Chapter 5: The Time Value of Money
69. Your brother, who is 6 years old, just received a trust fund that will be worth $25,000 when he is 21 years old.
If the fund earns 10 percent interest compounded annually, what is the value of the fund today?
a. $104,602
b. $6,575
c. $5,975
d. $6,875
70. California Life has just offered you a single premium annuity for $5,000 that will pay $5,144.12 per year for
20 years, the first payment being received exactly 31 years from today. What is the implied rate of return on
this annuity?
a. 7%
b. 8%
c. 9%
d. 6.5%
71. Jackie plans to open her own book store in 10 years. To raise the “seed” money she has committed $10,000 she
now has in a mutual fund. In addition, she plans to save $2,000 per year (end of year) for the next 5 years and
$3,000 per year (end of year) for the following 5 years. How much “seed” money will Jackie have in 10
years if the investments earn 10 percent per year compounded annually?
a. $76,129
b. $63,925
c. $44,255
d. $159,370
Chapter 5: The Time Value of Money
72. You just purchased a new $25,000 car and agreed to pay for the car in 50 monthly payments. If the monthly
interest rate is 1 percent, what is your total financing cost?
a. $637.82
b. $12,500
c. $574.25
d. $6,891
73. A zero coupon bond with a $1,000 par value (future value) is selling for $356 and matures in 12 years. What is
the implied discount rate (yield to maturity)?
a. 9%
b. 9.36%
c. 9.12%
d. 9.4%
74. Roy, who has just turned 40, would like to have an annual annuity of $20,000 paid over a 20 year period, the
first payment occurring on his 66th birthday. How much must Roy save each year (end of year) for the next 25
years to have this annuity, if the investment will earn 12 percent compounded annually?
a. $16,000
b. $19,046
c. $1,120
d. $944.10
Chapter 5: The Time Value of Money
75. Your local bank offers 4-year certificates of deposit (CD) at a 12 percent annual nominal interest rate compounded
quarterly. Determine how much additional interest you will earn over 4 years on a $10,000 CD that is compounded
quarterly compared with one that is compounded annually.
a. $6,050
b. $0
c. $310
d. $220
76. How much will you have at the end of 5 years in a European vacation account if you deposit $200 a month in
an account that is paying a nominal 12 percent per year, compounded monthly?
a. $16,334
b. $15,247
c. $16,497
d. $15,817
77. You wish to save $500,000 in the next 25 years. You notice that a corporate bond fund earns about 11 percent
per year and that is where you put your savings. How much must you save each year to obtain your goal?
a. $20,000.00
b. $ 3,749.98
c. $ 4,370.13
d. $ 2,000.00
Chapter 5: The Time Value of Money
78. You plan to lease a Saab automobile that sells for $22,657 and has no salvage value. If the monthly lease is
$499, with the first of 60 payments due immediately. What is the implied annual interest rate on your lease?
a. 10%
b. 11.5%
c. 12%
d. 13.5%
79. What is the present value of the following net cash flows if the discount rate is 12%:
Year Cash Flow
1-5 $10,000 each year
6-10 $15,000 each year
11-15 $17,000 each year
a. $151,400
b. $ 86,462
c. $144,037
d. $ 79,252
80. If the discount rate is 12%, what is the present value of the following cash flows:
Year Cash Flow
1 $10,000
2 $11,000
3 $12,000
4 $13,000
5 $14,000
6-15 $15,000 each year
a. $144,618
b. $127,923
c. $127,197
d. $ 90, 537
Chapter 5: The Time Value of Money
81. You wish to have $10,000 per year as a retirement supplement for 20 years (from age 65-85). You are now 40
years old. How much must you save each year for the next 25 years if you assume your savings will earn 12%
annually?
a. $560.17
b. $1,499.99
c. $5,403.87
d. none of these
82. What is the present value of the following net cash flows if the discount rate is 10%?
Year Net Cash Flow
1–10 $20,000 each year
11–15 $15,000 each year
16–20 $10,000 each year
a. $217,675
b. $153,895
c. $322,130
d. $167,515
83. The Summer Breeze Hotel borrowed $100,000 from the Meadowlands Bank to pay for a new air conditioning
system. The loan is for a period of 5 years at an interest rate of 10% and requires 5 equal end-of–year payments
that include both principal and interest on the outstanding balance. What will be the outstanding balance after
the third payment?
a. $60,000
b. $20,865
c. $45,788
d. $50,866
Chapter 5: The Time Value of Money
84. Keith Stone has a 10-year old daughter, Kate, who will be entering college in 8 years. Keith estimates college costs
to be $16,000, $17,000, $18,000 and $19,000 payable at the beginning of each of Kate’s four years in college. How
much must Keith save each year (assume end of year payments) for each of the next 8 years to have enough savings
to pay for Kate‘s education? Assume Keith can earn 9% on his savings.
a. $5,569
b. $7,720
c. $5,108
d. $7,677
85. 1st Bank offers you a car loan at an annual interest rate of 10% compounded monthly. What effective annual
interest rate is the bank charging you?
a. 10.38%
b. 10.42%
c. 10.45%
d. 10.47%
86. Your monthly statement from your bank credit card shows that the monthly rate of interest is 1.5%. What is the
annual effective rate of interest you are being charged on your credit card?
a. 18.00%
b. 18.64%
c. 19.56%
d. 29.74%
Chapter 5: The Time Value of Money
87. What monthly rate of interest will yield an annual effective rate of interest of 14%?
a. 1.17%
b. 1.10%
c. 1.08%
d. 1.14%
88. What is the present value of $1,000 received 2 years from today if the nominal interest rate is 9% and compounded
monthly?
a. $842
b. $914
c. $833
d. $836
89. Cosmos Touring wishes to replace its luxury bus in 10 years by accumulating funds in a special account. The new
bus is expected to cost $180,000. How much must Cosmos put into the fund in equal, end-of-year amounts if
earnings are expected to be 8% for the first 4 years and 10% thereafter?
a. $12,107
b. $11,465
c. $9,901
d. $14,727
Chapter 5: The Time Value of Money
90. Al Corbin is 25 years old today and he wishes to accumulate enough money over the next 35 years to provide for a
20 year retirement annuity of $100,000 at the beginning of each year, starting with his 60th birthday. He can save
$2,000 at the end of each of the next 10 years and $3,000 each year for the following 10 years. How much must
he save each year at the end of years 21 through 35 to obtain his goal? Assume that the average rate of return
over the entire period will be 10%.
a. $9,642
b. $26,969
c. $12,321
d. $24,289
91. If a 16 year old high school student put $2,000 at the end of each year for 4 years into an IRA that earned a rate
of 9%, how much would she have accumulated by age 65? Assume funds are left to accumulate for 45 years (age
20 – 65) at 9%.
a. $442,014
b. $386,616
c. $1,767,995
d. $9,146
Chapter 5: The Time Value of Money
92. If your parents put $2,000 a year into an IRA account for you in each of your last 4 teenage years (age 16,17,18, and
19), how much would the IRA account have in it at your retirement 45 years later if the account earned 12% each
year? (Assume end-of-year payments.)
a. $1,569,758
b. $68,613
c. $3,457,169
d. $1,148,958
93. What is the value in 10 years of $10,000 deposited in an account earning 8% compounded monthly?
a. $33,004
b. $22,285
c. $102,530
d. $21,589
94. Assume you purchased a home and borrowed $100,000 at a rate of 8% compounded monthly over 30 years.
What is your monthly payment?
a. $917.77
b. $733.76
c. $666.67
d. $878.14
Chapter 5: The Time Value of Money
95. Inco purchased a computer for $200,000 and this machine is expected to generate annual cash flows of $48,271
over the next 5 years. What is the expected rate of return on this investment?
a. 8.84%
b. 26.58%
c. 6.61%
d. none of these
96. When you purchased a car, you borrowed $20,000 from the bank and agreed to make monthly payments of $423.17
for 5 years. What rate of interest is the bank charging you?
a. 9.82%
b. 5.00%
c. 25.39%
d. 10.00%
9.82% by calculator
97. When you purchased a car, you borrowed $20,000 from the bank at 9.20% and agreed to make monthly payments
for 3 years. What is your monthly payment?
a. $153.33
b. $637.86
c. $584.12
d. $559.78
Chapter 5: The Time Value of Money
98. What is the present value of the following mixed cash flow stream if interest is 6% (rounded)?
YEAR
CASH FLOW
1
$5,000
2
$8,000
3
$9,500
a. $25,370
b. $19,813
c. $21,225
d. $18,750
99. Which of the following statements is/are correct?
I. At 6% interest, the present value of: $400 for the first year, $600 for the second year, and $800
for the third year is $1,603.00.
II. The future value of the following mixed cash flow stream (if it is from an annuity due at 6%
interest):$400 for the first year, $600 for the second year, and $800 for the third year is $1,999
(rounded).
a. Only statement I is correct.
b. Only statement II is correct.
c. Both statements I and II are correct.
d. Neither statement I nor II is correct.
Chapter 5: The Time Value of Money
100. Based on the Rule of 72, what interest rate do you need to earn to double your money in 6 years?
a. 8%
b. 12%
c. 7%
d. 6%
101. Approximately how long would it take to double my money if I invest it now at 18%?
a. 6 years
b. 4 years
c. 12 years
d. It cannot be determined
102. Jenny Genius wants to purchase a new car. She knows that she can afford to pay $250 per month and that her
bank will charge her 8% interest on the car loan. She intends to pay off the car in five years. Interest will be
compounded monthly. Of the following, which is the most expensive vehicle in her price range that she could
consider?
a. A Taurus selling for $11,900
b. A Malibu selling for $12,320
c. A Civic selling for $14,670
d. A Celica selling for $17,500
Chapter 5: The Time Value of Money
103. Bill Swill decides to try his luck at Powerball where the projected winnings are $12,000,000. If he wins, he can
choose the annuity option (to be paid over 20 years) or a lump sum settlement that he can invest at 8% interest.
How much must the lump sum option be to make the lump sum option equal to the annuity option (rounded)?
a. $2,574,578
b. $1,743,620
c. $1,130,668
d. $1,200,000
104. Nukin’ Gnats Pest Control wants to offer a contract to its customers that would protect the property of their existing
customers against termite infestation. Should termites invade a customer’s home, Nukin’ Gnats will pay for the
repairs to the home provided the customer has maintained service with Nukin’ Gnats. The corporation must develop
an account with a value of $500,000. They will accumulate this account over three years, after which they will offer
this new contract provision. How much must be deposited annually (rounded amount) to accumulate the needed
funds if they can get 5% interest at their local bank?
a. $275,026
b. $158,604
c. $80,255
d. $97,985
105. Sherry Smart is buying a $350,000 home and will pay the mortgage monthly for 30 years. She has a good credit
score and has qualified for a 5.125% loan interest. How much will she be paying monthly for the home?
a. $2,013.67
b. $1,572.72
c. $1,318.69
d. $975.88
Chapter 5: The Time Value of Money
106. What is/are the difference(s) between simple interest and compound interest?
107. What is the difference between the nominal interest rate and the effective interest rate?
108. Why does an annuity due have a greater future value than a regular annuity – all things being equal?
109. Explain the concept of interest and compare it to rate of interest.
110. Compare the difference between compound interest and simple interest.
111. Explain a perpetuity and list some investment vehicles that can be perpetuities.
Chapter 5: The Time Value of Money
112. Explain the sinking fund problem.
113. What is the net present value rule?