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Chapter 4 – Time Value of Money
54. Gomez Electronics needs to arrange financing for its expansion program. Bank A offers to lend Gomez the required
funds on a loan where interest must be paid monthly, and the quoted rate is 8 percent. Bank B will charge 9 percent,
with interest due at the end of the year. What is the difference in the effective annual rates charged by the two
banks?
a. 0.25%
b. 0.50%
c. 0.70%
d. 1.00%
e. 1.25%
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Chapter 4 – Time Value of Money
55. Assume that you can invest to earn a stated annual rate of return of 12 percent, but where interest is compounded
semiannually. If you make 20 consecutive semiannual deposits of $500 each, with the first deposit being made today,
what will your balance be at the end of Year 20?
a. $52,821.19
b. $57,900.83
c. $58,988.19
d. $62,527.47
e. $64,131.50
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Chapter 4 – Time Value of Money
56. Assume you are to receive a 20-year annuity with annual payments of $50. The first payment will be received at the
end of Year 1, and the last payment will be received at the end of Year 20. You will invest each payment in an
account that pays 10 percent. What will be the value in your account at the end of Year 30?
a. $6,354.81
b. $7,427.83
c. $7,922.33
d. $8,591.00
e. $6,752.46
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Chapter 4 – Time Value of Money
57. You expect to receive $1,000 at the end of each of the next 3 years. You will deposit these payments into an
account which pays 10 percent compounded semiannually. What is the future value of these payments, that is, the
value at the end of the third year?
a. $3,000
b. $3,310
c. $3,318
d. $3,401
e. $3,438
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Chapter 4 – Time Value of Money
58. You just graduated, and you plan to work for 10 years and then to leave for the Australian “Outback” bush country.
You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the next 5 years. These savings
cash flows will start one year from now. In addition, your family has just given you a $5,000 graduation gift. If you
put the gift now, and your future savings when they start, into an account which pays 8 percent compounded
annually, what will your financial “stake” be when you leave for Australia 10 years from now?
a. $21,432
b. $28,393
c. $16,651
d. $31,148
e. $20,000
59. As the winning contestant in a television game show, you are considering the prizes to be awarded. You must indicat
sponsor which of the following two choices you prefer, assuming you want to maximize your wealth. Assume it is no
January 1, and there is no danger whatever that the sponsor won’t pay off.
(1)
$1,000 now and another $1,000 at the beginning of each of the 11 subsequent months during
the remainder of the year, to be deposited in an account paying 12 percent simple annual
rate, but compounded monthly (to be left on deposit for the year).
(2) $12,750 at the end of the year.
Which one would you choose?
a. Choice 1
b. Choice 2
c. Choice 1, if the payments were made at the end of the year.
d. The choice would depend on how soon you need the money.
e. Either one, since they have the same present value.
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Chapter 4 – Time Value of Money
60. You want to buy a Nissan 350Z on your 27th birthday. You have priced these cars and found that they currently sell
for $30,000. You believe that the price will increase by 5 percent per year until you are ready to buy. You can
presently invest to earn 14 percent. If you just turned 20 years old, how much must you invest at the end of each of
the next 7 years to be able to purchase the Nissan in 7 years?
a. $4,945.57
b. $3,933.93
c. $7,714.72
d. $3,450.82
e. $6,030.43
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Chapter 4 – Time Value of Money
61. Assume that your required rate of return is 12 percent and you are given the following stream of cash flows:
Year
Cash Flow
0
$10,000
1
15,000
2
15,000
3
15,000
4
15,000
5
20,000
If payments are made at the end of each period, what is the present value of the cash flow stream?
a. $66,909
b. $57,323
c. $61,815
d. $52,345
e. $62,029
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Chapter 4 – Time Value of Money
62. You are given the following cash flows. What is the present value (t = 0) if the discount rate is 12 percent?
a. $3,277
b. $4,804
c. $5,302
d. $4,289
e. $2,804
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Chapter 4 – Time Value of Money
63. You are given the following cash flow information. The appropriate discount rate is 12 percent for Years 1-5 and 10
percent for Years 6-10. Payments are received at the end of the year.
Year Amount
1–5 $20,000
6–10 $25,000
What should you be willing to pay right now to receive the income stream above?
a. $166,866
b. $158,791
c. $225,000
d. $125,870
e. $198,433
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Chapter 4 – Time Value of Money
64. A project with a 3-year life has the following probability distributions for possible end of year cash flows in each of
the next three years:
Year 1
Year 2
Year 3
Prob
Cash Flow
Prob
Cash Flow
Prob
Cash Flow
0.30
$300
0.15
$100
0.25
$200
0.40
500
0.35
200
0.75
800
0.30
700
0.35
600
0.15
900
Using an interest rate of 8 percent, find the expected present value of these uncertain cash flows. (Hint: Find the
expected cash flow in each year, then evaluate those cash flows.)
a. $1,204.95
b. $835.42
c. $1,519.21
d. $1,580.00
e. $1,347.61
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Chapter 4 – Time Value of Money
65. If you buy a factory for $250,000 and the terms are 20 percent down, the balance to be paid off over 30 years at a 1
rate of interest on the unpaid balance, what are the 30 equal annual payments?
a. $20,593
b. $31,036
c. $24,829
d. $50,212
e. $6,667
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Chapter 4 – Time Value of Money
66. In its first year of operations, 2002, the Gourmet Cheese Shoppe had earnings per share (EPS) of $0.26. Four years l
in 2006, EPS was up to $0.38, and 7 years after that, in 2013, EPS was up to $0.535. It appears that the first 4 years
represented a supernormal growth situation and since then a more normal growth rate has been sustained. What are
rates of growth for the earlier period and for the later period?
a. 6%; 5%
b. 6%; 3%
c. 10%; 8%
d. 10%; 5%
e. 12%; 7%
67. Steaks Galore needs to arrange financing for its expansion program. One bank offers to lend the required $1,000,000
on a loan which requires interest to be paid at the end of each quarter. The quoted rate is 10 percent, and the
principal must be repaid at the end of the year. A second lender offers 9 percent, daily compounding (365–day year),
with interest and principal due at the end of the year. What is the difference in the effective annual rates (EFF%)
charged by the two banks?
a. 0.31%
b. 0.53%
c. 0.75%
d. 0.96%
e. 1.25%
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Chapter 4 – Time Value of Money
68. You are currently at time period 0, and you will receive the first payment on an annual payment annuity of $100 in
perpetuity at the end of this year. Six full years from now you will receive the first payment on an additional $150 in
perpetuity, and at the end of time period 10 you will receive the first payment on an additional $200 in perpetuity. If
you require a 10 percent rate of return, what is the combined present value of these three perpetuities?
a. $2,349.50
b. $2,526.85
c. $2,685.42
d. $2,779.58
e. $2,975.40
69. Find the present value of an income stream which has a negative flow of $100 per year for 3 years, a positive flow o
$200 in the 4th year, and a positive flow of $300 per year in Years 5 through 8. The appropriate discount rate is 4
percent for each of the first 3 years and 5 percent for each of the later years. Thus, a cash flow accruing in Year 8
should be discounted at 5 percent for some years and 4 percent in other years. All payments occur at year-end.
a. $528.21
b. $1,329.00
c. $792.49
d. $1,046.41
e. $875.18
70. Assume that you are graduating, that you plan to work for 4 years, and then to go to law school for 3 years. Right
now, going to law school would require $17,000 per year (for tuition, books, living expenses, etc.), but you expect this
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Chapter 4 – Time Value of Money
cost to rise by 8 percent per year in all future years. You now have $25,000 invested in an investment account which
pays a simple annual rate of 9 percent, quarterly compounding, and you expect that rate of return to continue into the
future. You want to maintain the same standard of living while in law school that $17,000 per year would currently
provide. You plan to save and to make 4 equal payments (deposits) which will be added to your account at the end of
each of the next 4 years; these new deposits will earn the same rate as your investment account currently earns.
How large must each of the 4 payments be in order to permit you to make 3 withdrawals, at the beginning of each of
your 3 years in law school? (Note: (1) The first payment is made a year from today and the last payment 4 years
from today, (2) the first withdrawal is made 4 years from today, and (3) the withdrawals will not be of a constant
amount.)
a. $13,242.67
b. $6,562.13
c. $10,440.00
d. $7,153.56
e. $14,922.85
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Chapter 4 – Time Value of Money
Financial Calculator Section
The following question(s) may require the use of a financial calculator.
71. You want to borrow $1,000 from a friend for one year, and you propose to pay her $1,120 at the end of the year.
She agrees to lend you the $1,000, but she wants you to pay her $10 of interest at the end of each of the first 11
months plus $1,010 at the end of the 12th month. How much higher is the effective annual rate under your friend’s
proposal than under your proposal?
a. 0.00%
b. 0.45%
c. 0.68%
d. 0.89%
e. 1.00%
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Chapter 4 – Time Value of Money
72. Suppose you put $100 into a savings account today, the account pays a simple annual interest rate of 6 percent, but
compounded semiannually, and you withdraw $100 after 6 months. What would your ending balance be 20 years afte
initial $100 deposit was made?
a. $226.20
b. $115.35
c. $62.91
d. $9.50
e. $3.00
73. A bank pays a quoted annual (simple) interest rate of 8 percent. However, it pays interest (compounds) daily using a
365-day year. What is the effective annual rate of return?
a. 7.86%
b. 7.54%
c. 8.57%
d. 8.33%
e. 9.21%
74. You can deposit your savings at the Darlington National Bank, which offers to pay 12.6 percent interest
compounded monthly, or at the Bartlett Bank, which will pay interest of 11.5 percent compounded daily. (Assume
365 days in a year.) Which bank offers the higher effective annual rate?
a. Darlington National Bank.
b. Bartlett Bank.
c. Both banks offer the same effective rate.
d. Cannot be determined from the information provided.
e. Workable only if the banks use the same compounding period.
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Chapter 4 – Time Value of Money
75. You have just taken out a 30-year, $120,000 mortgage on your new home. This mortgage is to be repaid in 360 equal
of-month installments. If each of the monthly installments is $1,500, what is the effective annual interest rate on this
mortgage?
a. 15.87%
b. 14.75%
c. 13.38%
d. 16.25%
e. 16.49%