Chapter 05 - The Time Value of Money
Chapter 05
The Time Value of Money
True / False Questions
1. Compound interest pays interest for each time period on the original investment plus the
accumulated interest.
True False
2. When money is invested at compound interest, the growth rate is the interest rate.
True False
3. The present value of an annuity due equals the present value of an ordinary annuity times
the discount rate.
True False
4. The more frequent the compounding, the higher the future value, other things equal.
True False
5. A dollar tomorrow is worth more than a dollar today.
True False
6. The Excel function for future value is FV (rate, nper, pmt, PV).
True False
7. For a given amount, the lower the discount rate, the less the present value.
True False
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Chapter 05 - The Time Value of Money
8. Comparing the values of undiscounted cash flows is analogous to comparing apples to
oranges.
True False
9. To calculate present value, we discount the future value by some interest rate r, the discount
rate.
True False
10. The discount factor is used to calculate the present value of $1 received in year t.
True False
11. You should never compare cash flows occurring at different times without first
discounting them to a common date.
True False
12. The Excel function for present value is PV (rate, nper, pmt, FV).
True False
13. A perpetuity is a special form of an annuity.
True False
14. An annuity factor represents the future value of $1 that is deposited today.
True False
15. Accrued interest declines with each payment on an amortizing loan.
True False
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Chapter 05 - The Time Value of Money
16. Converting an annuity to an annuity due decreases the present value.
True False
17. The term "constant dollars" refers to equal payments for amortizing a loan.
True False
18. An annuity due must have a present value at least as large as an equivalent ordinary
annuity.
True False
19. Any sequence of equally spaced, level cash flows is called an annuity. An annuity is also
known as a perpetuity.
True False
20. 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.
True False
21. The Excel function for interest rate is RATE (nper, pmt, PV, FV).
True False
22. An effective annual rate must be greater than an annual percentage rate.
True False
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Chapter 05 - The Time Value of Money
23. An annual percentage rate (APR) is determined by annualizing the rate using compound
interest.
True False
24. In 2002, the U.S. inflation rate was below 2% and a few countries were even experiencing
deflation.
True False
25. Nominal dollars refer to the amount of purchasing power.
True False
26. The appropriate manner of adjusting for inflationary effects is to discount nominal cash
flows with real interest rates.
True False
Multiple Choice Questions
27. What is the future value of $10,000 on deposit for 5 years at 6% simple interest?
A. $7,472.58
B. $10,303.62
C. $13,000.00
D. $13,382.26
28. Under which of the following conditions will a future value calculated with simple interest
exceed a future value calculated with compound interest at the same rate?
A. The interest rate is very high.
B. The investment period is very long.
C. The compounding is annually.
D. This is not possible with positive interest rates.
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Chapter 05 - The Time Value of Money
29. How much interest is earned in just the third year on a $1,000 deposit that earns 7%
interest compounded annually?
A. $70.00
B. $80.14
C. $105.62
D. $140.00
30. 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?
A. $88
B. $100
C. $112
D. $200
31. The concept of compound interest refers to:
A. earning interest on the original investment.
B. payment of interest on previously earned interest.
C. investing for a multiyear period of time.
D. determining the APR of the investment.
32. When an investment pays only simple interest, this means:
A. the interest rate is lower than on comparable investments.
B. the future value of the investment will be low.
C. the earned interest is nontaxable to the investor.
D. interest is earned only on the original investment.
33. Approximately how long must one wait (to the nearest year) for an initial investment of
$1,000 to triple in value if the investment earns 8% compounded annually?
A. 9 years
B. 14 years
C. 22 years
D. 25 years
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Chapter 05 - The Time Value of Money
34. How much will accumulate in an account with an initial deposit of $100, and which earns
10% interest compounded quarterly for 3 years?
A. $107.69
B. $133.10
C. $134.49
D. $313.84
35. 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?
A. 413 million
B. 430 million
C. 488 million
D. 492 million
36. How much interest can be accumulated during one year on a $1,000 deposit paying
continuously compounded interest at an APR of 10%?
A. $100.00
B. $105.17
C. $110.50
D. $115.70
37. 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?
A. $130.00
B. $138.83
C. $169.00
D. $353.34
38. What is the discount factor for $1 to be received in 5 years at a discount rate of 8%?
A. .4693
B. .5500
C. .6000
D. .6806
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Chapter 05 - The Time Value of Money
39. Assume the total expense for your current year in college equals $20,000. Approximately
how much would your parents have needed to invest 21 years ago in an account paying 8%
compounded annually to cover this amount?
A. $952.00
B. $1,600.00
C. $1,728.00
D. $3,973.00
40. How much must be deposited today in an account earning 6% annually to accumulate a
20% down payment to use in purchasing a car one year from now, assuming that the car's
current price is $20,000, and inflation will be 4%?
A. $3,774
B. $3,782
C. $3,925
D. $4,080
41. Given a set future value, which of the following will contribute to a lower present value?
A. Higher discount rate
B. Fewer time periods
C. Less frequent discounting
D. Lower discount factor
42. Cash flows occurring in different periods should not be compared unless:
A. interest rates are expected to be stable.
B. the flows occur no more than one year from each other.
C. high rates of interest can be earned on the flows.
D. the flows have been discounted to a common date.
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Chapter 05 - The Time Value of Money
43. A corporation has promised to pay $1,000 20 years from today for each bond sold now.
No interest will be paid on the bonds during the 20 years, and the bonds are discounted at a
7% interest rate. Approximately how much should an investor pay for each bond?
A. $70.00
B. $258.42
C. $629.56
D. $857.43
44. What is the present value of your trust fund if it promises to pay you $50,000 on your 30th
birthday (7 years from today) and earns 10% compounded annually?
A. $25,000.00
B. $25,657.91
C. $28,223.70
D. $29,411.76
45. How much more would you be willing to pay today for an investment offering $10,000 in
4 years rather than the normally advertised 5-year period? Your discount rate is 8%.
A. $544.47
B. $681.48
C. $740.74
D. $800.00
46. What is the present value of $100 to be deposited today into an account paying 8%,
compounded semiannually for 2 years?
A. $85.48
B. $100.00
C. $116.00
D. $116.99
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Chapter 05 - The Time Value of Money
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%?
A. $3,604.78
B. $3,746.25
C. $4,037.35
D. $4,604.78
48. The salesperson offers, "Buy this new car for $25,000 cash or, with 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.
A. $1,000.00
B. $4,520.64
C. $5,127.24
D. $8,000.00
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?
A. $5,022.11
B. $5,144.03
C. $5,423.87
D. $5,520.00
50. What is the present value of the following set of cash flows at an interest rate of 7%:
$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?
A. $9,731
B. $10,412
C. $10,524
D. $11,524
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Chapter 05 - The Time Value of Money
51. A cash-strapped young professional offers to buy your car with four, equal annual
payments of $3,000, beginning 2 years from today. Assuming you're indifferent to cash versus
credit, that you can invest at 10%, and that you want to receive $9,000 for the car, should you
accept?
A. Yes; present value is $9,510.
B. Yes; present value is $11,372.
C. No; present value is $8,645.
D. No; present value is $7,461.
52. How much more is a perpetuity of $1,000 worth than an annuity of the same amount for
20 years? Assume a 10% interest rate and cash flows at end of period.
A. $297.29
B. $1,486.44
C. $1,635.08
D. $2,000.00
53. A stream of equal cash payments lasting forever is termed:
A. an annuity.
B. an annuity due.
C. an installment plan.
D. a perpetuity.
54. Which of the following factors is fixed and thus cannot change for a specific perpetuity?
A. PV of a perpetuity
B. Cash payment of a perpetuity
C. Interest rate on a perpetuity
D. Discount rate of a perpetuity
55. The present value of a perpetuity can be determined by:
A. Multiplying the payment by the interest rate.
B. Dividing the interest rate by the payment.
C. Multiplying the payment by the number of payments to be made.
D. Dividing the payment by the interest rate.
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Chapter 05 - The Time Value of Money
56. A perpetuity of $5,000 per year beginning today is said to offer a 15% interest rate. What
is its present value?
A. $33,333.33
B. $37,681.16
C. $38,333.33
D. $65,217.39
57. Your car loan requires payments of $200 per month for the first year and payments of
$400 per month during the second year. The annual interest rate is 12% and payments begin in
one month. What is the present value of this 2-year loan?
A. $6,246.34
B. $6,389.78
C. $6,428.57
D. $6,753.05
58. Which of the following will increase the present value of an annuity, other things equal?
A. Increasing the interest rate
B. Decreasing the interest rate
C. Decreasing the number of payments
D. Decreasing the amount of the payment
59. What is the present value of a five-period annuity of $3,000 if the interest rate is 12% and
the first payment is made today?
A. $9,655.65
B. $10,814.33
C. $12,112.05
D. $13,200.00
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Chapter 05 - The Time Value of Money
60. $3,000 is deposited into an account paying 10% annually, to provide three annual
withdrawals of $1,206.34 beginning in one year. How much remains in the account after the
second payment has been withdrawn?
A. $1,326.97
B. $1,206.34
C. $1,096.69
D. $587.32
61. How many monthly payments remain to be paid on an 8% mortgage with a 30-year
amortization and monthly payments of $733.76, when the balance reaches one-half of the
$100,000 mortgage?
A. Approximately 268 payments
B. Approximately 180 payments
C. Approximately 92 payments
D. Approximately 68 payments
62. What is the present value of a four-period annuity of $100 per year that begins 2 years
from today if the discount rate is 9%?
A. $297.21
B. $323.86
C. $356.85
D. $388.97
63. If $120,000 is borrowed for a home mortgage, to be repaid at 9% interest over 30 years
with monthly payments of $965.55, how much interest is paid over the life of the loan?
A. $120,000
B. $162,000
C. $181,458
D. $227,598
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Chapter 05 - The Time Value of Money
64. $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?
A. $2,010.60
B. $5,000.00
C. $15,105.74
D. $20,105.74
65. An amortizing loan is one in which:
A. the principal remains unchanged with each payment.
B. accrued interest is paid regularly.
C. the maturity of the loan is variable.
D. the principal balance is reduced with each payment.
66. 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?
A. $28.68
B. $31.55
C. $100.00
D. $315.47
67. What will be the monthly payment on a home mortgage of $75,000 at 12% interest, to be
amortized over 30 years?
A. $771.46
B. $775.90
C. $1,028.61
D. $1,034.53
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Chapter 05 - The Time Value of Money
68. Your real estate agent mentions that homes in your price range require a payment of
approximately $1,200 per month over 30 years at 9% interest. What is the approximate size of
the mortgage with these terms?
A. $128,035
B. $147,940
C. $149,140
D. $393,120
69. Which of the following characteristics applies to the amortization of a loan such as a home
mortgage?
A. The amortization decreases with each payment.
B. The amortization increases with each payment.
C. The amortization is constant throughout the loan.
D. The amortization fluctuates monthly with changes in interest rates.
70. How much must be saved annually, beginning 1 year from now, in order to accumulate
$50,000 over the next 10 years, earning 9% annually?
A. $3,291
B. $3,587
C. $4,500
D. $4,587
71. Approximately how much should be accumulated by the beginning of retirement to
provide a $2,500 monthly check that will last for 25 years, during which time the fund will
earn 8% interest with monthly compounding?
A. $261,500.00
B. $323,800.00
C. $578,700.00
D. $690,000.00
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Chapter 05 - The Time Value of Money
72. 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?
A. An increase of $10
B. An increase of $61
C. An increase of $100
D. Unknown without knowing number of payments
73. 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 1
year from now?
A. $1,067,000
B. $1,250,000
C. $2,315,000
D. $2,500,000
74. With $1.5 million in an account expected to earn 8% annually over the retiree's 30 years
of life expectancy, what annual annuity can be withdrawn, beginning today?
A. $112,150
B. $120,000
C. $123,371
D. $133,241
75. How much can be accumulated for retirement if $2,000 is deposited annually, beginning 1
year from today, and the account earns 9% interest compounded annually for 40 years?
A. $87,200.00
B. $675,764.89
C. $736,583.73
D. $802,876.27
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Chapter 05 - The Time Value of Money
76. Which of the following strategies will allow real retirement spending to remain
approximately equal, assuming savings of $1,000,000 invested at 8%, a 25-year horizon, and
4% expected inflation?
A. Spend approximately $63,000 annually.
B. Spend approximately $78,225 annually.
C. Spend approximately $93,680 annually.
D. Spend approximately $127,500 annually.
77. In calculating the present value of $1,000 to be received 5 years from today, the discount
factor has been calculated to be .7008. What is the apparent interest rate?
A. 5.43%
B. 7.37%
C. 8.00%
D. 9.50%
78. If the future value of an annuity due = $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?
A. 1.04%
B. 4.17%
C. 5.00%
D. 8.19%
79. A furniture store is offering free credit on purchases over $1,000. You observe that a bigscreen 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 "free" credit?
A. The "free" credit costs about 8.75%.
B. The "free" credit costs about 9.13%.
C. The "free" credit costs about 9.59%.
D. The "free" credit effectively costs zero%.
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Chapter 05 - The Time Value of Money
80. The present value of the following cash flows is known to be $6,939.91; $500 today,
$2,000 in 1 year, and $5,000 in 2 years. What discount rate is being used?
A. 3%
B. 4%
C. 5%
D. 6%
81. Your retirement account has a current balance of $50,000. What interest rate would need
to be earned in order to accumulate a total of $1,000,000 in 30 years, by adding $6,000
annually?
A. 5.02%
B. 7.24%
C. 9.80%
D. 10.07%
82. If a borrower promises to pay you $1,900 9 years from now in return for a loan of $1,000
today, what effective annual interest rate is being offered?
A. 5.26%
B. 7.39%
C. 9.00%
D. 10.00%
83. "Give me $5,000 today and I'll return $20,000 to you in 5 years," offers the investment
broker. To the nearest percent, what annual interest rate is being offered?
A. 25%
B. 29%
C. 32%
D. 60%
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Chapter 05 - The Time Value of Money
84. 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?
A. 6%
B. 9%
C. 11%
D. 12%
85. What APR is being earned on a deposit of $5,000 made 10 years ago today if the deposit
is worth $9,948.94 today? The deposit pays interest semiannually.
A. 3.56%
B. 6.76%
C. 7.00%
D. 7.12%
86. An interest rate that has been annualized using compound interest is termed the:
A. simple interest rate.
B. annual percentage rate.
C. discounted interest rate.
D. effective annual interest rate.
87. 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?
A. The APR is lower than the annually compounded rate.
B. The APR is higher than the annually compounded rate.
C. The APR equals the annually compounded rate.
D. The answer depends on the interest rate.
88. What is the APR on a loan that charges interest at the rate of 1.4% per month?
A. 10.20%
B. 14.00%
C. 16.80%
D. 18.16%
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Chapter 05 - The Time Value of Money
89. If interest is paid m times per year, then the per-period interest rate equals the:
A. effective annual rate divided by m.
B. compound interest rate times m.
C. effective annual rate.
D. annual percentage rate divided by m.
90. 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?
A. 4.02%
B. 10.02%
C. 14.50%
D. 15.19%
91. Which account would be preferred by a depositor: an 8% APR with monthly
compounding or 8.5% APR with semiannual compounding?
A. 8.0% with monthly compounding.
B. 8.5% with semiannual compounding.
C. The depositor would be indifferent.
D. The time period must be known to select the preferred account.
92. What is the annually compounded rate of interest on an account with an APR of 10% and
monthly compounding?
A. 10.00%
B. 10.47%
C. 10.52%
D. 11.05%
93. What is the APR on a loan with an effective annual rate of 15.01% and weekly
compounding of interest?
A. 12.00%
B. 12.50%
C. 13.00%
D. 14.00%
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Chapter 05 - The Time Value of Money
94. What is the effective annual interest rate on a 9% APR automobile loan that has monthly
payments?
A. 9.00%
B. 9.38%
C. 9.81%
D. 10.94%
95. Other things being equal, the more frequent the compounding period, the:
A. higher the APR.
B. lower the APR.
C. higher the effective annual interest rate.
D. lower the effective annual interest rate.
96. An APR will be equal to an effective annual rate if:
A. compounding occurs monthly.
B. compounding occurs continuously.
C. compounding occurs annually.
D. an error has occurred; these terms cannot be equal.
97. 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 _______.
A. 16.08%; 15.00%
B. 14.55%; 16.08%
C. 12.68%; 15.00%
D. 15.00%; 14.55%
98. If inflation in Wonderland averaged about 20% per month in 2000, what was the
approximate annual inflation rate?
A. 20%
B. 240%
C. 790%
D. 890%
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Chapter 05 - The Time Value of Money
99. 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, how would you
describe his purchasing power, on average?
A. His purchasing power remained on par with inflation.
B. He "beat" inflation by nearly 1% annually.
C. He "beat" inflation by slightly below 2% annually.
D. He "beat" inflation by 5% annually.
100. Which of the following statements best describes the real interest rate?
A. Real interest rates exceed inflation rates.
B. Real interest rates can decline only to zero.
C. Real interest rates can be negative, zero, or positive.
D. Real interest rates traditionally exceed nominal rates.
101. 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?
A. 5.00%
B. 5.66%
C. 6.00%
D. 9.46%
102. 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?
A. The real cost is constant.
B. The real cost is increasing.
C. The real cost is decreasing.
D. The price index must be known to answer this question.
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Chapter 05 - The Time Value of Money
103. 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?
A. 7.36%
B. 7.50%
C. 7.64%
D. 8.01%
Essay Questions
104. Discuss the statement, "Money has a time value."
105. Would you prefer a savings account that paid 7% interest, compounded quarterly, over an
account that paid 7.5% with annual compounding if you had $1,000 to deposit? Would the
answer change if you had $100,000 to deposit?
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Chapter 05 - The Time Value of Money
106. If 4 years of college are expected to cost $150,000 18 years from now, how much must
be deposited now into an account that will average 8% annually in order to save the
$150,000? By how much would your answer change if you expected 11% annually?
107. Prizes are often not "worth" as much as claimed. Place a value on a prize of $5,000,000
which is to be received in equal payments over 20 years, with the first payment beginning
today. Assume an interest rate of 7% over the 20 years.
108. Show numerically that a savings account with a current balance of $1,000 that earns
interest at 9% annually is precisely sufficient to make the payments on a 3-year loan of $1,000
that carries equal annual payments at 9% interest.
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Chapter 05 - The Time Value of Money
109. 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 9% interest versus a 15-year mortgage with 8.5% interest. 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?
110. Some home loans involve "points," which are fees charged by the lender. Each point
charged means that the borrower must pay 1% of the loan amount as a fee. For example, if 0.5
point is charged on a $100,000 loan, the loan repayment schedule is calculated on the
$100,000 loan, but the net amount the borrower receives is only $99,500. What is the
effective annual interest rate charged on such a loan, assuming that loan repayment occurs
over 360 months, and that the interest rate is 1% per month?
111. In 1973 Gordon Moore, one of Intel's founders, predicted that the number of transistors
that could be placed on a single silicon chip would double every 18 months, equivalent to an
annual growth of 59% (i.e., 1.591.5 = 2.0). The first microprocessor was built in 1971 and had
2,250 transistors. By 2003 Intel chips contained 410 million transistors, over 182,000 times
the number 32 years earlier. What has been the annual compound rate of growth in processing
power? How does it compare with the prediction of Moore's law?
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Chapter 05 - The Time Value of Money
112. How should we compare interest rates quoted over different time intervals—for example,
monthly versus annual rates?
113. Discuss the statement, "It is always preferred to select an account that offers compound
interest over an account that offers simple interest."
114. 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. Now, to make you feel even worse, calculate
the effective annual interest rate.
115. Why is it difficult and perhaps risky to evaluate financial projects based on APR alone?
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Chapter 05 - The Time Value of Money
116. What is the difference between real and nominal cash flows and between real and
nominal interest rates?
117. What problem can be caused by "mixing" real and nominal cash flows in discounting
exercises?
118. In 2004 there was widespread dismay as the price of unleaded gasoline climbed to $2.03
a gallon. Motorists looked back longingly to 20 years earlier when they were paying just
$1.19 a gallon. But how much had the real price of gasoline changed over this period, if the
consumer price index was 1.81 times itself in 1984?
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Chapter 05 - The Time Value of Money
Chapter 05 The Time Value of Money Answer Key
True / False Questions
1. Compound interest pays interest for each time period on the original investment plus the
accumulated interest.
TRUE
AACSB: Communication Abilities
Blooms: Knowledge
Difficulty: 1 Easy
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
2. When money is invested at compound interest, the growth rate is the interest rate.
TRUE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
3. The present value of an annuity due equals the present value of an ordinary annuity times
the discount rate.
FALSE
AACSB: Communication Abilities
Blooms: Knowledge
Difficulty: 1 Easy
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Perpetuities and Annuities
5-27
Chapter 05 - The Time Value of Money
4. The more frequent the compounding, the higher the future value, other things equal.
TRUE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 1 Easy
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
5. A dollar tomorrow is worth more than a dollar today.
FALSE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
6. The Excel function for future value is FV (rate, nper, pmt, PV).
TRUE
AACSB: Use of Information Technology
Blooms: Knowledge
Difficulty: 2 Medium
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
7. For a given amount, the lower the discount rate, the less the present value.
FALSE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 1 Easy
Learning Objective: 05-02 Calculate the present value of a future payment.
Topic: Present and Future Value
5-28
Chapter 05 - The Time Value of Money
8. Comparing the values of undiscounted cash flows is analogous to comparing apples to
oranges.
TRUE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 1 Easy
Learning Objective: 05-02 Calculate the present value of a future payment.
Topic: Present and Future Value
9. To calculate present value, we discount the future value by some interest rate r, the discount
rate.
TRUE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-02 Calculate the present value of a future payment.
Topic: Present and Future Value
10. The discount factor is used to calculate the present value of $1 received in year t.
TRUE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-02 Calculate the present value of a future payment.
Topic: Present and Future Value
11. You should never compare cash flows occurring at different times without first
discounting them to a common date.
TRUE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-02 Calculate the present value of a future payment.
Topic: Present and Future Value
5-29
Chapter 05 - The Time Value of Money
12. The Excel function for present value is PV (rate, nper, pmt, FV).
TRUE
AACSB: Use of Information Technology
Blooms: Knowledge
Difficulty: 2 Medium
Learning Objective: 05-02 Calculate the present value of a future payment.
Topic: Present and Future Value
13. A perpetuity is a special form of an annuity.
TRUE
AACSB: Communication Abilities
Blooms: Knowledge
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
14. An annuity factor represents the future value of $1 that is deposited today.
FALSE
AACSB: Communication Abilities
Blooms: Knowledge
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
15. Accrued interest declines with each payment on an amortizing loan.
TRUE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Amortization
5-30
Chapter 05 - The Time Value of Money
16. Converting an annuity to an annuity due decreases the present value.
FALSE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 1 Easy
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
17. The term "constant dollars" refers to equal payments for amortizing a loan.
FALSE
AACSB: Communication Abilities
Blooms: Knowledge
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Amortization
18. An annuity due must have a present value at least as large as an equivalent ordinary
annuity.
TRUE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
19. Any sequence of equally spaced, level cash flows is called an annuity. An annuity is also
known as a perpetuity.
FALSE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-31
Chapter 05 - The Time Value of Money
20. 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.
TRUE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Amortization
21. The Excel function for interest rate is RATE (nper, pmt, PV, FV).
TRUE
AACSB: Use of Information Technology
Blooms: Knowledge
Difficulty: 2 Medium
Learning Objective: 05-04 Find the interest rate implied by present and future values.
Topic: Present and Future Value
22. An effective annual rate must be greater than an annual percentage rate.
FALSE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—-for example; monthly versus annual rates.
Topic: EAR and APR
23. An annual percentage rate (APR) is determined by annualizing the rate using compound
interest.
FALSE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
5-32
Chapter 05 - The Time Value of Money
24. In 2002, the U.S. inflation rate was below 2% and a few countries were even experiencing
deflation.
TRUE
AACSB: Communication Abilities
Blooms: Knowledge
Difficulty: 2 Medium
Learning Objective: 05-06 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Topic: Inflation
25. Nominal dollars refer to the amount of purchasing power.
FALSE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-06 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Topic: Inflation
26. The appropriate manner of adjusting for inflationary effects is to discount nominal cash
flows with real interest rates.
FALSE
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-06 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Topic: Inflation
5-33
Chapter 05 - The Time Value of Money
Multiple Choice Questions
27. What is the future value of $10,000 on deposit for 5 years at 6% simple interest?
A. $7,472.58
B. $10,303.62
C. $13,000.00
D. $13,382.26
FV = PV + (PV  r  t)
($10,000) + [($10,000  .06)  5] = $13,000.00
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
28. Under which of the following conditions will a future value calculated with simple interest
exceed a future value calculated with compound interest at the same rate?
A. The interest rate is very high.
B. The investment period is very long.
C. The compounding is annually.
D. This is not possible with positive interest rates.
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
5-34
Chapter 05 - The Time Value of Money
29. How much interest is earned in just the third year on a $1,000 deposit that earns 7%
interest compounded annually?
A. $70.00
B. $80.14
C. $105.62
D. $140.00
$1000.00  (1.07)2 = $1,144.90 after 2 years
$1,144.90  .07 = $80.14
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
30. 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?
A. $88
B. $100
C. $112
D. $200
The investment will again pay $100 plus interest on the previous interest:
$100  1.12 = $112
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
5-35
Chapter 05 - The Time Value of Money
31. The concept of compound interest refers to:
A. earning interest on the original investment.
B. payment of interest on previously earned interest.
C. investing for a multiyear period of time.
D. determining the APR of the investment.
AACSB: Communication Abilities
Blooms: Knowledge
Difficulty: 1 Easy
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
32. When an investment pays only simple interest, this means:
A. the interest rate is lower than on comparable investments.
B. the future value of the investment will be low.
C. the earned interest is nontaxable to the investor.
D. interest is earned only on the original investment.
AACSB: Communication Abilities
Blooms: Knowledge
Difficulty: 1 Easy
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
33. Approximately how long must one wait (to the nearest year) for an initial investment of
$1,000 to triple in value if the investment earns 8% compounded annually?
A. 9 years
B. 14 years
C. 22 years
D. 25 years
$3,000 = $1,000(1.08)n
3 = (1.08)n
14.27, or approximately 14 years = N
Solved with financial calculator; can also be solved with tables or logarithms.
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
5-36
Chapter 05 - The Time Value of Money
34. How much will accumulate in an account with an initial deposit of $100, and which earns
10% interest compounded quarterly for 3 years?
A. $107.69
B. $133.10
C. $134.49
D. $313.84
FV = PV (1 + r)2
$100 (1.025)12 = $134.49
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
35. 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?
A. 413 million
B. 430 million
C. 488 million
D. 492 million
300 million  (1.02)25 = 492.2 million
492 million
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
5-37
Chapter 05 - The Time Value of Money
36. How much interest can be accumulated during one year on a $1,000 deposit paying
continuously compounded interest at an APR of 10%?
A. $100.00
B. $105.17
C. $110.50
D. $115.70
Interest = $1,000  e.1 - $1,000
= $1,000  1.1052 - $1,000
= $1,105.17- $1,000
= $105.17
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: EAR and APR
37. 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?
A. $130.00
B. $138.83
C. $169.00
D. $353.34
$1,000 (e0.13) = $1,000  1.1388 = $1,138.83
Thus, $138.83 was earned in interest.
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
5-38
Chapter 05 - The Time Value of Money
38. What is the discount factor for $1 to be received in 5 years at a discount rate of 8%?
A. .4693
B. .5500
C. .6000
D. .6806
Discount factor = 1/(1.08)5 = 1/1.4693 = .6806
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
39. Assume the total expense for your current year in college equals $20,000. Approximately
how much would your parents have needed to invest 21 years ago in an account paying 8%
compounded annually to cover this amount?
A. $952.00
B. $1,600.00
C. $1,728.00
D. $3,973.00
$20,000 = x(1.08)21
$20,000 = 5.0338x
$3,973.12 = x
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-02 Calculate the present value of a future payment.
Topic: Present and Future Value
5-39
Chapter 05 - The Time Value of Money
40. How much must be deposited today in an account earning 6% annually to accumulate a
20% down payment to use in purchasing a car one year from now, assuming that the car's
current price is $20,000, and inflation will be 4%?
A. $3,774
B. $3,782
C. $3,925
D. $4,080
Need $20,800  .2 = $4,160
PV = $4,160/(1.06)
= $3,924.53
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-02 Calculate the present value of a future payment.
Topic: Present and Future Value
41. Given a set future value, which of the following will contribute to a lower present value?
A. Higher discount rate
B. Fewer time periods
C. Less frequent discounting
D. Lower discount factor
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-02 Calculate the present value of a future payment.
Topic: Present and Future Value
42. Cash flows occurring in different periods should not be compared unless:
A. interest rates are expected to be stable.
B. the flows occur no more than one year from each other.
C. high rates of interest can be earned on the flows.
D. the flows have been discounted to a common date.
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 1 Easy
Learning Objective: 05-02 Calculate the present value of a future payment.
Topic: Present and Future Value
5-40
Chapter 05 - The Time Value of Money
43. A corporation has promised to pay $1,000 20 years from today for each bond sold now.
No interest will be paid on the bonds during the 20 years, and the bonds are discounted at a
7% interest rate. Approximately how much should an investor pay for each bond?
A. $70.00
B. $258.42
C. $629.56
D. $857.43
PV = $1,000/(1.07)20 = $1,000/3.8697 = $258.42
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-02 Calculate the present value of a future payment.
Topic: Present and Future Value
44. What is the present value of your trust fund if it promises to pay you $50,000 on your 30th
birthday (7 years from today) and earns 10% compounded annually?
A. $25,000.00
B. $25,657.91
C. $28,223.70
D. $29,411.76
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-02 Calculate the present value of a future payment.
Topic: Present and Future Value
5-41
Chapter 05 - The Time Value of Money
45. How much more would you be willing to pay today for an investment offering $10,000 in
4 years rather than the normally advertised 5-year period? Your discount rate is 8%.
A. $544.47
B. $681.48
C. $740.74
D. $800.00
$7,350.30 vs. $6,805.83
$544.47 difference.
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-02 Calculate the present value of a future payment.
Topic: Present and Future Value
46. What is the present value of $100 to be deposited today into an account paying 8%,
compounded semiannually for 2 years?
A. $85.48
B. $100.00
C. $116.00
D. $116.99
$100  (1.0375)0 = $100
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-02 Calculate the present value of a future payment.
Topic: Present and Future Value
5-42
Chapter 05 - The Time Value of Money
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%?
A. $3,604.78
B. $3,746.25
C. $4,037.35
D. $4,604.78
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
48. The salesperson offers, "Buy this new car for $25,000 cash or, with 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.
A. $1,000.00
B. $4,520.64
C. $5,127.24
D. $8,000.00
A difference of $4,520.64 exists between cash price and loan value. This should be the down
payment.
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-43
Chapter 05 - The Time Value of Money
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?
A. $5,022.11
B. $5,144.03
C. $5,423.87
D. $5,520.00
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
50. What is the present value of the following set of cash flows at an interest rate of 7%:
$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?
A. $9,731
B. $10,412
C. $10,524
D. $11,524
PV = $1,000/(1.07)0 + $2,000/(1.07)1 = $4,000/(1.07)3 + $6,000/(1.07)5
= $1,000 + $1,869.16 + $3,265.19 + $4,277.92
= $10,412.27
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Present and Future Value
5-44
Chapter 05 - The Time Value of Money
51. A cash-strapped young professional offers to buy your car with four, equal annual
payments of $3,000, beginning 2 years from today. Assuming you're indifferent to cash versus
credit, that you can invest at 10%, and that you want to receive $9,000 for the car, should you
accept?
A. Yes; present value is $9,510.
B. Yes; present value is $11,372.
C. No; present value is $8,645.
D. No; present value is $7,461.
PV = $3,000[1/.1 - 1/.1(1.1)4]/1.1
= $3,000(10 - 6.8301)/1.1
= $3,000  3.1699/1.1
= $9,509.60/1.1
= $8,645.09
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
52. How much more is a perpetuity of $1,000 worth than an annuity of the same amount for
20 years? Assume a 10% interest rate and cash flows at end of period.
A. $297.29
B. $1,486.44
C. $1,635.08
D. $2,000.00
Difference = $1,000/.10 - $1,000[1/.10 - 1/.10(1.10)20]
= $10,000 - $8,513.56 = $1,486.44
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-45
Chapter 05 - The Time Value of Money
53. A stream of equal cash payments lasting forever is termed:
A. an annuity.
B. an annuity due.
C. an installment plan.
D. a perpetuity.
AACSB: Communication Abilities
Blooms: Knowledge
Difficulty: 1 Easy
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
54. Which of the following factors is fixed and thus cannot change for a specific perpetuity?
A. PV of a perpetuity
B. Cash payment of a perpetuity
C. Interest rate on a perpetuity
D. Discount rate of a perpetuity
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 1 Easy
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
55. The present value of a perpetuity can be determined by:
A. Multiplying the payment by the interest rate.
B. Dividing the interest rate by the payment.
C. Multiplying the payment by the number of payments to be made.
D. Dividing the payment by the interest rate.
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 1 Easy
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-46
Chapter 05 - The Time Value of Money
56. A perpetuity of $5,000 per year beginning today is said to offer a 15% interest rate. What
is its present value?
A. $33,333.33
B. $37,681.16
C. $38,333.33
D. $65,217.39
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-47
Chapter 05 - The Time Value of Money
57. Your car loan requires payments of $200 per month for the first year and payments of
$400 per month during the second year. The annual interest rate is 12% and payments begin in
one month. What is the present value of this 2-year loan?
A. $6,246.34
B. $6,389.78
C. $6,428.57
D. $6,753.05
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
58. Which of the following will increase the present value of an annuity, other things equal?
A. Increasing the interest rate
B. Decreasing the interest rate
C. Decreasing the number of payments
D. Decreasing the amount of the payment
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 1 Easy
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-48
Chapter 05 - The Time Value of Money
59. What is the present value of a five-period annuity of $3,000 if the interest rate is 12% and
the first payment is made today?
A. $9,655.65
B. $10,814.33
C. $12,112.05
D. $13,200.00
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
60. $3,000 is deposited into an account paying 10% annually, to provide three annual
withdrawals of $1,206.34 beginning in one year. How much remains in the account after the
second payment has been withdrawn?
A. $1,326.97
B. $1,206.34
C. $1,096.69
D. $587.32
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-49
Chapter 05 - The Time Value of Money
61. How many monthly payments remain to be paid on an 8% mortgage with a 30-year
amortization and monthly payments of $733.76, when the balance reaches one-half of the
$100,000 mortgage?
A. Approximately 268 payments
B. Approximately 180 payments
C. Approximately 92 payments
D. Approximately 68 payments
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-50
Chapter 05 - The Time Value of Money
62. What is the present value of a four-period annuity of $100 per year that begins 2 years
from today if the discount rate is 9%?
A. $297.21
B. $323.86
C. $356.85
D. $388.97
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
63. If $120,000 is borrowed for a home mortgage, to be repaid at 9% interest over 30 years
with monthly payments of $965.55, how much interest is paid over the life of the loan?
A. $120,000
B. $162,000
C. $181,458
D. $227,598
(965.55  360) - 120,000 = $227,598
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-51
Chapter 05 - The Time Value of Money
64. $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?
A. $2,010.60
B. $5,000.00
C. $15,105.74
D. $20,105.74
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
65. An amortizing loan is one in which:
A. the principal remains unchanged with each payment.
B. accrued interest is paid regularly.
C. the maturity of the loan is variable.
D. the principal balance is reduced with each payment.
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 1 Easy
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Amortization
5-52
Chapter 05 - The Time Value of Money
66. 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?
A. $28.68
B. $31.55
C. $100.00
D. $315.47
$315.47 - ($315.47/1.1) = $28.68
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Amortization
67. What will be the monthly payment on a home mortgage of $75,000 at 12% interest, to be
amortized over 30 years?
A. $771.46
B. $775.90
C. $1,028.61
D. $1,034.53
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-53
Chapter 05 - The Time Value of Money
68. Your real estate agent mentions that homes in your price range require a payment of
approximately $1,200 per month over 30 years at 9% interest. What is the approximate size of
the mortgage with these terms?
A. $128,035
B. $147,940
C. $149,140
D. $393,120
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
69. Which of the following characteristics applies to the amortization of a loan such as a home
mortgage?
A. The amortization decreases with each payment.
B. The amortization increases with each payment.
C. The amortization is constant throughout the loan.
D. The amortization fluctuates monthly with changes in interest rates.
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Amortization
5-54
Chapter 05 - The Time Value of Money
70. How much must be saved annually, beginning 1 year from now, in order to accumulate
$50,000 over the next 10 years, earning 9% annually?
A. $3,291
B. $3,587
C. $4,500
D. $4,587
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Present and Future Value
71. Approximately how much should be accumulated by the beginning of retirement to
provide a $2,500 monthly check that will last for 25 years, during which time the fund will
earn 8% interest with monthly compounding?
A. $261,500.00
B. $323,800.00
C. $578,700.00
D. $690,000.00
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-55
Chapter 05 - The Time Value of Money
72. 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?
A. An increase of $10
B. An increase of $61
C. An increase of $100
D. Unknown without knowing number of payments
Difference = $614(1.1) - $614 = $61
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
73. 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 1
year from now?
A. $1,067,000
B. $1,250,000
C. $2,315,000
D. $2,500,000
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-56
Chapter 05 - The Time Value of Money
74. With $1.5 million in an account expected to earn 8% annually over the retiree's 30 years
of life expectancy, what annual annuity can be withdrawn, beginning today?
A. $112,150
B. $120,000
C. $123,371
D. $133,241
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
75. How much can be accumulated for retirement if $2,000 is deposited annually, beginning 1
year from today, and the account earns 9% interest compounded annually for 40 years?
A. $87,200.00
B. $675,764.89
C. $736,583.73
D. $802,876.27
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Present and Future Value
5-57
Chapter 05 - The Time Value of Money
76. Which of the following strategies will allow real retirement spending to remain
approximately equal, assuming savings of $1,000,000 invested at 8%, a 25-year horizon, and
4% expected inflation?
A. Spend approximately $63,000 annually.
B. Spend approximately $78,225 annually.
C. Spend approximately $93,680 annually.
D. Spend approximately $127,500 annually.
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-58
Chapter 05 - The Time Value of Money
77. In calculating the present value of $1,000 to be received 5 years from today, the discount
factor has been calculated to be .7008. What is the apparent interest rate?
A. 5.43%
B. 7.37%
C. 8.00%
D. 9.50%
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-04 Find the interest rate implied by present and future values.
Topic: Present and Future Value
78. If the future value of an annuity due = $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?
A. 1.04%
B. 4.17%
C. 5.00%
D. 8.19%
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-04 Find the interest rate implied by present and future values.
Topic: Perpetuities and Annuities
5-59
Chapter 05 - The Time Value of Money
79. A furniture store is offering free credit on purchases over $1,000. You observe that a bigscreen 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 "free" credit?
A. The "free" credit costs about 8.75%.
B. The "free" credit costs about 9.13%.
C. The "free" credit costs about 9.59%.
D. The "free" credit effectively costs zero%.
$350/$4,000 = 8.75%
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-04 Find the interest rate implied by present and future values.
Topic: Present and Future Value
80. The present value of the following cash flows is known to be $6,939.91; $500 today,
$2,000 in 1 year, and $5,000 in 2 years. What discount rate is being used?
A. 3%
B. 4%
C. 5%
D. 6%
$6,939.91 = $500/(1 + i)0 + $2,000/(1 + i)1 + $5,000/(1 + i)2
i = 5% by financial calculator
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-04 Find the interest rate implied by present and future values.
Topic: Present and Future Value
5-60
Chapter 05 - The Time Value of Money
81. Your retirement account has a current balance of $50,000. What interest rate would need
to be earned in order to accumulate a total of $1,000,000 in 30 years, by adding $6,000
annually?
A. 5.02%
B. 7.24%
C. 9.80%
D. 10.07%
i = 7.24% by financial calculator
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-04 Find the interest rate implied by present and future values.
Topic: Perpetuities and Annuities
5-61
Chapter 05 - The Time Value of Money
82. If a borrower promises to pay you $1,900 9 years from now in return for a loan of $1,000
today, what effective annual interest rate is being offered?
A. 5.26%
B. 7.39%
C. 9.00%
D. 10.00%
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-04 Find the interest rate implied by present and future values.
Topic: EAR and APR
5-62
Chapter 05 - The Time Value of Money
83. "Give me $5,000 today and I'll return $20,000 to you in 5 years," offers the investment
broker. To the nearest percent, what annual interest rate is being offered?
A. 25%
B. 29%
C. 32%
D. 60%
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-04 Find the interest rate implied by present and future values.
Topic: Present and Future Value
5-63
Chapter 05 - The Time Value of Money
84. 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?
A. 6%
B. 9%
C. 11%
D. 12%
r = .0075; or 9% annualized rate
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-04 Find the interest rate implied by present and future values.
Topic: EAR and APR
5-64
Chapter 05 - The Time Value of Money
85. What APR is being earned on a deposit of $5,000 made 10 years ago today if the deposit
is worth $9,948.94 today? The deposit pays interest semiannually.
A. 3.56%
B. 6.76%
C. 7.00%
D. 7.12%
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
86. An interest rate that has been annualized using compound interest is termed the:
A. simple interest rate.
B. annual percentage rate.
C. discounted interest rate.
D. effective annual interest rate.
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 1 Easy
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
5-65
Chapter 05 - The Time Value of Money
87. 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?
A. The APR is lower than the annually compounded rate.
B. The APR is higher than the annually compounded rate.
C. The APR equals the annually compounded rate.
D. The answer depends on the interest rate.
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
88. What is the APR on a loan that charges interest at the rate of 1.4% per month?
A. 10.20%
B. 14.00%
C. 16.80%
D. 18.16%
1.4% monthly  12 = 16.8% APR
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
89. If interest is paid m times per year, then the per-period interest rate equals the:
A. effective annual rate divided by m.
B. compound interest rate times m.
C. effective annual rate.
D. annual percentage rate divided by m.
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
5-66
Chapter 05 - The Time Value of Money
90. 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?
A. 4.02%
B. 10.02%
C. 14.50%
D. 15.19%
(1.1608).25 = 1 + quarterly rate
1.0380 - 1 = quarterly rate
.0380 = quarterly rate
.1519 = quarterly rate  4
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
91. Which account would be preferred by a depositor: an 8% APR with monthly
compounding or 8.5% APR with semiannual compounding?
A. 8.0% with monthly compounding.
B. 8.5% with semiannual compounding.
C. The depositor would be indifferent.
D. The time period must be known to select the preferred account.
(1.0667)12 - 1 = 8.3%
(1.0425)2 - 1 = 8.68%
Therefore, B is preferred
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
5-67
Chapter 05 - The Time Value of Money
92. What is the annually compounded rate of interest on an account with an APR of 10% and
monthly compounding?
A. 10.00%
B. 10.47%
C. 10.52%
D. 11.05%
(1.00833) 12 - 1 = 10.47%
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
93. What is the APR on a loan with an effective annual rate of 15.01% and weekly
compounding of interest?
A. 12.00%
B. 12.50%
C. 13.00%
D. 14.00%
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
5-68
Chapter 05 - The Time Value of Money
94. What is the effective annual interest rate on a 9% APR automobile loan that has monthly
payments?
A. 9.00%
B. 9.38%
C. 9.81%
D. 10.94%
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
95. Other things being equal, the more frequent the compounding period, the:
A. higher the APR.
B. lower the APR.
C. higher the effective annual interest rate.
D. lower the effective annual interest rate.
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 1 Easy
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
5-69
Chapter 05 - The Time Value of Money
96. An APR will be equal to an effective annual rate if:
A. compounding occurs monthly.
B. compounding occurs continuously.
C. compounding occurs annually.
D. an error has occurred; these terms cannot be equal.
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 1 Easy
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
97. 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 _______.
A. 16.08%; 15.00%
B. 14.55%; 16.08%
C. 12.68%; 15.00%
D. 15.00%; 14.55%
Annually compounded rate = (1.0125)12 - 1 = 16.08%
APR = 1.25%  12 = 15.00%
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
5-70
Chapter 05 - The Time Value of Money
98. If inflation in Wonderland averaged about 20% per month in 2000, what was the
approximate annual inflation rate?
A. 20%
B. 240%
C. 790%
D. 890%
(1.20)12 - 1 = 7.916 = 791.6%
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 3 Hard
Learning Objective: 05-06 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Topic: Inflation
99. 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, how would you
describe his purchasing power, on average?
A. His purchasing power remained on par with inflation.
B. He "beat" inflation by nearly 1% annually.
C. He "beat" inflation by slightly below 2% annually.
D. He "beat" inflation by 5% annually.
10 = 1(1 + i)40, i = 5.925% by financial calculator
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 2 Medium
Learning Objective: 05-06 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Topic: Inflation
5-71
Chapter 05 - The Time Value of Money
100. Which of the following statements best describes the real interest rate?
A. Real interest rates exceed inflation rates.
B. Real interest rates can decline only to zero.
C. Real interest rates can be negative, zero, or positive.
D. Real interest rates traditionally exceed nominal rates.
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-06 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Topic: Inflation
101. 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?
A. 5.00%
B. 5.66%
C. 6.00%
D. 9.46%
1 + real interest rate = (1 + nominal interest rate)/(1 + inflation)
1 + real interest rate = 1.12/1.06
Real interest rate = 5.66%
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 1 Easy
Learning Objective: 05-06 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Topic: Inflation
102. 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?
A. The real cost is constant.
B. The real cost is increasing.
C. The real cost is decreasing.
D. The price index must be known to answer this question.
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-06 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Topic: Inflation
5-72
Chapter 05 - The Time Value of Money
103. 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?
A. 7.36%
B. 7.50%
C. 7.64%
D. 8.01%
7.64% = nominal rate
AACSB: Reflective Thinking Skills
Blooms: Application
Difficulty: 1 Easy
Learning Objective: 05-06 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Topic: Inflation
Essay Questions
104. Discuss the statement, "Money has a time value."
Money has a time value due to the concept of opportunity cost. In other words, if receipt of
funds is forgone until a later period, you lose the opportunity to earn a return on the funds in
the interim. Thus, cash flows that occur in different periods cannot be directly compared
without adjusting for these opportunity costs. Discounting cash flows to a common period
adjusts for the time value, and makes cash flows comparable.
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
5-73
Chapter 05 - The Time Value of Money
105. Would you prefer a savings account that paid 7% interest, compounded quarterly, over an
account that paid 7.5% with annual compounding if you had $1,000 to deposit? Would the
answer change if you had $100,000 to deposit?
FV = (1 + i)n for simple interest
FV = (1 + i/m)nxm for compound interest
Then, FV = (1 + .07/4)1 x 4 = 1.0719
Versus FV = (1 + 0.75)1 = 1.075
Thus, the 7.5% account will earn .31% more in the first year than the 7% account with
quarterly compounding. The amount to be deposited will not change your preference: In this
case the compounding is not enough to overcome the difference in APR.
AACSB: Analytical Skills
Blooms: Evaluation
Difficulty: 2 Medium
Learning Objective: 05-01 Calculate the future value to which money invested at a given interest rate will grow.
Topic: Present and Future Value
106. If 4 years of college are expected to cost $150,000 18 years from now, how much must
be deposited now into an account that will average 8% annually in order to save the
$150,000? By how much would your answer change if you expected 11% annually?
FV = PV (1 + i)n
$150,000 = PV (1.08)18
$150,000 = PV  3.996
$37,537.35 = PV
If the interest rate increases to 11%, the necessary deposit is reduced to $22,923.33.
AACSB: Analytical Skills
Blooms: Evaluation
Difficulty: 2 Medium
Learning Objective: 05-02 Calculate the present value of a future payment.
Topic: Present and Future Value
5-74
Chapter 05 - The Time Value of Money
107. Prizes are often not "worth" as much as claimed. Place a value on a prize of $5,000,000
which is to be received in equal payments over 20 years, with the first payment beginning
today. Assume an interest rate of 7% over the 20 years.
AACSB: Analytical Skills
Blooms: Evaluation
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-75
Chapter 05 - The Time Value of Money
108. Show numerically that a savings account with a current balance of $1,000 that earns
interest at 9% annually is precisely sufficient to make the payments on a 3-year loan of $1,000
that carries equal annual payments at 9% interest.
The loan payments are:
After the first year's addition of interest, the account has $1,090.00 and $395.06 is withdrawn
to make the first payment. The balance of $694.94 grows to $757.48 at the end of the second
year. After making the second payment of $395.06, $362.42 is left in the account. This
amount grows to $395.04 by the end of the third year, which is within a 2-cent rounding error
of making the final payment.
AACSB: Analytical Skills
Blooms: Evaluation
Difficulty: 3 Hard
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-76
Chapter 05 - The Time Value of Money
109. 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 9% interest versus a 15-year mortgage with 8.5% interest. 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?
Difference in total dollars
= (804.62  360) - (984.69  180)
= 289,663.20 - 177,244.20
= $112,419
AACSB: Analytical Skills
Blooms: Evaluation
Difficulty: 2 Medium
Learning Objective: 05-03 Calculate present and future values of a series of cash payments.
Topic: Perpetuities and Annuities
5-77
Chapter 05 - The Time Value of Money
110. Some home loans involve "points," which are fees charged by the lender. Each point
charged means that the borrower must pay 1% of the loan amount as a fee. For example, if 0.5
point is charged on a $100,000 loan, the loan repayment schedule is calculated on the
$100,000 loan, but the net amount the borrower receives is only $99,500. What is the
effective annual interest rate charged on such a loan, assuming that loan repayment occurs
over 360 months, and that the interest rate is 1% per month?
Since the monthly payment is based on a $100,000 loan:
Mortgage payment  annuity factor(1%, 360) = 100,000
monthly mortgage payment = $1,028.61
The net amount received is $99,500. Therefore:
$1,028.61  annuity factor(r, 360) = $99,500
r = 1.006% per month
The effective annual rate is: (1.01006)12 - 1 = 0.1276 = 12.76%
AACSB: Analytical Skills
Blooms: Evaluation
Difficulty: 2 Medium
Learning Objective: 05-04 Find the interest rate implied by present and future values.
Topic: EAR and APR
111. In 1973 Gordon Moore, one of Intel's founders, predicted that the number of transistors
that could be placed on a single silicon chip would double every 18 months, equivalent to an
annual growth of 59% (i.e., 1.591.5 = 2.0). The first microprocessor was built in 1971 and had
2,250 transistors. By 2003 Intel chips contained 410 million transistors, over 182,000 times
the number 32 years earlier. What has been the annual compound rate of growth in processing
power? How does it compare with the prediction of Moore's law?
Call g the annual growth rate of transistors over the 32-year period between 1971 and 2003.
Then
2,250  (1 + g)32 = 410,000,000
(1 + g)32 = 182,222
1 + g = 182,2221/32 = 1.46
So the actual growth rate has been g = .46, or 46%, not quite as high as Moore's prediction,
but not so shabby either.
AACSB: Analytical Skills
Blooms: Evaluation
Difficulty: 2 Medium
Learning Objective: 05-04 Find the interest rate implied by present and future values.
Topic: Present and Future Value
5-78
Chapter 05 - The Time Value of Money
112. How should we compare interest rates quoted over different time intervals—for example,
monthly versus annual rates?
Interest rates for short time periods are often quoted as annual rates by multiplying the period
rate by the number of periods in a year. These annual percentage rates (APRs) do not
recognize the effect of compound interest; that is, they annualize assuming simple interest.
The effective annual rate annualizes using compound interest. It equals the rate of interest per
period compounded for the number of periods in a year.
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
113. Discuss the statement, "It is always preferred to select an account that offers compound
interest over an account that offers simple interest."
This statement is true if the APRs are equal on the different accounts, and if the compounding
occurs more frequently than annually. The statement may be false if the APRs are not equal,
however. A point is reached where the benefit of more frequent compounding is
overshadowed by the reduction in APR.
AACSB: Analytical Skills
Blooms: Analysis
Difficulty: 2 Medium
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: Present and Future Value
5-79
Chapter 05 - The Time Value of Money
114. 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. Now, to make you feel even worse, calculate
the effective annual interest rate.
AACSB: Analytical Skills
Blooms: Evaluation
Difficulty: 2 Medium
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
115. Why is it difficult and perhaps risky to evaluate financial projects based on APR alone?
Evaluating a project by APR alone ignores the potential significant effects that accrue as a
result of compounding on a more frequent than annual basis. For example, over a long period
of time there is a significant difference to the value of an account that carries monthly as
opposed to annual compounding. In a similar manner, the cost of a loan can best be evaluated
through the effective annual rate that considers the cost of payments occurring more
frequently than annually.
AACSB: Analytical Skills
Blooms: Analysis
Difficulty: 2 Medium
Learning Objective: 05-05 Compare interest rates quoted over different time intervals—for example; monthly versus annual rates.
Topic: EAR and APR
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Chapter 05 - The Time Value of Money
116. What is the difference between real and nominal cash flows and between real and
nominal interest rates?
A dollar is a dollar, but the amount of goods that a dollar can buy is eroded by inflation. If
prices double, the real value of a dollar halves. Financial managers and economists often find
it helpful to re-express future cash flows in terms of real dollars—that is, dollars of constant
purchasing power.
Be careful to distinguish the nominal interest rate and the real interest rate—the rate at which
the real value of the investment grows. Discount nominal cash flows (that is, cash flows
measured in current dollars) at nominal interest rates; discount real cash flows (cash flows
measured in constant dollars) at real interest rates. Never mix and match nominal and real.
AACSB: Communication Abilities
Blooms: Knowledge
Difficulty: 2 Medium
Learning Objective: 05-06 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Topic: Inflation
117. What problem can be caused by "mixing" real and nominal cash flows in discounting
exercises?
One of the primary components of a nominal interest rate is a premium for the rate of inflation
that is expected during the time period that the interest rate is in effect. On the other hand, the
adjustment that takes a nominal rate to a real rate is typically a downward adjustment that
"backs out" the expected impact of inflation. Thus, to discount real flows with a nominal rate
would be to overcompensate for the effects of inflation. Alternatively, to discount nominal
flows with a real rate would be to under compensate for inflationary impact. The only safe,
correct method is to discount nominal flows with nominal rates, or discount real flows with
real rates.
AACSB: Reflective Thinking Skills
Blooms: Understanding
Difficulty: 2 Medium
Learning Objective: 05-06 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Topic: Inflation
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Chapter 05 - The Time Value of Money
118. In 2004 there was widespread dismay as the price of unleaded gasoline climbed to $2.03
a gallon. Motorists looked back longingly to 20 years earlier when they were paying just
$1.19 a gallon. But how much had the real price of gasoline changed over this period, if the
consumer price index was 1.81 times itself in 1984?
In 2004 the consumer price index was 1.81 times its level in 1984. If the price of gasoline had
risen in line with inflation, it would have cost 1.81  $1.19 = $2.15 a gallon in 2004. That was
the cost of gasoline 20 years ago but measured in terms of 2004 dollars rather than 1984
dollars. Thus over the 20 years the real price of gasoline declined from $2.15 a gallon to
$2.03, a fall of 6%.
AACSB: Analytical Skills
Blooms: Evaluation
Difficulty: 2 Medium
Learning Objective: 05-06 Understand the difference between real and nominal cash flows and between real and nominal interest rates.
Topic: Inflation
5-82