Chapter 5: Time Value of Money M/C Problems Page 155
73. How much would $100, growing at 5% per year, be worth after 75 years?
a. $3,689.11
b. $3,883.27
c. $4,077.43
d. $4,281.30
e. $4,495.37
74. You deposit $1,000 today in a savings account that pays 3.5% interest,
compounded annually. How much will your account be worth at the end of
25 years?
a. $2,245.08
b. $2,363.24
c. $2,481.41
d. $2,605.48
e. $2,735.75
75. You deposit $500 today in a savings account that pays 3.5% interest,
compounded annually. How much will your account be worth at the end of
25 years?
a. $1,122.54
b. $1,181.62
c. $1,240.70
d. $1,302.74
e. $1,367.88
76. Suppose a State of New York bond will pay $1,000 ten years from now.
If the going interest rate on these 10-year bonds is 5.5%, how much is
the bond worth today?
a. $585.43
b. $614.70
c. $645.44
d. $677.71
e. $711.59
77. Suppose a State of California bond will pay $1,000 eight years from
now. If the going interest rate on these 8-year bonds is 5.5%, how
much is the bond worth today?
a. $651.60
b. $684.18
c. $718.39
d. $754.31
e. $792.02
Page 156 M/C Problems Chapter 5: Time Value of Money
78. How much would $20,000 due in 50 years be worth today if the discount
rate were 7.5%?
a. $438.03
b. $461.08
c. $485.35
d. $510.89
e. $537.78
79. How much would $5,000 due in 25 years be worth today if the discount
rate were 5.5%?
a. $1,067.95
b. $1,124.16
c. $1,183.33
d. $1,245.61
e. $1,311.17
80. Suppose a U.S. treasury bond will pay $2,500 five years from now. If
the going interest rate on 5-year treasury bonds is 4.25%, how much is
the bond worth today?
a. $1,928.78
b. $2,030.30
c. $2,131.81
d. $2,238.40
e. $2,350.32
81. Suppose an Exxon Corporation bond will pay $4,500 ten years from now.
If the going interest rate on safe 10-year bonds is 4.25%, how much is
the bond worth today?
a. $2,819.52
b. $2,967.92
c. $3,116.31
d. $3,272.13
e. $3,435.74
82. Suppose the U.S. Treasury offers to sell you a bond for $747.25. No
payments will be made until the bond matures 5 years from now, at which
time it will be redeemed for $1,000. What interest rate would you earn
if you bought this bond at the offer price?
a. 4.37%
b. 4.86%
c. 5.40%
d. 6.00%
e. 6.60%
Chapter 5: Time Value of Money M/C Problems Page 157
83. Suppose the U.S. Treasury offers to sell you a bond for $3,000. No
payments will be made until the bond matures 10 years from now, at
which time it will be redeemed for $5,000. What interest rate would
you earn if you bought this bond at the offer price?
a. 3.82%
b. 4.25%
c. 4.72%
d. 5.24%
e. 5.77%
84. Ten years ago, Lucas Inc. earned $0.50 per share. Its earnings this
year were $2.20. What was the growth rate in earnings per share (EPS)
over the 10-year period?
a. 15.17%
b. 15.97%
c. 16.77%
d. 17.61%
e. 18.49%
85. Five years ago, Weed Go Inc. earned $1.50 per share. Its earnings this
year were $3.20. What was the growth rate in earnings per share (EPS)
over the 5-year period?
a. 15.54%
b. 16.36%
c. 17.18%
d. 18.04%
e. 18.94%
86. Janice has $5,000 invested in a bank that pays 3.8% annually. How long
will it take for her funds to triple?
a. 23.99
b. 25.26
c. 26.58
d. 27.98
e. 29.46
87. Bob has $2,500 invested in a bank that pays 4% annually. How long will
it take for his funds to double?
a. 14.39
b. 15.15
c. 15.95
d. 16.79
e. 17.67
Page 158 M/C Problems Chapter 5: Time Value of Money
88. Last year Thomson Inc’s earnings per share were $3.50, and its growth
rate during the prior 5 years was 9.0% per year. If that growth rate
were maintained, how many years would it take for Thomson’s EPS to
triple?
a. 9.29
b. 10.33
c. 11.47
d. 12.75
e. 14.02
89. You plan to invest in securities that pay 8.0%, compounded annually.
If you invest $5,000 today, how many years will it take for your
investment to grow to $9,140.20?
a. 5.14
b. 5.71
c. 6.35
d. 7.05
e. 7.84
90. You plan to invest in bonds that pay 6.0%, compounded annually. If you
invest $10,000 today, how many years will it take for your investment
to grow to $30,000?
a. 12.37
b. 13.74
c. 15.27
d. 16.97
e. 18.85
91. You want to buy a new sports car 3 years from now, and you plan to save
$4,200 per year, beginning one year from today. You will deposit your
savings in an account that pays 5.2% interest. How much will you have
just after you make the 3rd deposit, 3 years from now?
a. $11,973
b. $12,603
c. $13,267
d. $13,930
e. $14,626
92. You want to buy a new ski boat 2 years from now, and you plan to save
$8,200 per year, beginning one year from today. You will deposit your
savings in an account that pays 6.2% interest. How much will you have
just after you make the 2nd deposit, 2 years from now?
a. $15,260
b. $16,063
Chapter 5: Time Value of Money M/C Problems Page 159
c. $16,908
d. $17,754
e. $18,642
93. You want to go to Europe 5 years from now, and you can save $3,100 per
year, beginning one year from today. You plan to deposit the funds in
a mutual fund that you think will return 8.5% per year. Under these
conditions, how much would you have just after you make the 5th
deposit, 5 years from now?
a. $18,369
b. $19,287
c. $20,251
d. $21,264
e. $22,327
94. You want to quit your job and go back to school for a law degree 4
years from now, and you plan to save $3,500 per year, beginning
immediately. You will make 4 deposits in an account that pays 5.7%
interest. Under these assumptions, how much will you have 4 years from
today?
a. $16,112
b. $16,918
c. $17,763
d. $18,652
e. $19,584
95. You want to quit your job and return to school for an MBA degree 3
years from now, and you plan to save $7,000 per year, beginning
immediately. You will make 3 deposits in an account that pays 5.2%
interest. Under these assumptions, how much will you have 3 years from
today?
a. $20,993
b. $22,098
c. $23,261
d. $24,424
e. $25,645
96. What is the PV of an ordinary annuity with 10 payments of $2,700 if the
appropriate interest rate is 5.5%?
a. $16,576
b. $17,449
c. $18,367
d. $19,334
e. $20,352
Page 160 M/C Problems Chapter 5: Time Value of Money
97. What is the PV of an ordinary annuity with 5 payments of $4,700 if the
appropriate interest rate is 4.5%?
a. $16,806
b. $17,690
c. $18,621
d. $19,601
e. $20,633
Chapter 5: Time Value of Money M/C Problems Page 161
98. You have a chance to buy an annuity that pays $2,500 at the end of each
year for 3 years. You could earn 5.5% on your money in other
investments with equal risk. What is the most you should pay for the
annuity?
a. $5,493.71
b. $5,782.85
c. $6,087.21
d. $6,407.59
e. $6,744.83
99. You just inherited some money, and a broker offers to sell you an
annuity that pays $5,000 at the end of each year for 20 years. You
could earn 5% on your money in other investments with equal risk. What
is the most you should pay for the annuity?
a. $50,753
b. $53,424
c. $56,236
d. $59,195
e. $62,311
100. Your aunt is about to retire, and she wants to sell some of her stock
and buy an annuity that will provide her with income of $50,000 per
year for 30 years, beginning a year from today. The going rate on such
annuities is 7.25%. How much would it cost her to buy such an annuity
today?
a. $574,924
b. $605,183
c. $635,442
d. $667,214
e. $700,575
101. What is the PV of an annuity due with 5 payments of $2,500 at an
interest rate of 5.5%?
a. $11,262.88
b. $11,826.02
c. $12,417.32
d. $13,038.19
e. $13,690.10
102. What’s the present value of a perpetuity that pays $250 per year if the
appropriate interest rate is 5%?
a. $4,750
b. $5,000
c. $5,250
Page 162 M/C Problems Chapter 5: Time Value of Money
d. $5,513
e. $5,788
Chapter 5: Time Value of Money M/C Problems Page 163
103. What’s the rate of return you would earn if you paid $950 for a
perpetuity that pays $85 per year?
a. 8.95%
b. 9.39%
c. 9.86%
d. 10.36%
e. 10.88%
104. You have a chance to buy an annuity that pays $550 at the beginning of
each year for 3 years. You could earn 5.5% on your money in other
investments with equal risk. What is the most you should pay for the
annuity?
a. $1,412.84
b. $1,487.20
c. $1,565.48
d. $1,643.75
e. $1,725.94
105. You have a chance to buy an annuity that pays $5,000 at the beginning
of each year for 5 years. You could earn 4.5% on your money in other
investments with equal risk. What is the most you should pay for the
annuity?
a. $20,701
b. $21,791
c. $22,938
d. $24,085
e. $25,289
106. Your uncle is about to retire, and he wants to buy an annuity that will
provide him with $75,000 of income a year for 20 years, with the first
payment coming immediately. The going rate on such annuities is 5.25%.
How much would it cost him to buy the annuity today?
a. $ 825,835
b. $ 869,300
c. $ 915,052
d. $ 963,213
e. $1,011,374
107. Your father is about to retire, and he wants to buy an annuity that
will provide him with $85,000 of income a year for 25 years, with the
first payment coming immediately. The going rate on such annuities is
5.15%. How much would it cost him to buy the annuity today?
a. $1,063,968
b. $1,119,966
Page 164 M/C Problems Chapter 5: Time Value of Money
c. $1,178,912
d. $1,240,960
e. $1,303,008
108. You inherited an oil well that will pay you $25,000 per year for 25
years, with the first payment being made today. If you think a fair
return on the well is 7.5%, how much should you ask for it if you
decide to sell it?
a. $284,595
b. $299,574
c. $314,553
d. $330,281
e. $346,795
109. Sam was injured in an accident, and the insurance company has offered
him the choice of $25,000 per year for 15 years, with the first payment
being made today, or a lump sum. If a fair return is 7.5%, how large
must the lump sum be to leave him as well off financially as with the
annuity?
a. $225,367
b. $237,229
c. $249,090
d. $261,545
e. $274,622
110. What’s the present value of a 4–year ordinary annuity of $2,250 per
year plus an additional $3,000 at the end of Year 4 if the interest
rate is 5%?
a. $ 8,509
b. $ 8,957
c. $ 9,428
d. $ 9,924
e. $10,446
111. Suppose you inherited $275,000 and invested it at 8.25% per year. How
much could you withdraw at the end of each of the next 20 years?
a. $28,532
b. $29,959
c. $31,457
d. $33,030
e. $34,681
112. Your uncle has $375,000 and wants to retire. He expects to live for
another 25 years and to earn 7.5% on his invested funds. How much
Chapter 5: Time Value of Money M/C Problems Page 165
could he withdraw at the end of each of the next 25 years and end up
with zero in the account?
a. $28,843.38
b. $30,361.46
c. $31,959.43
d. $33,641.50
e. $35,323.58
113. Your uncle has $375,000 and wants to retire. He expects to live for
another 25 years, and he also expects to earn 7.5% on his invested
funds. How much could he withdraw at the beginning of each of the next
25 years and end up with zero in the account?
a. $28,243.21
b. $29,729.70
c. $31,294.42
d. $32,859.14
e. $34,502.10
114. Your grandmother just died and left you $100,000 in a trust fund that
pays 6.5% interest. You must spend the money on your college
education, and you must withdraw the money in 4 equal installments,
beginning immediately. How much could you withdraw today and at the
beginning of each of the next 3 years and end up with zero in the
account?
a. $24,736
b. $26,038
c. $27,409
d. $28,779
e. $30,218
115. Suppose you inherited $275,000 and invested it at 8.25% per year. How
much could you withdraw at the beginning of each of the next 20 years?
a. $22,598.63
b. $23,788.03
c. $25,040.03
d. $26,357.92
e. $27,675.82
116. Your father’s employer was just acquired, and he was given a severance
payment of $375,000, which he invested at a 7.5% annual rate. He now
plans to retire, and he wants to withdraw $35,000 at the end of each
year, starting at the end of this year. How many years will it take to
exhaust his funds, i.e., run the account down to zero?
a. 22.50
b. 23.63
Page 166 M/C Problems Chapter 5: Time Value of Money
c. 24.81
d. 26.05
e. 27.35
Chapter 5: Time Value of Money M/C Problems Page 167
117. Your uncle has $300,000 invested at 7.5%, and he now wants to retire.
He wants to withdraw $35,000 at the end of each year, starting at the
end of this year. He also wants to have $25,000 left to give you when
he ceases to withdraw funds from the account. For how many years can
he make the $35,000 withdrawals and still have $25,000 left in the end?
a. 14.21
b. 14.96
c. 15.71
d. 16.49
e. 17.32
118. Your Aunt Ruth has $500,000 invested at 6.5%, and she plans to retire.
She wants to withdraw $40,000 at the beginning of each year, starting
immediately. How many years will it take to exhaust her funds, i.e.,
run the account down to zero?
a. 18.62
b. 19.60
c. 20.63
d. 21.71
e. 22.86
119. Your aunt has $500,000 invested at 5.5%, and she now wants to retire.
She wants to withdraw $45,000 at the beginning of each year, beginning
immediately. She also wants to have $50,000 left to give you when she
ceases to withdraw funds from the account. For how many years can she
make the $45,000 withdrawals and still have $50,000 left in the end?
a. 15.54
b. 16.36
c. 17.22
d. 18.08
e. 18.99
120. Suppose you just won the state lottery, and you have a choice between
receiving $2,550,000 today or a 20-year annuity of $250,000, with the
first payment coming one year from today. What rate of return is built
into the annuity? Disregard taxes.
a. 7.12%
b. 7.49%
c. 7.87%
d. 8.26%
e. 8.67%
Page 168 M/C Problems Chapter 5: Time Value of Money
121. Your girlfriend just won the Florida lottery. She has the choice of
$15,000,000 today or a 20-year annuity of $1,050,000, with the first
payment coming one year from today. What rate of return is built into
the annuity?
a. 3.44%
b. 3.79%
c. 4.17%
d. 4.58%
e. 5.04%
122. Assume that you own an annuity that will pay you $15,000 per year for
12 years, with the first payment being made today. You need money
today to start a new business, and your uncle offers to give you
$120,000 for the annuity. If you sell it, what rate of return would
your uncle earn on his investment?
a. 6.85%
b. 7.21%
c. 7.59%
d. 7.99%
e. 8.41%
123. What annual payment must you receive in order to earn a 6.5% rate of
return on a perpetuity that has a cost of $1,250?
a. $77.19
b. $81.25
c. $85.31
d. $89.58
e. $94.06
124. What is the present value of the following cash flow stream at a rate
of 6.25%?
Years: 0 1 2 3 4
| | | | |
CFs: $0 $75 $225 $0 $300
a. $411.57
b. $433.23
c. $456.03
d. $480.03
e. $505.30
Chapter 5: Time Value of Money M/C Problems Page 169
125. What is the present value of the following cash flow stream at a rate
of 12.0%?
Years: 0 1 2 3 4
| | | | |
CFs: $0 $1,500 $3,000 $4,500 $6,000
a. $ 9,699
b. $10,210
c. $10,747
d. $11,284
e. $11,849
126. What is the present value of the following cash flow stream at a rate
of 8.0%?
Years: 0 1 2 3
| | | |
CFs: $750 $2,450 $3,175 $4,400
a. $7,917
b. $8,333
c. $8,772
d. $9,233
e. $9,695
127. You sold a car and accepted a note with the following cash flow stream
as your payment. What was the effective price you received for the car
assuming an interest rate of 6.0%?
Years: 0 1 2 3 4
| | | | |
CFs: $0 $1,000 $2,000 $2,000 $2,000
a. $5,987
b. $6,286
c. $6,600
d. $6,930
e. $7,277
128. At a rate of 6.5%, what is the future value of the following cash flow
stream?
Years: 0 1 2 3 4
| | | | |
CFs: $0 $75 $225 $0 $300
a. $526.01
b. $553.69
c. $582.83
Page 170 M/C Problems Chapter 5: Time Value of Money
d. $613.51
e. $645.80
129. Your father paid $10,000 (CF at t = 0) for an investment that promises
to pay $750 at the end of each of the next 5 years, then an additional
lump sum payment of $10,000 at the end of the 5th year. What is the
expected rate of return on this investment?
a. 6.77%
b. 7.13%
c. 7.50%
d. 7.88%
e. 8.27%
130. You are offered a chance to buy an asset for $7,250 that is expected to
produce cash flows of $750 at the end of Year 1, $1,000 at the end of
Year 2, $850 at the end of Year 3, and $6,250 at the end of Year 4.
What rate of return would you earn if you bought this asset?
a. 4.93%
b. 5.19%
c. 5.46%
d. 5.75%
e. 6.05%
131. What’s the future value of $1,500 after 5 years if the appropriate
interest rate is 6%, compounded semiannually?
a. $1,819
b. $1,915
c. $2,016
d. $2,117
e. $2,223
132. What’s the present value of $4,500 discounted back 5 years if the
appropriate interest rate is 4.5%, compounded semiannually?
a. $3,089
b. $3,251
c. $3,422
d. $3,602
e. $3,782
133. What’s the future value of $1,200 after 5 years if the appropriate
interest rate is 6%, compounded monthly?
a. $1,537.69
b. $1,618.62
c. $1,699.55
Chapter 5: Time Value of Money M/C Problems Page 171
d. $1,784.53
e. $1,873.76
Page 172 M/C Problems Chapter 5: Time Value of Money
134. What’s the present value of $1,525 discounted back 5 years if the
appropriate interest rate is 6%, compounded monthly?
a. $ 969
b. $1,020
c. $1,074
d. $1,131
e. $1,187
135. Master Card and other credit card issuers must by law print the Annual
Percentage Rate (APR) on their monthly statements. If the APR is
stated to be 18.00%, with interest paid monthly, what is the card’s
EFF%?
a. 18.58%
b. 19.56%
c. 20.54%
d. 21.57%
e. 22.65%
136. Riverside Bank offers to lend you $50,000 at a nominal rate of 6.5%,
compounded monthly. The loan (principal plus interest) must be repaid
at the end of the year. Midwest Bank also offers to lend you the
$50,000, but it will charge an annual rate of 7.0%, with no interest
due until the end of the year. How much higher or lower is the
effective annual rate charged by Midwest versus the rate charged by
Riverside?
a. 0.52%
b. 0.44%
c. 0.36%
d. 0.30%
e. 0.24%
137. Suppose Community Bank offers to lend you $10,000 for one year at a
nominal annual rate of 8.00%, but you must make interest payments at
the end of each quarter and then pay off the $10,000 principal amount
at the end of the year. What is the effective annual rate on the loan?
a. 8.24%
b. 8.45%
c. 8.66%
d. 8.88%
e. 9.10%
138. Suppose a bank offers to lend you $10,000 for 1 year on a loan contract
that calls for you to make interest payments of $250.00 at the end of
each quarter and then pay off the principal amount at the end of the
year. What is the effective annual rate on the loan?
Chapter 5: Time Value of Money M/C Problems Page 173
a. 8.46%
b. 8.90%
c. 9.37%
d. 9.86%
e. 10.38%
139. Charter Bank pays a 4.50% nominal rate on deposits, with monthly
compounding. What effective annual rate (EFF%) does the bank pay?
a. 3.72%
b. 4.13%
c. 4.59%
d. 5.05%
e. 5.56%
140. Suppose your credit card issuer states that it charges a 15.00% nominal
annual rate, but you must make monthly payments, which amounts to
monthly compounding. What is the effective annual rate?
a. 15.27%
b. 16.08%
c. 16.88%
d. 17.72%
e. 18.61%
141. Pace Co. borrowed $20,000 at a rate of 7.25%, simple interest, with
interest paid at the end of each month. The bank uses a 360-day year.
How much interest would Pace have to pay in a 30-day month?
a. $120.83
b. $126.88
c. $133.22
d. $139.88
e. $146.87
142. Suppose you deposited $5,000 in a bank account that pays 5.25% with
daily compounding based on a 360-day year. How much would be in the
account after 8 months, assuming each month has 30 days?
a. $5,178.09
b. $5,436.99
c. $5,708.84
d. $5,994.28
e. $6,294.00
143. Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4
equal installments at the end of each of the next 4 years. How large
would your payments be?
Page 174 M/C Problems Chapter 5: Time Value of Money
a. $3,704.02
b. $3,889.23
c. $4,083.69
d. $4,287.87
e. $4,502.26