Chapter 04: Time Value of Money
116. Which of the following statements is CORRECT?
a. Time lines cannot be constructed where some of the payments constitute an annuity but others are unequal and
thus are not part of the annuity.
b. A time line is not meaningful unless all cash flows occur annually.
c. Time lines are not useful for visualizing complex problems prior to doing actual calculations.
d. Time lines can be constructed to deal with situations where some of the cash flows occur annually but others
occur quarterly.
e. Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for
ordinary annuities.
117. Which of the following statements is CORRECT?
a. A time line is not meaningful unless all cash flows occur annually.
b. Time lines are not useful for visualizing complex problems prior to doing actual calculations.
c. Time lines cannot be constructed to deal with situations where some of the cash flows occur annually but others
occur quarterly.
d. Time lines can only be constructed for annuities where the payments occur at the end of the periods, i.e., for
ordinary annuities.
e. Time lines can be constructed where some of the payments constitute an annuity but others are unequal and thus
are not part of the annuity.
Chapter 04: Time Value of Money
118. Suppose you earned a $275,000 bonus this year 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
119. Your aunt wants to retire and has $375,000. She expects to live for another 25 years and to earn 7.5% on her invested
funds. How much could she 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
Chapter 04: Time Value of Money
120. Your aunt wants to retire and has $375,000. She expects to live for another 25 years, and she also expects to earn
7.5% on her invested funds. How much could she 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
121. You were left $100,000 in a trust fund set up by your grandfather. The fund 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
Chapter 04: Time Value of Money
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122. 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
123. Your uncle just won the weekly lottery, receiving $375,000, which he invested at a 7.5% annual rate. He now has
decided to retire, and he wants to withdraw $35,000 at the end of each year, starting at the end of this year. What is the
maximum number of whole payments that can be withdrawn before the account is exhausted, i.e., before the account
balance would become negative? (Hint: Round down to the nearest whole number.)
a. 22
Chapter 04: Time Value of Money
b. 23
c. 24
d. 25
e. 26
124. 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, beginning 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. What is the maximum number of $35,000 withdrawals that he can make and still have at least
$25,000 left in the account? (Hint: If your solution for N is not an integer, round down to the nearest whole number.)
a. 12
b. 13
c. 14
d. 15
e. 16
Chapter 04: Time Value of Money
125. Your Aunt Elsa 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. What is the maximum number of whole payments that can be withdrawn
before the account is exhausted, i.e., before the account balance would become negative? (Hint: Round down to the
nearest whole number.)
a. 18
b. 19
c. 20
d. 21
e. 22
126. 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. When she makes her last withdrawal (at the beginning of a year), she also
wants to have enough left in the account so that you can make a final withdrawal of $50,000 at the end of that year (her
last withdrawal is at the beginning of the year, your withdrawal is at the end of that same year). What is the maximum
number of $45,000 withdrawals that she can make and still have enough in the account so that you can make a $50,000
withdrawal at the end of the year of her last withdrawal? (Hint: If your solution for N is not an integer, round down to the
nearest whole number.)
a. 13
b. 14
c. 15
d. 16
e. 17
Chapter 04: Time Value of Money
127. 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%
128. 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%
Chapter 04: Time Value of Money
c. 4.17%
d. 4.58%
e. 5.04%
129. 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 open a new restaurant, 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%
Chapter 04: Time Value of Money
130. Your Green Investment Tips subscription is about to expire. You plan to subscribe to the magazine for the rest of
your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for
$850, also payable immediately. Assuming that you can earn 6.0% on your funds and that the annual renewal rate will
remain constant, how many years must you live to make the lifetime subscription the better buy?
a. 7.48
b. 8.80
c. 10.35
d. 12.18
e. 14.33
131. You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th
month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate
will you be earning?
a. 7.62%
b. 8.00%
c. 8.40%
d. 8.82%
e. 9.26%
Chapter 04: Time Value of Money
132. Which of the following statements is CORRECT?
a. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the
textbook defines as a variable annuity.
b. The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
c. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an
annuity.
d. The cash flows for an annuity due must all occur at the ends of the periods.
e. The cash flows for an annuity must all be equal, and they must occur at regular intervals, such as once a year or
once a month.
133. Which of the following statements is CORRECT?
a. If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the
textbook defines as a variable annuity.
b. The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
c. If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an
annuity.
d. The cash flows for an annuity due must all occur at the beginning of the periods.
e. The cash flows for an annuity may vary from period to period, but they must occur at regular intervals, such as
once a year or once a month.
Chapter 04: Time Value of Money
134. Which of the following statements is CORRECT?
a. If CF0 is positive and all the other CFs are negative, then you cannot solve for I.
b. If you have a series of cash flows, each of which is positive, you can solve for I, where the solution value of I
causes the PV of the cash flows to equal the cash flow at Time 0.
c. If you have a series of cash flows, and CF0 is negative but each of the following CFs is positive, you can solve for
I, but only if the sum of the undiscounted cash flows exceeds the cost.
d. To solve for I, one must identify the value of I that causes the PV of the positive CFs to equal the absolute value
of the PV of the negative CFs. This is, essentially, a trial-and-error procedure that is easy with a computer or financial
calculator but quite difficult otherwise.
e. If you solve for I and get a negative number, then you must have made a mistake.
135. Which of the following statements is CORRECT?
a. If CF0 is positive and all the other CFs are negative, then you can still solve for I.
b. If you have a series of cash flows, each of which is positive, you can solve for I, where the solution value of I
causes the PV of the cash flows to equal the cash flow at Time 0.
c. If you have a series of cash flows, and CF0 is negative but each of the following CFs is positive, you can solve for
I, but only if the sum of the undiscounted cash flows exceeds the cost.
d. To solve for I, one must identify the value of I that causes the PV of the positive CFs to equal the absolute value
of the FV of the negative CFs. It is impossible to find the value of I without a computer or financial calculator.
e. If you solve for I and get a negative number, then you must have made a mistake.
Chapter 04: Time Value of Money
136. Your sister 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%
137. 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%
Chapter 04: Time Value of Money
138. You have just purchased a U.S. Treasury 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 will you earn on this bond?
a. 4.37%
b. 4.86%
c. 5.40%
d. 6.00%
e. 6.60%
139. You have purchased a U.S. Treasury 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 will you earn on this bond?
a. 3.82%
b. 4.25%
Chapter 04: Time Value of Money
c. 4.72%
d. 5.24%
e. 5.77%
140. Ten years ago, Kronan Corporation 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%
Chapter 04: Time Value of Money
141. Wildwoods, Inc. earned $1.50 per share five years ago. 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%
142. You have $5,000 invested in a bank that pays 3.8% annually. How long will it take for your funds to triple?
a. 23.99
b. 25.26
c. 26.58
d. 27.98
e. 29.46
Chapter 04: Time Value of Money
143. Your bank pays 4% interest annually. You have $2,500 invested in the bank. How long will it take for your funds to
double?
a. 14.39
b. 15.15
c. 15.95
d. 16.79
e. 17.67
144. Brockman Corporation’s earnings per share were $3.50 last year, 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 Brockman’s EPS to triple?
a. 9.29
b. 10.33
c. 11.47
d. 12.75
e. 14.02