Fundamentals of Corporate Finance Dick Brealey 10e - Test Bank Instant Download - Complete Test Bank With Answers Sample Questions Are Posted Below Fundamentals of Corporate Finance, 10e (Brealey) Chapter 5 The Time Value of Money 1) Compound interest pays interest for each time period on the original investment plus …
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Fundamentals of Corporate Finance Dick Brealey 10e – Test Bank
Instant Download – Complete Test Bank With Answers
Sample Questions Are Posted Below
Fundamentals of Corporate Finance, 10e (Brealey)
Chapter 5 The Time Value of Money
1) Compound interest pays interest for each time period on the original investment plus the accumulated interest.
Answer: TRUE
Difficulty: 1 Easy
Topic: Simple and compound interest
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
2) When money is invested at compound interest, the growth rate is the interest rate.
Answer: TRUE
Difficulty: 2 Medium
Topic: Simple and compound interest
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
3) For a given amount, the lower the discount rate, the less the present value.
Answer: FALSE
Difficulty: 1 Easy
Topic: Present value-single cash flow
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
4) Present values decline as the time to the cash flows increases.
Answer: TRUE
Difficulty: 1 Easy
Topic: Present value-multiple cash flows
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
5) The present value of an annuity due equals the present value of an ordinary annuity times the discount rate.
Answer: FALSE
Difficulty: 1 Easy
Topic: Annuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
6) A perpetuity is a special form of an annuity.
Answer: TRUE
Difficulty: 1 Easy
Topic: Perpetuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
7) An annuity factor represents the future value of $1 that is deposited today.
Answer: FALSE
Difficulty: 2 Medium
Topic: Annuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
8) With a fixed-rate mortgage, the proportion of each payment used to pay interest on the loan declines over time.
Answer: TRUE
Difficulty: 2 Medium
Topic: Amortization
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
9) Converting an annuity to an annuity due decreases the present value.
Answer: FALSE
Difficulty: 1 Easy
Topic: Annuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
10) It is important to discount both real and nominal cash flows at the real interest rate.
Answer: FALSE
Difficulty: 2 Medium
Topic: Nominal and real rates
Learning Objective: 05-05 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
11) The term “constant dollars” refers to equal payments for amortizing a loan.
Answer: FALSE
Difficulty: 2 Medium
Topic: Present value-multiple cash flows
Learning Objective: 05-05 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
12) Nominal dollars refer to their purchasing power.
Answer: FALSE
Difficulty: 2 Medium
Topic: Nominal and real rates
Learning Objective: 05-05 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
13) When inflation is positive, the nominal interest rate is larger than the real rate.
Answer: TRUE
Difficulty: 2 Medium
Topic: Nominal and real rates
Learning Objective: 05-05 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
14) The effective annual interest rate cannot be less than the annual percentage rate.
Answer: TRUE
Difficulty: 2 Medium
Topic: Simple and compound interest
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
15) The more frequent the compounding, the higher the future value, other things equal.
Answer: TRUE
Difficulty: 1 Easy
Topic: Future value-single cash flow
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
16) An annual percentage rate (APR) is determined by annualizing the rate using compound interest.
Answer: FALSE
Difficulty: 2 Medium
Topic: Simple and compound interest
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
17) A dollar tomorrow is worth more than a dollar today.
Answer: FALSE
Difficulty: 2 Medium
Topic: Future value-single cash flow
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
18) To calculate present value, we discount the future value by some interest rate r, the discount rate.
Answer: TRUE
Difficulty: 2 Medium
Topic: Present value-single cash flow
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
19) The discount factor is used to calculate the present value of $1 received in year t.
Answer: TRUE
Difficulty: 2 Medium
Topic: Present value-single cash flow
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
20) You should never compare cash flows occurring at different times without first discounting them to a common date.
Answer: TRUE
Difficulty: 2 Medium
Topic: Present value-multiple cash flows
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
21) Present values can always be calculated by dividing the cash flow by a discount factor.
Answer: FALSE
Difficulty: 2 Medium
Topic: Present value-single cash flow
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
22) The five-year discount factor is less than the four-year discount factor.
Answer: TRUE
Difficulty: 2 Medium
Topic: Present value-single cash flow
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
23) As long as the interest rate is positive, the future value will always be larger than the present value given any period of time.
Answer: TRUE
Difficulty: 2 Medium
Topic: Future value-single cash flow
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
24) An annuity due must have a present value at least as large as an equivalent ordinary annuity.
Answer: TRUE
Difficulty: 2 Medium
Topic: Annuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
25) Any sequence of equally spaced, level cash flows is called an annuity. An annuity is also known as a perpetuity.
Answer: FALSE
Difficulty: 2 Medium
Topic: Perpetuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
26) Increasing the frequency in payments on a loan can decrease the annual percentage rate paid on the loan.
Answer: FALSE
Difficulty: 2 Medium
Topic: Perpetuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
27) A mortgage loan is an example of an amortizing loan. “Amortizing” means that part of the monthly payment is used to pay interest on the loan and part is used to reduce the amount of the loan.
Answer: TRUE
Difficulty: 2 Medium
Topic: Amortization
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
28) When considering compounding, a semi-annual interest rate will need to be one half the annual rate to achieve the same return.
Answer: FALSE
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Understand; Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
29) What is the future value of $10,000 on deposit for 2 years at 6% simple interest?
Answer: C
Explanation: FV = $10,000 + 2 × 0.06 × 10,000 = $11,200
Difficulty: 2 Medium
Topic: Simple and compound interest
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
30) If the five-year discount factor is d, what is the present value of $1 received in five years’ time?
Answer: D
Difficulty: 2 Medium
Topic: Present value-single cash flow
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
31) How much interest is earned in just the third year on a $1,000 deposit that earns 7% interest compounded annually?
Answer: B
Explanation: $1000.00 × (1.07)2 = $1,144.90 after 2 years
$1,144.90 × 0.07 = $80.14
Difficulty: 2 Medium
Topic: Simple and compound interest
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
32) How much interest will be earned in the next year on an investment paying 12% compounded annually if $100 was just credited to the account for interest?
Answer: C
Explanation: The investment will again pay $100 plus interest on the previous interest:
$100 × 1.12 = $112
Difficulty: 3 Hard
Topic: Simple and compound interest
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
33) The concept of compound interest refers to:
Answer: B
Difficulty: 1 Easy
Topic: Simple and compound interest
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
34) If interest is compounded semi-annually rather than annually, then:
Answer: D
Difficulty: 2 Medium
Topic: Simple and compound interest
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
35) Assume the total expense for your current year in college equals $20,000. How much would your parents have needed to invest 21 years ago in an account paying 8% compounded annually to cover this amount?
Answer: D
Explanation: PV = $20,000 / (1.08)21
PV = $3,973.11
Difficulty: 2 Medium
Topic: Present value-single cash flow
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
36) An investment offers to pay $100 a year forever starting at the end of year 6. If the interest rate is 8%, what is the investment’s value today?
Answer: B
Explanation: It will be worth 100 / 0.08 = $1,250 at the end of year 5, and therefore worth $1,250 / 1.085 = $850.73 today.
Difficulty: 2 Medium
Topic: Perpetuities
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
37) An investment of $100 pays interest of 2.5% per quarter. What will be the value of this investment at the end of 3 years?
Answer: C
Explanation: FV = PV(1 + r)t
=100 × 1.02512 = $134.49
Difficulty: 2 Medium
Topic: Simple and compound interest
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
38) To achieve an annual return of 7.0%, an investment that is compounded semi-annually, would need to earn how much every six months?
Answer: A
Explanation: 1.07 = (1 + r)2
R = 0.0344 or 3.44 %
Difficulty: 2 Medium
Topic: Simple and compound interest
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
39) A car’s price is currently $20,000 and is expected to rise by 4% a year. If the interest rate is 6%, how much do you need to put aside today to buy the car one year from now?
Answer: C
Explanation: Future price of car = ($20,000 × 1.04) = $20,800
PV = $ 20,800 / (1.06) = $19,623
Difficulty: 2 Medium
Topic: Present value-single cash flow
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
40) If the 5-year discount factor is 0.7008, what is the interest rate?
Answer: B
Explanation: FV = PV(1 + r)t
0.7008 = 1/(1 + r)5
r = 0.0737, or 7.37%
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
41) The bank offers a credit card with an initial promotional rate of 0.0%. After six months, the rate adjusts to 21%. If no payments are required on an initial balance of $10,000, and the bank calculates payments based on a five year repayment schedule, what will the monthly payment be after six months?
Answer: C
Explanation: $10,000 = PMT([1/(1.75)] – 1/{(1.75)[(2.75)]5 × 12})
PMT = $270.53
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
42) Given the future value, which of the following will contribute to a lower present value?
Answer: A
Difficulty: 2 Medium
Topic: Present value-single cash flow
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
43) Cash flows occurring in different periods should not be compared unless:
Answer: D
Difficulty: 1 Easy
Topic: Present value-multiple cash flows
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
44) What will be the approximate population of the United States, if its current population of 300 million grows at a compound rate of 2% annually for 25 years?
Answer: D
Explanation: FV = PV(1 + r)t
FV = 300 million × (1.02)25
FV = 492.2 million ≈ 492 million
Difficulty: 2 Medium
Topic: Future value-single cash flow
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
45) If the future value of an annuity due is $25,000 and $24,000 is the future value of an ordinary annuity that is otherwise similar to the annuity due, what is the implied discount rate?
Answer: B
Explanation: FVAD = FVOA × (1 + r)
$25,000 = $24,000 × (1 + r)
r = 0.0417, or 4.17%
Difficulty: 2 Medium
Topic: Annuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
46) A furniture store is offering free credit on purchases over $1,000. You observe that a big-screen television can be purchased for nothing down and $4,000 due in one year. The store next door offers an identical television for $3,650 but does not offer credit terms. Which statement below best describes the cost of the “free” credit?
Answer: C
Explanation: FV = PV(1 + r)t
$4,000 = $3,650(1 + r)
r = 0.0959, or 9.59%
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
47) How much must be invested today in order to generate a 5-year annuity of $1,000 per year, with the first payment 1 year from today, at an interest rate of 12%?
Answer: A
Explanation: PV = $1,000{(1 / 0.12) − [1 / 0.12(1.125)]}
PV = $3,604.78
Difficulty: 2 Medium
Topic: Present value-annuity
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
48) The salesperson offers, “Buy this new car for $25,000 cash or, with an appropriate down payment, pay $500 per month for 48 months at 8% interest.” Assuming that the salesperson does not offer a free lunch, calculate the “appropriate” down payment.
Answer: B
Explanation: PV = $500 × {[1 / (0.08 / 12)] − [1/(0.08 / 12)(1 + (0.08 / 12)48)]}
PV = $20,480.96
Down payment = $25,000 − 20,480.96 = $4,519.04
Difficulty: 2 Medium
Topic: Annuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
49) What is the present value of the following payment stream, discounted at 8% annually: $1,000 at the end of year 1, $2,000 at the end of year 2, and $3,000 at the end of year 3?
Answer: A
Explanation: PV = $1,000 / 1.08 + $2,000 / 1.082 + $3,000 / 1.083
PV = $5,022.10
Difficulty: 2 Medium
Topic: Present value-multiple cash flows
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
50) You invested $1,200 three years ago. During the three years, you earned annual rates of return of 4.8%, 9.2%, and 11.6%. What is the value of this investment today?
Answer: C
Explanation: FV = PV(1 + r)t
FV = PV(1 + r)t (1 + r)t (1 + r)t
FV = $1,200(1.048)1 (1.092)1 (1.116)1
FV = $1,532.60
Difficulty: 3 Hard
Topic: Future value-single cash flow
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
51) You will be receiving cash flows of: $1,000 today, $2,000 at end of year 1, $4,000 at end of year 3, and $6,000 at end of year 5. What is the present value of these cash flows at an interest rate of 7%?
Answer: B
Explanation: PV = FV / (1 + r)t
PV = $1,000 + $2,000 / 1.071 + $4,000 / 1.073 + $6,000 / 1.075
PV = $10,412.27
Difficulty: 3 Hard
Topic: Present value-multiple cash flows
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
52) Someone offers to buy your car for four, equal annual payments, beginning 2 years from today. If you think that the present value of your car is $9,000 and the interest rate is 10%, what is the minimum annual payment that you would accept?
Answer: C
Explanation: PV = C{(1 / 0.1) − [1 / (0.1 × 1.14)]} / 1.1 = $9,000
C = $3,123.16
Difficulty: 3 Hard
Topic: Annuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
53) How much more is a perpetuity of $1,000 worth than an annuity of the same amount for 20 years? Assume an interest rate of 10% and cash flows at the end of each period.
Answer: B
Explanation: PVPerpetuity = $1,000 / 0.10 = $10,000
PVAnnuity = $1,000[1 / 0.10 − 1 / 0.10(1.10)20]
PVAnnuity = $8,513.56
Difference = $10,000 − 8,513.56 = $1,486.44
Difficulty: 3 Hard
Topic: Perpetuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
54) A stream of equal cash payments lasting forever is termed:
Answer: D
Difficulty: 1 Easy
Topic: Perpetuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Remember
AACSB: Communication
Accessibility: Keyboard Navigation
55) If the interest rate is 6%, which of these investments would you prefer?
Answer: C
Explanation: PV($500 in year 3) = 500 / 1.063 = $419.81
PV ($40 a year for 20 years) = 40(1 / 0.06 − 1 / (0.06 × 1.0620)) = $458.80
PV ($30 in perpetuity) = 30 / 0.06 = $500
Difficulty: 3 Hard
Topic: Present value-multiple cash flows
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
56) The present value of a perpetuity can be determined by:
Answer: D
Difficulty: 1 Easy
Topic: Perpetuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
57) You are borrowing $245,000 to purchase a home. The loan agreement requires a monthly payment based upon a 4.5% quoted APR over 20 years. What is your monthly mortgage payment? (Round to two decimal places)
Answer: B
Explanation: $245,000 = PMT([1/(.00375)] – 1/{(.00375)[(1.00375)]20 × 12})
PMT = $1,549.99
Difficulty: 2 Medium
Topic: Loan payments
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Apply
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
58) A perpetuity of $5,000 per year beginning today offers a 15% return. What is its present value?
Answer: C
Explanation: PV = $5,000 + $5,000 / r
PV = $5,000 + $5,000 / 0.15
PV = $5,000 + $5,000 / 0.15
PV = $38,333.33
Difficulty: 3 Hard
Topic: Perpetuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
59) A bond promises to pay $1,000 20 years from today. No interest will be paid on the bonds during the 20 years If the interest rate is 7%, what is the bond’s present value?
Answer: B
Explanation: PV = FV / (1 + r)t
= $1,000 / 1.0720
= $258.42
Difficulty: 2 Medium
Topic: Present value-single cash flow
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
60) Your car loan requires payments of $200 per month for the first year and payments of $400 per month during the second year. The APR is 12% and payments begin in one month. What is the present value of this 2-year loan?
Answer: A
Explanation: PV = {$200 {(1 / 0.01) − [1 / 0.01(1.01)12]}} + ({$400 {(1 / 0.01) − [1 / 0.01(1.01)12]} / 1.0112)}
PV = $6,246.34
Difficulty: 3 Hard
Topic: Present value-annuity
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
61) Which one of the following will increase the present value of an annuity, other things equal?
Answer: B
Difficulty: 1 Easy
Topic: Present value-annuity
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
62) What is the present value of a five-period annuity of $3,000 if the interest rate per period is 12% and the first payment is made today?
Answer: C
Explanation: PVAD = PVOA × (1 + r)
PVAD = {$3,000[1 / 0.12 − 1 / 0.12(1.12)5]} × 1.12
PVAD = $12,112.05
Difficulty: 2 Medium
Topic: Present value-annuity
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
63) The sum of $3,000 is deposited into an account paying 10% annually. If $1,206 is withdrawn at the end of years 1 and 2, how much then remains in the account?”
Answer: C
Explanation: FVYear 1 = PV(1 + r) − Withdrawal
FVYear 1 = $3,000(1.1) − $1,206
FVYear 1 = $2,094
FVYear 2 = FVYear 1 (1 + r) − Withdrawal
FVYear 2 = $2,094(1.1) − $1,206FVYear 2 = $1,097.40
Difficulty: 3 Hard
Topic: Future value-single cash flow
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
64) Suppose you take out a 30-year mortgage for $100,000 with annual payments. The interest rate on the mortgage is 8%. When you have paid off half the mortgage, so that the value of the remaining payments is reduced to $50,000, how many more payments need to be made?
Answer: C
Explanation: Solve first for the annual payment: $100,000 = PMT(1 / 0.08 − 0.08 × 1.0830). PMT = $8,882.74
PV = PMT [(1 / r) − 1 / r(1 + r)t]
$50,000 = 8,882.74{1 / 0.08−1 / (0.08 × 1.08t}
Either use logs or trial and error to find t ≈ 8
Difficulty: 3 Hard
Topic: Amortization
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
65) What is the present value of a four-year annuity of $100 per year that makes its first payment 2 years from today if the discount rate is 9%?
Answer: A
Explanation: PV = {$100[(1 / 0.09) − 1 / 0.09(1.09)4]} / 1.09
PV = $297.22
Difficulty: 3 Hard
Topic: Present value-annuity
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
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66) If $120,000 is borrowed for a home mortgage, to be repaid at 9% interest over 30 years with annual payments of $11,680.36, how much interest (as opposed to return of capital) is paid in the last year of the loan?
Answer: D
Explanation: Value of loan at start of last year = $11,680.36 / 1.09 = $10,715.93
Interest on loan in last year = 0.09 × $10,715.93 = $964.43
Difficulty: 2 Medium
Topic: Amortization
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
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67) $50,000 is borrowed, to be repaid in three equal, annual payments with 10% interest. Approximately how much principal is amortized with the first payment?
Answer: C
Explanation: Payment = $50,000 / [1 / 0.1 − 1 / 0.1(1.1)3]
Payment = $20,105.74
Principal payment = $20,105.74 − ($50,000 × 0.1)
Principal payment = $15,105.74
Difficulty: 2 Medium
Topic: Amortization
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
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68) An amortizing loan is one in which:
Answer: D
Difficulty: 1 Easy
Topic: Amortization
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Understand
AACSB: Reflective Thinking
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69) You’re ready to make the last of four equal, annual payments on a $1,000 loan with a 10% interest rate. If the amount of the payment is $315.47, how much of that payment is accrued interest?
Answer: A
Explanation: $315.47 − ($315.47 / 1.1) = $28.68
Difficulty: 3 Hard
Topic: Amortization
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
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70) What will be the monthly payment on a $75,000 30-year home mortgage at 1% interest per month?
Answer: A
Explanation: Payment = $75,000 / [(1 / 0.01) − 1 / 0.01(1.01)360]
Payment = $771.46
Difficulty: 2 Medium
Topic: Annuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
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71) Your real estate agent mentions that homes in your price range require a payment of $1,200 per month for 30 years at 0.75% interest per month. What is the size of the mortgage with these terms?
Answer: C
Explanation: PV = $1,200[(1 / 0.0075) − 1 / 0.0075(1.0075)360]
PV = $149,138.24
Difficulty: 2 Medium
Topic: Present value-annuity
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
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72) Assume you are making $989 monthly payments on your amortized mortgage. The amount of each payment that is applied to the principal balance:
Answer: B
Difficulty: 1 Easy
Topic: Amortization
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Understand
AACSB: Reflective Thinking
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73) How much must be saved at the end of each year for the next 10 years in order to accumulate $50,000, if you can earn 9% annually? Assume you contribute the same amount to your savings every year.
Answer: A
Explanation: Payment = $50,000 / [(1.0910 − 1) / 0.09]
Payment = $3,291.00
Difficulty: 2 Medium
Topic: Annuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
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74) Your retirement account has a current balance of $50,000. You plan to add $6,000 a year to the account for each of the next 30 years. Use a financial calculator or Excel to find what interest rate you need to earn in order to have $1,000,000 in the account at the end of the 30 years?
Answer: B
Explanation: Financial calculator: n = 30; PV = −50,000; PMT = −6,000; FV = 1,000,000; CPT i = 7.24%, or
Excel function Rate(nper, PMT, PV, FV)
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Analyze
AACSB: Analytical Thinking
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75) How much do you need when you retire to provide a $2,500 monthly check that will last for 25 years? Assume that your savings can earn 0.5% a month.
Answer: B
Explanation: Monthly interest rate = 0.06 / 12 = 0.005
PV = $2,500 {(1 / 0.005) − [1 / 0.005(1.005)12 × 25]}
PV = $388,017.16
Difficulty: 2 Medium
Topic: Present value-annuity
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
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76) The present value of an annuity stream of $100 per year is $614 when valued at a 10% rate. By approximately how much would the value change if these were annuities due?
Answer: B
Explanation: PVAnnuity due = PV ordinary annuity × (1 + r)
Difference = $614(1.1) − $614 = $61.40
Difficulty: 2 Medium
Topic: Annuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
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77) Approximately how much must be saved for retirement in order to withdraw $100,000 per year for the next 25 years if the balance earns 8% annually, and the first payment occurs one year from now?
Answer: A
Explanation: PV = $100,000 {(1 / 0.08) − [1 / 0.08(1.08)25]}
PV = $1,067,477.62
Difficulty: 2 Medium
Topic: Present value-annuity
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
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78) You have just retired with savings of $1.5 million. If you expect to live for 30 years and to earn 8% a year on your savings, how much can you afford to spend each year? Assume that you spend the money at the start of each year.
Answer: C
Explanation: $1,500,000 = PmtOA {(1 / 0.08) − [1 / 0.08(1.08)30]}
PMTOA = $133,241.15
PMTAD = PMTOA / (1 + r)
PMTAD = $133,241.15 / 1.08
PMTAD = $123,371.44
Difficulty: 2 Medium
Topic: Annuities
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
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79) How much can be accumulated for retirement if $2,000 is put aside at the end of each of the next 40 years? Assume that you can earn 9% a year on your savings.
Answer: B
Explanation: FV = $2,000 {[(1 + 0.09)40 − 1] / 0.09}
FV = $675,764.89
Difficulty: 2 Medium
Topic: Future value-annuity
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Analyze
AACSB: Analytical Thinking
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80) If inflation in Wonderland was 3% per month in 2016, what was the annual rate of inflation?
Answer: B
Explanation: (1.03)12 − 1 = 0.4258, or 42.58%
Difficulty: 2 Medium
Topic: Simple and compound interest
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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81) Assume your uncle recorded his salary history during a 40-year career and found that it had increased 10-fold. If inflation averaged 4% annually during the period, then over his career his purchasing power:
Answer: C
Explanation: FV = PV(1 + r)t
10 = 1(1 + i)40
r = 5.93%
Real rate = (1.0593 / 1.04) − 1 = 0.0186, or 1.86%
Difficulty: 2 Medium
Topic: Nominal and real rates
Learning Objective: 05-05 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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82) Real interest rates:
Answer: C
Difficulty: 2 Medium
Topic: Nominal and real rates
Learning Objective: 05-05 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Bloom’s: Understand
AACSB: Reflective Thinking
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83) On the day you retire you have $1,000,000 saved. You expect to live another 25 years during which time you expect to earn 6.19% on your savings while inflation averages 2.5% annually. Assume you want to spend the same amount each year in real terms and die on the day you spend your last dime. What real amount will you be able to spend each year?
Answer: A
Explanation: Real rate = (1.0619 / 1.025) − 1 = 0.036
$1,000,000 = PMT {(1 / 0.036) − [1 / 0.036(1.036)25]}
PMT = $61,334.36
Difficulty: 2 Medium
Topic: Nominal and real rates
Learning Objective: 05-05 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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84) What is the expected real rate of interest for an account that offers a 12% nominal rate of return when the rate of inflation is 6% annually?
Answer: B
Explanation: 1 + real interest rate = (1 + nominal interest rate) / (1 + inflation)
1 + real interest rate = 1.12 / 1.06
Real interest rate = 5.66%
Difficulty: 1 Easy
Topic: Nominal and real rates
Learning Objective: 05-05 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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85) What happens over time to the real cost of purchasing a home if the mortgage payments are fixed in nominal terms and inflation is in existence?
Answer: C
Difficulty: 2 Medium
Topic: Nominal and real rates
Learning Objective: 05-05 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Bloom’s: Understand
AACSB: Reflective Thinking
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86) What is the minimum nominal rate of return that you should accept if you require a 4% real rate of return and the rate of inflation is expected to average 3.5% during the investment period?
Answer: C
Explanation: 1 + nominal rate = (1 + real rate)(1 + inflation rate)
Nominal rate = (1.04 × 1.035) − 1
Nominal rate = 7.64%
Difficulty: 1 Easy
Topic: Nominal and real rates
Learning Objective: 05-05 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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87) What APR is being earned on a deposit of $5,000 made 10 years ago today if the deposit is worth $9,848.21 today? The deposit pays interest semiannually.
Answer: C
Explanation: FV = PV (1 + r)t
$9,848.21 = $5,000 [1 + (r / 2)]10 × 2
r = 6.89%
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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88) An interest rate that has been annualized using compound interest is termed the:
Answer: D
Difficulty: 1 Easy
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Understand
AACSB: Reflective Thinking
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89) What is the effective annual rate of interest on a deposit that pays interest of 10% continuously compounded?
Answer: B
Explanation: Effective interest rate = e0.1 − 1 = 0.10517, or 10.517%
Difficulty: 3 Hard
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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90) What is the relationship between an annually compounded rate and the annual percentage rate (APR) which is calculated for truth-in-lending laws for a loan requiring monthly payments?
Answer: A
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Understand
AACSB: Reflective Thinking
Accessibility: Keyboard Navigation
91) What is the APR on a loan that charges interest at the rate of 1.4% per month?
Answer: C
Explanation: APR = 1.4% × 12 = 16.80%
Difficulty: 1 Easy
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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92) If interest is paid m times per year, then the per-period interest rate equals the:
Answer: D
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Understand
AACSB: Reflective Thinking
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93) If the effective annual rate of interest is known to be 16.08% on a debt that has quarterly payments, what is the annual percentage rate?
Answer: D
Explanation: APR = [(1.1608)0.25 − 1] × 4
APR = 0.1519, or 15.19%
Difficulty: 3 Hard
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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94) Would a depositor prefer an APR of 8% with monthly compounding or an APR of 8.5% with semiannual compounding?
Answer: B
Explanation: EAR = [1 + (0.08 / 12)]12 − 1 = 8.30%
EAR = [1 + (0.085 / 2)]2 − 1 = 8.68%
The depositor will prefer the option with the higher EAR (effective annual rate).
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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95) What is the annually compounded rate of interest on an account with an APR of 10% and monthly compounding?
Answer: B
Explanation: EAR = [1 + (0.10 / 12)] 12 − 1 = 0.1047, or 10.47%
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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96) What is the APR on a loan with an effective annual rate of 15.26% and weekly compounding of interest?
Answer: D
Explanation: APR = [(1.1526)1 / 52 − 1] × 52 = 0.1422, or 14.22%
Difficulty: 3 Hard
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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97) What is the effective annual interest rate on a 9% APR automobile loan that has monthly payments?
Answer: B
Explanation: EAR = [1 + (0.09 / 12)]12 − 1 = 0.0938, or 9.38%
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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98) Other things being equal, the more frequent the compounding period, the:
Answer: C
Difficulty: 1 Easy
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Understand
AACSB: Reflective Thinking
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99) How much interest will be earned in an account into which $1,000 is deposited for one year with continuous compounding at a 13% rate?
Answer: B
Explanation: Interest = $1,000(e0.13) − $1,000 = $138.83
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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100) What is the present value of $100 to be deposited today into an account paying 8%, compounded semiannually for 2 years?
Answer: B
Difficulty: 1 Easy
Topic: Present value-single cash flow
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
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101) If a borrower promises to pay you $1,900 nine years from now in return for a loan of $1,000 today, what effective annual interest rate is being offered if interest is compounded annually?
Answer: B
Explanation: FV = PV × (1 + r)t
$1,900 = $1,000 × (1 + r)9
r = 1.91 / 9 − 1
r = 0.0739, or 7.39%
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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102) What is the present value of your trust fund if you have projected that it will provide you with $50,000 7 years from today and it earns 10% compounded annually?
Answer: B
Explanation: PV = FV / (1 + r)t
PV = $50,000 / 1.107
PV = $25,657.91
Difficulty: 2 Medium
Topic: Present value-single cash flow
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
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103) What is the discount factor for $1 to be received in 5 years at a discount rate of 8%?
Answer: D
Explanation: PV = FV / (1 + r)t
PV = 1 / 1.085
PV = 0.6806
Difficulty: 2 Medium
Topic: Present value-single cash flow
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
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104) How much more would you be willing to pay today for an investment offering $10,000 in 4 years rather than in 5 years? Your discount rate is 8%.
Answer: A
Explanation: Difference = FV / (1 + r)t − 1 − FV / (1 + r)
Difference = $10,000 / 1.084 − $10,000 / 1.085
Difference = $544.47
Difficulty: 2 Medium
Topic: Present value-multiple cash flows
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
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105) “Give me $5,000 today and I’ll return $10,000 to you in 5 years,” offers the investment broker. To the nearest percent, what annual interest rate is being offered?
Answer: C
Explanation: FV = PV(1 + r)t
$10,000 = $5,000(1 + r)5
r = 21 / 5 − 1
r = 0.1487, or 14.87%
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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106) The APR on a loan must be equal to the effective annual rate when:
Answer: B
Difficulty: 1 Easy
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Understand
AACSB: Reflective Thinking
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107) A car dealer offers payments of $522.59 per month for 48 months on a $25,000 car after making a $4,000 down payment. What is the loan’s APR?
Answer: B
Explanation: $25,000 − 4,000 = $522.59 {(1 / r) − [1 / r(1 + r)48]}
Using a financial calculator or Excel, r = 0.0075
APR = 0.0075 × 12
APR = 0.09, or 9%
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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108) A credit card account that charges interest at the rate of 1.25% per month would have an annually compounded rate of ________ and an APR of ________.
Answer: A
Explanation: EAR = (1 + 0.0125)12 − 1 = 0.1608, or 16.08%
APR = 1.25% × 12 = 15.00%
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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109) Eighteen years from now, 4 years of college are expected to cost $150,000. How much more must be deposited into an account today to fund this expense if you can earn only 8% on your savings rather than the 11% you hope to earn?
Answer: D
Explanation: Additional deposit = $150,000 / 1.0818 − $150,000 / 1.1118
Additional deposit = $14,614.03
Difficulty: 2 Medium
Topic: Present value-multiple cash flows
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
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110) Prizes are often not “worth” as much as claimed. What is the value of a prize of $5,000,000 that is to be received in 20 equal yearly payments, with the first payment beginning today? Assume an interest rate of 7%.
Answer: A
Explanation: Annual payment = $5,000,000 / 20 = $250,000
PV = ($250,000 {(1 / 0.07) − [1 / 0.07(1.07)20]}) × (1.07)
PV = $2,833,898.81
Difficulty: 2 Medium
Topic: Present value-annuity
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
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111) A loan officer states, “Thousands of dollars can be saved by switching to a 15-year mortgage from a 30-year mortgage.” Calculate the difference in payments on a 30-year mortgage at an interest rate of .75% a month versus a 15-year mortgage with an interest rate of .7% a month. Both mortgages are for $100,000 and have monthly payments. What is the difference in total dollars that will be paid to the lender under each loan? (Round the monthly payment amounts to 2 decimal places.)
Answer: C
Explanation: $100,000 = PMT([1 / (0.0075)] − 1 / {(0.0075)[(1.0075)]30 × 12})
PMT = $804.62
$100,000 = PMT([1 / (0.007)] − 1 / {(0.007 )[ 1.007)]15 × 12})
PMT = $ 978.87
Total difference = ($804.62 × 12 × 30) − ($978.87 × 12 × 15) = $113,465
Difficulty: 2 Medium
Topic: Loan payments
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
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112) Would you prefer a savings account that paid 7% interest compounded quarterly, 6.8% compounded monthly, 7.2% compounded weekly, or an account that paid 7.5% with annual compounding?
Answer: D
Explanation: EAR = [1 + (0.07 / 4)]4 − 1 = 0.0719, or 7.19%
EAR = [1 + (0.068 / 12)]12 − 1 = 0.0702, or 7.02%
EAR = [1 + (0.072 / 52)]52 − 1 = 0.0746, or 7.46%
EAR = APR = 7.5%
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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113) After reading the fine print in your credit card agreement, you find that the “low” interest rate is actually an 18% APR, or 1.5% per month. What is the effective annual rate?
Answer: B
Explanation: EAR = 1.01512 − 1 = 0.1956, or 19.56%
Difficulty: 2 Medium
Topic: Interest rates
Learning Objective: 05-04 Compare interest rates quoted over different time intervals–for example, monthly versus annual rates.
Bloom’s: Analyze
AACSB: Analytical Thinking
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114) You are considering the purchase of a home that would require a mortgage of $150,000. How much more in total interest will you pay if you select a 30-year mortgage at 5.65% rather than a 15-year mortgage at 4.9%? (Round the monthly payment amount to 2 decimal places.)
Answer: C
Explanation: $150,000 = PMT([1 / (0.0565 / 12)] − 1 / {(0.0565 / 12)[1 + (0.0565 / 12)]30 × 12})
PMT = $865.85
$150,000 = PMT([1 / (0.049 / 12)] − 1 / {(0.049 / 12)[1 + (0.049 / 12)]15 × 12})
PMT = $1,178.39
Total difference = ($865.85 × 12 × 30) − ($1,178.39 × 12 × 15) = $99,595.80
Difficulty: 3 Hard
Topic: Loan payments
Learning Objective: 05-03 Calculate present and future values of a level stream of cash payments.
Bloom’s: Analyze
AACSB: Analytical Thinking
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115) Lester’s just signed a contract that will provide the firm with annual cash inflows of $28,000, $35,000, and $42,000 over the next three years with the first payment of $28,000 occurring one year from today. What is this contract worth today at a discount rate of 7.25%?
Answer: C
Explanation: PV = $28,000 / 1.0725 + $35,000 / 1.07252 + $42,000 / 1.07253
PV = $90,580.55
Difficulty: 2 Medium
Topic: Present value-multiple cash flows
Learning Objective: 05-02 Calculate the present value of a future payment.
Bloom’s: Analyze
AACSB: Analytical Thinking
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116) Miller’s Hardware plans on saving $42,000, $54,000, and $58,000 at the end of each year for the next three years, respectively. How much will the firm have saved at the end of the three years if it can earn 4.5% on its savings?
Answer: A
Explanation: FV = ($42,000 × 1.0452) + ($54,000 × 1.045) + $58,000
FV = $160,295.05
Difficulty: 2 Medium
Topic: Future value-multiple cash flows
Learning Objective: 05-01 Calculate the future value of money that is invested at a particular interest rate.
Bloom’s: Analyze
AACSB: Analytical Thinking
Accessibility: Keyboard Navigation
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
