulty: 3 Hard

Topic: Amortization

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-09 Compute payments and amortization schedules for car and mortgage loans.

160) A mortgage broker is offering a 30-year mortgage with a teaser rate. In the first two years of the mortgage, the borrower makes monthly payments on only a 2.5 percent APR interest rate. After the second year, the mortgage interest charged increases to 4.25 percent APR. What is the effective interest rate in the first two years? What is the effective interest rate after the second year?

A) 2.08 percent, 3.54 percent respectively
B) 2.50 percent, 4.25 percent respectively
C) 2.53 percent, 4.33 percent respectively
D) 5.00 percent, 8.50 percent respectively

Answer: C

Explanation: (1 + 0.025/12)^12 − 1 = 0.0253 = 2.53 percent.

(1 + 0.0425/12)^12 − 1 = 0.0433 = 4.33 percent.

Difficulty: 3 Hard

Topic: Loan interest and rates

Bloom’s: Analyze; Apply

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-07 Explain the impact of compound frequency and the difference between the annual percentage rate and the effective annual rate.

161) A furniture company is offering a choice of deals. You can receive $500 cash back on the purchase, or a 4 percent APR, 2-year loan. The price of the dining room set is $5,000 and you could obtain a 2-year loan from your credit union at 3 percent APR. What is the cost per month of each deal?

A) cash back: $193.42, 4 percent APR: $217.12
B) cash back: $193.42, 2 percent APR: $214.91
C) cash back: $195.41, 2 percent APR: $217.12
D) cash back: $195.41, 2 percent APR: $214.91

Answer: A

Explanation: Step 1: Cash back: PV = 4500, N = 2 × 12=24, I = 3/12 = 0.25, FV = 0, => PMT = 193.4155.

Step 2: 4 percent APR: PV = 5000, N = 2 × 12=24, I = 4/12 = 0.3333, FV = 0, PMT = 217.1246.

Difficulty: 3 Hard

Topic: Loan payments

Bloom’s: Apply; Evaluate

AACSB: Analytical Thinking

Accessibility: Keyboard Navigation

Learning Goal: 05-04 Compute the present value of an annuity.; 05-09 Compute payments and amortization schedules for car and mortgage loans.

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