Principles of Managerial Finance 8th Edition by Chad J. Zutter – Test Bank

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Principles of Managerial Finance, Brief Ed., 8e (Zutter/Smart)
Chapter 5 Time Value of Money
5.1 The role of time value in finance
1) The main idea behind the time value of money is that a dollar today is worth more than a
dollar in the future because ________.
A) inflation erodes the value of money over time
B) investors can earn a return on money they have today and thereby have more money in the
future
C) the future is more uncertain than the present
D) investors are impatient
Answer: B
Diff: 1
Topic: Basic Time Value Concepts
Learning Obj.: LG 1
Learning Outcome: F-03
AACSB: Reflective Thinking
2) You invest a certain amount of money today. The process of determining how much money
that investment will produce in the future is called ________.
A) discounting
B) compounding
C) present value
D) annuitizing the cash flow
Answer: B
Diff: 1
Topic: Basic Time Value Concepts
Learning Obj.: LG 1
Learning Outcome: F-03
AACSB: Reflective Thinking
3) The process of taking cash flow that is received or paid in the future and stating that cash flow
in present value terms is called discounting.
Answer: TRUE
Diff: 1
Topic: Basic Time Value Concepts
Learning Obj.: LG 1
Learning Outcome: F-03
AACSB: Reflective Thinking
2
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4) A certain investment that costs $10,000 today promises to pay you $10,500 in five years. This
investment ________.
A) is unambiguously a good investment
B) is unambiguously a bad investment
C) may be a good investment if the rate of return you can earn an alternative investments is very
low
D) may be a good investment if the rate of return you can earn on alternative investments is very
high
Answer: C
Diff: 1
Topic: Basic Time Value Concepts
Learning Obj.: LG 1
Learning Outcome: F-03
AACSB: Reflective Thinking
5) Since individuals generally have opportunities to earn positive rates of return on their funds,
the timing of cash flows does not have any significant economic consequences.
Answer: FALSE
Diff: 1
Topic: Role of Time Value in Finance
Learning Obj.: LG 1
Learning Outcome: F-03
AACSB: Analytical Thinking
6) The time value of money is based on the belief that a dollar that will be received at some
future date is worth more than a dollar today.
Answer: FALSE
Diff: 1
Topic: Role of Time Value in Finance
Learning Obj.: LG 1
Learning Outcome: F-03
AACSB: Analytical Thinking
5.2 Single amounts
1) For any positive interest rate, the future value of $100 increases with the passage of time.
Thus, the longer the period of time, the greater the future value.
Answer: TRUE
Diff: 1
Topic: Future Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
3
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2) Future value is the value of a future amount at the present time, found by applying compound
interest over a specified period of time.
Answer: FALSE
Diff: 1
Topic: Future Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
3) The greater the interest rate and the longer the period of time, the higher the present value.
Answer: FALSE
Diff: 1
Topic: Present Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
4) Everything else being equal, the higher the interest rate, the higher the future value.
Answer: TRUE
Diff: 1
Topic: Future Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
5) Future value increases with increases in the interest rate or the period of time funds are left on
deposit.
Answer: TRUE
Diff: 1
Topic: Future Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
6) Everything else being equal, the higher the discount rate, the higher the present value.
Answer: FALSE
Diff: 1
Topic: Present Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
4
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7) Everything else being equal, the longer the period of time, the lower the present value.
Answer: TRUE
Diff: 1
Topic: Present Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
8) ________ is the amount earned on a deposit that has become the part of the principal at the
end of a specified time period.
A) Discount interest
B) Compound interest
C) Primary interest
D) Future value
Answer: B
Diff: 1
Topic: Future Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
9) The future value of $100 received today and deposited at 6 percent for four years is closest to
________.
A) $126
B) $79
C) $124
D) $116
Answer: A
Diff: 1
Topic: Future Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
10) The future value of $200 received today and deposited at 8 percent for three years is
approximately ________.
A) $248
B) $252
C) $159
D) $253
Answer: B
Diff: 1
Topic: Future Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
5
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11) The present value of $100 to be received 10 years from today, assuming an opportunity cost
of 9 percent, is approximately ________.
A) $237
B) $190
C) $42
D) $10
Answer: C
Diff: 1
Topic: Present Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
12) The amount of money that would have to be invested today at a given interest rate over a
specified period in order to equal a future amount is called ________.
A) future value
B) present value
C) future value of an annuity
D) compounded value
Answer: B
Diff: 1
Topic: Present Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
13) The present value of $200 to be received 10 years from today, assuming an opportunity cost
of 10 percent, is approximately ________.
A) $50
B) $400
C) $519
D) $77
Answer: D
Diff: 1
Topic: Present Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
6
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14) The future value of a dollar ________ as the interest rate increases and ________ the longer
the money remains invested.
A) decreases; decreases
B) decreases; increases
C) increases; increases
D) increases; decreases
Answer: C
Diff: 1
Topic: Future Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
15) The annual rate of return is referred to as the ________.
A) discount rate
B) marginal rate
C) risk-free rate
D) marginal cost
Answer: A
Diff: 1
Topic: Basic Time Value Concepts
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
16) Your current income is $50,000 per year, and you would like to maintain your current
standard of living (i.e., your purchasing power) when you retire. If you expect to retire in 30
years and expect inflation to average 3% over the next 30 years, what amount of annual income
will you need to live at the same comfort level in 30 years?
A) $121,363
B) $95,000
C) $20,599
D) $51,500
Answer: A
Diff: 1
Topic: Future Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Reflective Thinking
7
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17) Calculate the future value of $4,600 received today if it is deposited at 9 percent for three
years.
Answer: FV = PV (1+ r)n = $4,600(1.09)3 = $5,957.13
Diff: 1
Topic: Future Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Reflective Thinking
18) Calculate the present value of $89,000 to be received in 15 years, assuming an opportunity
cost of 14 percent.
Answer: PV = 89,000(1.14)-15 = $12,468.59
Diff: 1
Topic: Present Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Analytical Thinking
19) Aunt Tillie has deposited $33,000 today in an account which will earn 10 percent annually.
She plans to leave the funds in this account for seven years earning interest. If the goal of this
deposit is to cover a future obligation of $65,000, what recommendation would you make to
Aunt Tillie?
Answer: FV = 33,000(1.1)7 = $64,307.66
Aunt Tillie will only have $64,308 at the end of seven years under the stated arrangement. She
must find an account with a higher interest rate or deposit a larger sum today.
The amount Aunt Tillie should invest today to receive $65,000 after 7 years, PV = 65,000 /
(1.1)7 = $33,355.28
Diff: 1
Topic: Future Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Reflective Thinking
20) China Manufacturing Agents, Inc. is preparing a five-year plan. Today, sales are $1,000,000.
If the growth rate in sales is projected to be 10 percent over the next five years, what will the
dollar amount of sales be in year five?
Answer: FV = 1,000,000(1.1)5 = $1,610,510
Diff: 1
Topic: Future Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Reflective Thinking
8
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21) Colin has inherited $6,000 from his grandmother. He would like to invest this money for two
years and then use the proceeds from that investment to buy a new high-end gaming computer
for $7,000. Will Colin have enough money to buy the computer if he deposits his money in an
account paying 8 percent compounded semiannually?
Answer: n = 2, m = 2, r = 8%
FV = 6,000(1+.08/2)2 × 2 = 6,000(1.04)4 = $7,019.15
Yes, Colin will have enough money to buy the computer.
Diff: 1
Topic: Future Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Reflective Thinking
22) Dan and Jia are have just purchased a condominium for $70,000. Since the condo is very
small, they hope to move into a single-family house in 5 years. How much will their condo be
worth in 5 years if inflation is expected to be 8 percent?
Answer: PV = $70,000, r = 8%, n = 5
FV = 70,000(1.08)5 = $102,852.97.
Diff: 1
Topic: Future Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Reflective Thinking
9
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23) Congratulations! You have just won the lottery! However, the lottery bureau has just
informed you that you can take your winnings in one of two ways. You can elect to receive a
payment of $1,000,000 now or a payment of $1,750,000 in five years. Assume you can earn 5%
on funds that you invest today. How much money would you have in five years if you take the
immediate $1,000,000 payment and invest it? What does this tell you about the wisdom of
selecting the immediate payment versus the future payment? Using the same 5% interest rate,
what is the present value of the $1,750,000 that you could receive in five years? What does this
calculation tell you about which lottery payout option you should choose? What do your results
suggest as a general rule for approaching such problems? (Make your choices based purely on
the time value of money.)
Answer: If you take the immediate $1 million and invest it, in five years you will have
$1,276,2282 ($1,000,000 × 1.055). Thus, you will have more money in five years if you wait and
take the lottery payment later rather than taking it now.
Similarly, the present value of the immediate payment = $1,000,000. The PV of the future
payment = $1,371,171 ($1,750,000 / 1.055). Thus, the present value of the payment that you
receive is greater if you wait five years to take the payout.
Based on both present values and future values, taking the payout in five years is the better
choice. Finding present values and future values are simply reverse processes of one another, and
choosing between two lump sums based on PV will always give the same result as choosing
between the same two lump sums based on FV.
Diff: 1
Topic: Present Value and Future Value
Learning Obj.: LG 2
Learning Outcome: F-03
AACSB: Reflective Thinking
5.3 Annuities
1) An annuity due is a stream of equal cash flows with each cash flow arriving at the beginning
of each period.
Answer: TRUE
Diff: 1
Topic: Annuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
2) An ordinary annuity is an annuity in which cash flows occur at the beginning of each period.
Answer: FALSE
Diff: 1
Topic: Annuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
10
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3) The future value of an annuity due is always greater than the future value of an otherwise
identical ordinary annuity for interest rates greater than zero.
Answer: TRUE
Diff: 2
Topic: Annuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
4) Which of the following is TRUE of annuities?
A) An ordinary annuity is an equal payment paid or received at the beginning of each period.
B) An annuity due is a payment paid or received at the beginning of each period that increases by
an equal amount each period.
C) An annuity due is an equal stream of cash flows that is paid or received at the beginning of
each period.
D) An ordinary annuity is an equal payment paid or received at the end of each period that
increases by an equal amount each period.
Answer: C
Diff: 1
Topic: Annuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
5) The present value of a $25,000 perpetuity at a 14 percent discount rate is ________.
A) $178,571
B) $285,000
C) $350,000
D) $219,298
Answer: A
Diff: 1
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
6) An annuity with an infinite life is called a(n) ________.
A) perpetuity
B) primia
C) option
D) deep discount
Answer: A
Diff: 1
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
11
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7) The present value of a $20,000 perpetuity at a 7 percent discount rate is ________.
A) $186,915
B) $285,714
C) $140,000
D) $325,000
Answer: B
Diff: 1
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
8) A(n) ________ is an annuity with an infinite life making continual annual payments.
A) amortized loan
B) principal
C) perpetuity
D) APR
Answer: C
Diff: 1
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
9) Bill plans to fund his individual retirement account (IRA) by contributing $2,000 at the end of
each year for the next 20 years. If Bill can earn 12 percent on his contributions, how much will
he have at the end of the twentieth year?
A) $19,293
B) $14,939
C) $40,000
D) $144,105
Answer: D
Diff: 1
Topic: Future Value of an Annuity
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
12
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10) Dan plans to fund his individual retirement account (IRA) by contributing $2,000 at the end
of each year for the next 10 years. If Dan can earn 10 percent on his contributions, how much
will he have at the end of the tenth year?
A) $12,289
B) $20,000
C) $31,875
D) $51,880
Answer: C
Diff: 1
Topic: Future Value of an Annuity
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
11) In comparing an ordinary annuity and an annuity due, which of the following is TRUE?
A) The future value of an annuity due is always greater than the future value of an otherwise
identical ordinary annuity.
B) The future value of an ordinary annuity is always greater than the future value of an otherwise
identical annuity due.
C) The present value of an annuity due is always less than the future value of an otherwise
identical ordinary annuity, since one less payment is received with an annuity due.
D) All things being equal, one would prefer to receive an ordinary annuity compared to an
annuity due.
Answer: A
Diff: 1
Topic: Future Value of an Annuity Due
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
12) The future value of a $2,000 annuity due deposited at 8 percent compounded annually for
each of the next 10 years is ________.
A) $28,973
B) $31,291
C) $14,494
D) $13,420
Answer: B
Diff: 2
Topic: Future Value of an Annuity Due
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
13
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13) The future value of a $10,000 annuity due deposited at 12 percent compounded annually for
each of the next 5 years is ________.
A) $36,050
B) $63,528
C) $40,376
D) $71,152
Answer: D
Diff: 2
Topic: Future Value of an Annuity Due
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
14) The future value of an ordinary annuity of $1,000 each year for 10 years, deposited at 3
percent, is ________.
A) $11,808.
B) $11,464.
C) $8,530.
D) $8,786.
Answer: B
Diff: 2
Topic: Future Value of an Annuity
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
15) The future value of an ordinary annuity of $2,000 each year for 10 years, deposited at 12
percent, is ________.
A) $35,097
B) $12,656
C) $39,309
D) $11,300
Answer: A
Diff: 2
Topic: Future Value of an Annuity
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
14
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16) A college received a contribution to its endowment fund of $2 million. It can never touch the
principal, but can use the earnings. At an assumed interest rate of 9.5 percent, how much can the
college earn to help its operations each year?
A) $95,000
B) $19,000
C) $190,000
D) $18,000
Answer: C
Diff: 2
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
17) The present value of a perpetual income stream increases when the discount rate ________.
A) increases
B) decreases
C) changing unpredictably
D) increasing proportionally
Answer: B
Diff: 1
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
18) The present value of an ordinary annuity of $350 each year for five years, assuming an
opportunity cost of 4 percent, is ________.
A) $1,620
B) $1,896
C) $1,971
D) $1,558
Answer: D
Diff: 1
Topic: Present Value of an Annuity
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
15
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19) The present value of an ordinary annuity of $2,350 each year for eight years, assuming an
opportunity cost of 11 percent, is ________.
A) $30,935
B) $27,870
C) $13,424
D) $12,093
Answer: D
Diff: 2
Topic: Present Value of an Annuity
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
20) A generous benefactor to a local ballet plans to make a one-time endowment that would
provide the ballet with $150,000 per year into perpetuity. The rate of interest is expected to be 5
percent for all future time periods. How large must the endowment be?
A) $300,000
B) $3,000,000
C) $750,000
D) $1,428,571
Answer: B
Diff: 2
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
21) A generous philanthropist plans to make a one-time endowment to a renowned heart research
center which would provide the facility with $250,000 per year into perpetuity. The rate of
interest is expected to be 8 percent for all future time periods. How large must the endowment
be?
A) $2,314,814
B) $2,000,000
C) $3,125,000
D) $3,000,000
Answer: C
Diff: 3
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
16
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22) Mary will receive $12,000 per year for the next 10 years as royalty for her work on a finance
book. What is the present value of her royalty income if the opportunity cost is 12 percent?
Assume that payments come at the end of each year.
A) $235,855
B) $67,803
C) $210,585
D) $75,939
Answer: B
Diff: 2
Topic: Present Value of an Annuity
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
23) To pay for her college education, Gina is saving $2,000 at the beginning of each year for the
next eight years in a bank account paying 12 percent interest. How much will Gina have in that
account at the end of 8th year?
A) $11,128
B) $9,935
C) $24,599
D) $27,551
Answer: D
Diff: 2
Topic: Future Value of an Annuity Due
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
24) James plans to fund his individual retirement account, beginning today, with 20 annual
deposits of $2,000. If he can earn an annual compound rate of 8 percent on his deposits, the
amount in the account 20 years from today will be ________.
A) $19,636
B) $91,524
C) $98,846
D) $21,207
Answer: C
Diff: 2
Topic: Future Value of an Annuity Due
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
17
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25) You have been offered a project paying $300 at the beginning of each year for the next 20
years. What is the maximum amount of money you would invest in this project if you expect 9
percent rate of return to your investment?
A) $2,739
B) $2,985
C) $15,348
D) $16,729
Answer: B
Diff: 2
Topic: Present Value of an Annuity Due
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
26) Calculate the present value of a $10,000 perpetuity at a 6 percent discount rate.
Answer: PV = 10,000/0.06 = $166,666.67
Diff: 1
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
27) Calculate the future value of an annuity of $5,000 each year for eight years, deposited at 6
percent.
Answer: FV = CF[(1 + r)n – 1] / r = $5,000[(1.06)8 – 1] / 0.06 = $49,487.34
Diff: 2
Topic: Future Value of an Annuity
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
28) Calculate the present value of an annuity of $3,900 each year for four years, assuming an
opportunity cost of 10 percent.
Answer: PV = (3,900/0.1)[1-(1/(1.1)4)] = $12,362.48
Diff: 2
Topic: Present Value of an Annuity
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
18
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29) Dottie has decided to set up an account that will pay her granddaughter $5,000 a year
indefinitely. How much should Dottie deposit in an account paying 8 percent annual interest?
Answer: PV = 5,000/0.08 = $62,500
Diff: 2
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
30) A wealthy industrialist wishes to establish a $2,000,000 trust fund which will provide income
for his grandchild into perpetuity. He stipulates in the trust agreement that the principal may not
be distributed. The grandchild may only receive the interest earned. If the interest rate earned on
the trust is expected to be at least 7 percent in all future periods, how much income will the
grandchild receive each year?
Answer: $2,000,000 × 0.07 = $140,000
Diff: 2
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
31) Rachel takes out a seven-year, 8 percent loan with a bank requiring annual end-of-year
payments of $960.43. Calculate the original principal amount.
Answer: PVA = (960.43/0.08)[1-(1/(1.08)7)] = $5,000.35
Diff: 2
Topic: Present Value of an Annuity
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
19
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32) A lottery administrator has just completed the state’s most recent $50 million lottery.
Receipts from lottery sales were $50 million and the payout will be $5 million at the end of each
year for 10 years. The expenses of running the lottery were $800,000. The state can earn an
annual compound rate of 8 percent on any funds invested.
(a) Calculate the gross profit to the state from this lottery.
(b) Calculate the net profit to the state from this lottery (no taxes).
Answer:
Diff: 3
Topic: Present Value of an Annuity
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
33) Jia has just won a $20 million lottery, which will pay her $1 million at the end of each year
for 20 years. An investor has offered her $10 million for this annuity. She estimates that she can
earn 10 percent interest, compounded annually, on any amounts she invests. She asks your
advice on whether to accept or reject the offer. What will you tell her? (Ignore Taxes)
Answer: P = ($1,000,000/0.1) × [1-(1/(1.1)20] = $8,513,564
$10,000,000 > $8,513,564Accept the offer.
Diff: 3
Topic: Present Value of an Annuity
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
34) Mr. Jackson has been awarded a bonus for his outstanding work. His employer offers him a
choice of a lump-sum of $5,000 today, or an annuity of $1,250 a year for the next five years.
Which option should Mr. Jackson choose if his opportunity cost is 9 percent?
Answer: PVA = ($1,250/0.09) × [1-1/(1.09)5] = $4,862.06
Mr. Jackson should choose a lump-sum of $5,000 today.
Diff: 3
Topic: Present Value of an Annuity
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
20
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35) In their meeting with their advisor, Mr. and Mrs. O’Rourke concluded that they would need
$40,000 per year during their retirement years in order to live comfortably. They will retire 10
years from now and expect a 20-year retirement period. How much should Mr. and Mrs.
O’Rourke deposit now in a bank account paying 9 percent to reach financial happiness during
retirement? Assume that once they retire, the O’Rourkes will withdraw $40,000 from their
retirement account at the end of each year.
Answer: The amount of money required at the beginning of the retirement period is:
n = 20, i = 9%
PVA = (CF/r) × [1-1/(1+r)n] = (40,000/.09) × [1-1/(1.09)20]= $365,141.83
n = 10, i = 9%
PV = 365,141.83(1.09)-10 = $154,239.85
Diff: 3
Topic: Complex Time Value Problems
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
36) Nico is 30 years old and will retire at age 65. He will receive retirement benefits, but the
benefits are not going to be enough to make a comfortable retirement life for him. Nico has
estimated that an additional $25,000 a year over his retirement benefits will allow him to have a
satisfactory life. How much should Nico deposit today in an account paying 6 percent interest to
meet his goal? Assume Nico will have 15 years of retirement. Assume that he withdraws
$25,000 at the end of each year during retirement.
Answer: PMT = $25,000, n = 15, r = 6%
PV(65) = (25,000/.06) × [1-1/(1.06)15] = $242,806.72
FV = $242,806, n = 35, r = 6%
P(30) = 242,806.72(1.06)-35 = 242,800(0.130) = $31,590.36
Diff: 3
Topic: Complex Time Value Problems
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
21
Copyright © 2019 Pearson Education, Inc.
37) You have been given a choice between two retirement policies as described below.
Policy A: You will receive equal annual payments of $10,000 beginning 35 years from now for
10 years.
Policy B: You will receive one lump-sum of $100,000 in 40 years from now.
Which policy would you choose? Assume rate of interest is 6 percent.
Answer: This is a tricky problem, and it may be helpful to carefully draw timelines showing the
cash flows from each Policy before calculating their present values as of 35 years from today.
Policy A: If the first payment comes 35 years from now, then we can calculate the present value
of a 10-year annuity due that starts 35 years from now as follows:
PV = (10,000/0.06) × [1-1/(1.06)10] (1.06)= $78,016.92
Notice that we are using the annuity due calculation here because the payment comes in 35 years
and we also want to know the present value of the payment stream as of exactly 35 years from
now. If we used the annuity formula, we would be calculating the PV of the payment stream as
of 34 years from now because the annuity formula assumes that the first payment comes one year
after the time at which the PV is calculated (in other words, the ordinary annuity formula gives
us the present value of an annuity at time “t” if the annuity’s first cash flow comes at time “t+1”).
In this problem, the first payment comes in 35 years and we want to know the PV at exactly that
time.
Policy B: We want to know the present value of the lump-sum as of 35 years from now so we
can compare that to the value we calculated for Policy A. If the lump sum payment arrives in 40
years, then its present value 35 years from now will be:
PV = 100,000(1.06)-5 = $74,725.82
Policy A has a higher present value.
Diff: 3
Topic: Complex Time Value Problems
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
38) A charitable foundation has $500,000 invested in an account that earns 7%. The foundation
has promised to begin making annual payments to beneficiaries in one year, and the first
payment will be $25,000. The foundation has promised that future payments will grow at a
constant rate forever. At what rate can the foundation afford to increase payments assuming that
it makes no additional deposits into the account?
A) 0%; it can’t afford to increase payments forever without adding more money to the account.
B) 1%
C) 2%
D) 3%
Answer: C
Diff: 2
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
22
Copyright © 2019 Pearson Education, Inc.
39) A university has $16,000,000 invested in its endowment. The university wants to withdraw
$800,000 from this endowment starting next year and continuing at annual intervals forever, with
each subsequent payment growing at 4% per year. What rate of return does the endowment have
to earn to sustain the desired withdrawals?
Answer: The present value of this growing perpetuity is $16,000,000. The equation for a
growing perpetuity tells us that this present value equals the first payment divided by the
difference between the rate of return and the growth rate of future payments:
PV = CF / (r – g)
$16,000,000 = $800,000 / (r – 0.04)
Solve for r to find the rate of return needed to generate the desired cash payouts.
(r – 0.04) = $800,000 / $16,000,000
r = 0.04 + 0.05 = 0.09 = 9%
Diff: 2
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
40) A wealthy benefactor wants to make a donation to a charity that will provide the charity with
annual income of $250,000 forever, with the first payment to the charity made exactly 10 years
from today. Assume that money donated to the charity will be invested in an account that earns
6%. How large must the donation be to generate the desired income stream?
Answer: The equation for a perpetuity tells us that the present value today equals that cash
payment made one year from today divided by the discount rate. In this case, the first payment
doesn’t come a year from today, but rather 10 years from today. So if we apply the perpetuity
equation, it would give us the present value of the income stream one year before the stream
starts, i.e., year 9. So the PV of the perpetuity as of year 9 is
PV as of year 9 = $250,000 / 0.06 = $4,166,166.67
This is the amount of money needed in the investment account 9 years from today. To get the
amount needed today, just discount this value by 9 years at 6%
PV needed today = $4,166,166.67 / 1.069 = $2,466.243.60
Diff: 3
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
23
Copyright © 2019 Pearson Education, Inc.
41) How much money would you have to deposit today to create an income stream that pays
$10,000 one year from today and continues to make annual payments forever, with payments
after the first $10,000 growing at 4% per year? Assume money that you invest today to fund this
income stream earns a 7% rate of return.
A) $142,857
B) $250,000
C) $1,250,000
D) $333,333
Answer: D
Diff: 1
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
42) A certain investment promises to pay you $2,500 per year forever with the first payment
starting next year. If you can earn a 5% return on similar investments, what’s the most you would
pay for this investment today?
A) $50,000
B) $5,000
C) $41,667
D) $62,500
Answer: A
Diff: 2
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
24
Copyright © 2019 Pearson Education, Inc.
43) A perpetuity will pay you $100 starting next year and continuing at that level forever. The
appropriate discount rate for the perpetuity is 10%. Calculate the present value of (1) the infinite
stream of payments, i.e., the entire perpetuity, and (2) the first 20 payments. Compare these two
present values and comment on what they can tell you about the present value of the perpetuity’s
payments in the very distant future (i.e., payments made later than 20 years in the future).
Answer: The PV of the perpetuity is just $100 / 0.10 = $1,000. The present value of the first 20
payments is found using the annuity formula as follows:
PV = (100/0.10)[1 – 1/(1.10)20] = $851.36
If the entire payment stream is worth $1,000 and the first 20 payments are worth $851.36, then
the value of all payments beyond the 20th payment is $148.64. The vast majority of the
perpetuity’s value comes from the payment makes in the early years, and more distant payments,
though there are an infinite number of them, account for a relatively small portion of the
perpetuity’s overall value.
Diff: 3
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
44) You inherited an investment portfolio worth $1 million. The portfolio earns a return of 9%
per year. You want to withdraw money from this portfolio once per year starting one year from
today, and you want to continue making withdrawals forever. Furthermore, you want to increase
your withdrawals at 3% per year to keep up with inflation. How large can your first withdrawal
be?
Answer: Here we want to create a growing perpetuity that has a present value of $1 million,
earns a 9% return, and provides payments growing at 3% per year. Using the equation for the PV
of a growing perpetuity we have
PV = CF / (r-g)
$1,000,000 = CF / (0.09-0.03)
Solve for CF
$1,000,000 × (0.09-0.03) = CF = $60,000
Diff: 2
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
25
Copyright © 2019 Pearson Education, Inc.
45) A certain investment promises to pay you $2,500 per year forever with the first payment
starting 5 years from now. If you can earn a 5% return on similar investments, what’s the most
you would pay for this investment today?
A) $50,000
B) $39,176
C) $41,135
D) $37,311
Answer: C
Diff: 2
Topic: Perpetuities
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Analytical Thinking
26
Copyright © 2019 Pearson Education, Inc.
46) Ashley is planning to attend college when she graduates from high school 7 years from now.
She anticipates that she will need $20,000 at the beginning of each of the four college years to
pay for tuition and fees, and have some spending money (i.e., she needs to be able to withdraw
$20,000 from savings four times, with the first withdrawal taking place 7 years from now).
Ashley’s father has promised to help her save for college by making 7 deposits of $7,000 each
into an investment accounting earning 8 percent interest. His first payment comes a year from
today. Will there be enough money in the account for Ashley to pay for her college expenses?
Assume the rate of interest stays at 8 percent during the college years.
Answer: There are several ways to approach this problem. One way is to calculate the present
value of Ashley’s college expenses and then compare that to the present value of the deposits
made into the investment account. If the two PVs match, then she has exactly enough money to
pay for college. Start with the PV of college expenses. One way to get that number is to discount
each payment at 8 percent for the appropriate number of years as follows:
PV = $20,000/(1.08)7 + $20,000/(1.08)8 + $20,000/(1.089) + $20,000/(1.08)10 = $41,744.03
Another way to get the PV of the college costs is to treat them as a 4-year annuity starting in 6
years (we calculate the PV of the ordinary annuity as of year 6 because the first payment comes a
year later at year 7). The PV of this annuity, as of year 6, is
PV = ($20,000 / 0.08)[1 – 1/(1.08)4] = $66,242.54
and discounting that figure back to the present gives $66,242.54 / 1.086 = $41,744.03.
Now, we simply need to compare that figure to the present value of the 7-year annuity of $7,000
payments.
PV = ($7,000/0.08)[1 – 1/(1.08)7] = $36,444.59
Because the PV of the deposits is less than the PV of college costs, Ashley will not have enough
money to pay for college. The difference in PVs is $5,299.44. If Ashley or her father could put
this amount into the investment account today AND continue with the $7,000 annual payments,
she would have enough to pay for college.
Diff: 3
Topic: Complex Time Value Problems
Learning Obj.: LG 3
Learning Outcome: F-03
AACSB: Reflective Thinking
27
Copyright © 2019 Pearson Education, Inc.
5.4 Mixed streams
1) You receive $100 today, $200 in one year, and $300 in two years. If you deposit these cash
flows into an account earning 12 percent, the value in the account three years from now is
________.
A) less than $600
B) $649
C) $727
D) $815
Answer: C
Diff: 1
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
2) You receive $1,200 today, $2,200 in one year, and $3,300 in two years. If you deposit these
cash flows in an account earning 12%, how much money is in the account three years from now?
A) $6,221
B) $5,554
C) $7,269
D) $8,142
Answer: D
Diff: 2
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
3) Find the future value at the end of year 3 of the following stream of cash flows received at the
end of each year, assuming the firm can earn 17 percent on its investments.
A) $16,320
B) $20,127
C) $23,548
D) $27,551
Answer: B
Diff: 2
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
28
Copyright © 2019 Pearson Education, Inc.
4) Find the future value at the end of year 3 of the following stream of cash flows received at the
end of each year, assuming the firm can earn 8 percent on its investments.
A) $51,780
B) $39,248
C) $47,944
D) $40,981
Answer: C
Diff: 2
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
5) You receive $1,000 in 1 year, $1,200 in 2 years, and $1,300 in 3 years. The present value
today of these future receipts is ________ if the opportunity cost is 7 percent.
A) $2,500
B) $3,044
C) $4,036
D) $3,257
Answer: B
Diff: 1
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
6) You will receive $100 in 1 year, $200 in 2 years, and $300 in 3 years. If you can earn 13% on
your investments, the present value of these future receipts is ________.
A) $453
B) $512
C) $801
D) $600
Answer: A
Diff: 1
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
29
Copyright © 2019 Pearson Education, Inc.
7) Find the present value of the following stream of cash flows assuming an opportunity cost of
14 percent.
A) $59,169
B) $92,443
C) $81,090
D) $51,903
Answer: D
Diff: 1
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
8) Find the present value of the following stream of cash flows assuming an opportunity cost of
25 percent.
A) $27,168
B) $33,960
C) $72,656
D) $41,674
Answer: A
Diff: 1
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
30
Copyright © 2019 Pearson Education, Inc.
9) Find the present value of the following stream of cash flows assuming an opportunity cost of 9
percent.
A) $85,791
B) $187,838
C) $65,213
D) $79,345
Answer: D
Diff: 3
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
10) Find the present value of the following stream of a firm’s cash flows, assuming that the firm’s
opportunity cost is 14 percent.
A) $131,068
B) $149,417
C) $485,897
D) $104,322
Answer: A
Diff: 2
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
31
Copyright © 2019 Pearson Education, Inc.
11) During her four years at college, Hayley received the following amounts of money at the end
of each year from her grandmother. She deposited her money in a savings account paying 6
percent rate of interest. How much money will Hayley have on graduation day?
Answer:
Diff: 2
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
12) You have provided your friend with a service worth $8,500. Your friend offers you the
following sequence of end-of-year cash flows instead of paying $8,500 today. Should you accept
his offer if your opportunity cost is 8 percent?
Answer:
Diff: 2
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
32
Copyright © 2019 Pearson Education, Inc.
13) Calculate the present value of $5,800 received at the end of year 1, $6,400 received at the
end of year 2, and $8,700 at the end of year 3, assuming an opportunity cost of 13 percent.
Answer: PV = 5,800(1.13)-1 + 6,400(1.13)-2 + 8,700(1.13)-3 = $16,174.42
Diff: 1
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
14) Calculate the present value of $800 received at the beginning of year 1, $400 received at the
beginning of year 2, and $700 received at the beginning of year 3, assuming an opportunity cost
of 9 percent.
Answer: PV = 800 + 400(1.09) + 700(1.09)2 = $1,756.15
Diff: 1
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
15) Calculate the combined future value at the end of year 3 of $1,000 received at the end of year
1, $3,000 received at the end of year 2, and $5,000 received at the end of year 3, all sums
deposited at 5 percent.
Answer: FV = 1,000(1.05)2 + 3,000(1.05) + 5,000 = $9,252
Diff: 2
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
33
Copyright © 2019 Pearson Education, Inc.
16) You are considering the purchase of new equipment for your company and you have
narrowed down the possibilities to two models which perform equally well. However, the
method of paying for the two models is different. Model A requires $5,000 per year payment for
the next five years. Model B requires the following payment schedule. Which model should you
buy if your opportunity cost is 8 percent?
Answer: Model A: PV = (CF/i) × [1-1/(1+r)n] = (5,000/.08) × [1-1/(1.08)5] = $19,963.55
Buy Model A.
Diff: 2
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
34
Copyright © 2019 Pearson Education, Inc.
17) Last Christmas, Danny received an annual bonus of $1,500. These annual bonuses are
expected to grow by 5 percent for the next 5 years. How much will Danny have at the end of the
fifth year if he invests his Christmas bonuses (including the most recent bonus) in an account
paying 8 percent per year?
Answer:
Diff: 3
Topic: Complex Time Value Problems
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
18) Calculate the present value of the following stream of cash flows, assuming that the firm’s
opportunity cost is 15 percent.
Answer: PV = (12,000/.15) × [1-1/(1.15)7] + {(14,000/.15) × [1-1/(1.15)3]} × (1.15)-7 =
$61,942
Diff: 1
Topic: Mixed Streams
Learning Obj.: LG 4
Learning Outcome: F-03
AACSB: Analytical Thinking
5.5 Compounding interest more frequently than annually
1) The nominal (stated) annual rate is the rate of interest actually paid or earned.
Answer: FALSE
Diff: 1
Topic: Nominal and Effective Interest Rates
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
35
Copyright © 2019 Pearson Education, Inc.
2) The nominal and effective rates are equivalent for annual compounding.
Answer: TRUE
Diff: 1
Topic: Nominal and Effective Interest Rates
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
3) The effective annual rate increases with increasing compounding frequency.
Answer: TRUE
Diff: 1
Topic: Nominal and Effective Interest Rates
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
4) The annual percentage rate (APR) is the nominal rate of interest, found by multiplying the
periodic rate by the number of periods in one year.
Answer: TRUE
Diff: 1
Topic: Nominal and Effective Interest Rates
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
5) The annual percentage yield (APY) is the effective rate of interest that must be disclosed to
customers by banks on their savings products as a result of “truth in savings laws.”
Answer: TRUE
Diff: 1
Topic: Nominal and Effective Interest Rates
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
6) The effective rate of interest is the contractual rate of interest charged by a lender or promised
by a borrower.
Answer: FALSE
Diff: 1
Topic: Nominal and Effective Interest Rates
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
36
Copyright © 2019 Pearson Education, Inc.
7) The effective rate of interest differs from the nominal rate of interest in that it reflects the
impact of compounding frequency.
Answer: TRUE
Diff: 1
Topic: Nominal and Effective Interest Rates
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
8) For any interest rate and for any period of time, the more frequently interest is compounded,
the greater the amount of money that has to be invested today in order to accumulate a given
future amount.
Answer: FALSE
Diff: 2
Topic: Nominal and Effective Interest Rates
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Reflective Thinking
9) The effective rate of interest and compounding frequency are inversely related.
Answer: FALSE
Diff: 1
Topic: Nominal and Effective Interest Rates
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Reflective Thinking
10) The rate of interest agreed upon contractually charged by a lender or promised by a borrower
is the ________ interest rate.
A) effective
B) nominal
C) discounted
D) continuous
Answer: B
Diff: 1
Topic: Nominal and Effective Interest Rates
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
37
Copyright © 2019 Pearson Education, Inc.
11) The rate of interest actually paid or earned, also called the annual percentage rate (APR), is
the ________ interest rate.
A) effective
B) nominal
C) discounted
D) continuous
Answer: A
Diff: 1
Topic: Nominal and Effective Interest Rates
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
12) The future value of $200 received today and deposited at 8 percent compounded
semiannually for three years is ________.
A) $380
B) $158
C) $253
D) $252
Answer: C
Diff: 2
Topic: Future Value
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
13) The future value of $100 received today and deposited in an account for four years paying
semiannual interest of 6 percent is ________.
A) $450
B) $127
C) $889
D) $134
Answer: B
Diff: 2
Topic: Future Value
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
38
Copyright © 2019 Pearson Education, Inc.
14) The future value of $200 received today and deposited for three years in an account which
pays semiannual interest of 8 percent is ________.
A) $253.00
B) $252.00
C) $158.00
D) $134.66
Answer: A
Diff: 2
Topic: Future Value
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
15) The future value of an annuity of $1,000 each quarter for 10 years, deposited at 12 percent
compounded quarterly is ________.
A) $17,549
B) $75,401
C) $93,049
D) $11,200
Answer: B
Diff: 2
Topic: Future Value of an Annuity
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
16) What is the highest effective rate attainable with a 12 percent nominal rate?
A) 12.00%
B) 12.55%
C) 12.75%
D) 12.95%
Answer: C
Diff: 1
Topic: Nominal and Effective Interest Rates
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
39
Copyright © 2019 Pearson Education, Inc.
17) Gina has planned to start her college education four years from now. To pay for her college
education, she has decided to save $1,000 a quarter for the next four years in an investment
account paying 12 percent interest. How much will she have at the end of the fourth year?
A) $1,574
B) $19,116
C) $20,157
D) $16,000
Answer: C
Diff: 2
Topic: Future Value of an Annuity
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
18) How much would Sophie have in her account at the end of 10 years if she deposit $2,000
into the account today if she earned 8 percent interest and interest is compounded continuously?
A) $4,317
B) $4,134
C) $4,451
D) $4,521
Answer: C
Diff: 1
Topic: Continuous Compounding
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
19) Assume Julian has a choice between two deposit accounts. Account A has an annual
percentage rate of 7.55 percent but with interest compounded monthly. Account B has an annual
percentage rate of 7.45 percent with interest compounded continuously. Which account provides
the highest effective annual return?
A) Account A
B) Account B
C) Both provide the same effective annual return.
D) We don’t have sufficient information to make a choice.
Answer: A
Diff: 2
Topic: Continuous Compounding and Effective Annual Rate
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
40
Copyright © 2019 Pearson Education, Inc.
20) Calculate the future value of $6,490 received today and deposited for five years in an
account which pays interest of 14 percent compounded semiannually.
Answer: FV = 6,490{[(1.14/2)5×2 – 1]/.14/2} = 6,490{[(1.07)10 – 1]/.07} = $12,766
Diff: 1
Topic: Future Value
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
21) Calculate the future value of $10,000 received today and deposited for six years in an
account which pays interest of 12 percent compounded quarterly.
Answer: FV = 10,000{[(1.12/4)6×4 – 1]/.12/4} = 10,000{[(1.03)24 – 1]/.03} = $20,328
Diff: 1
Topic: Future Value
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
22) Jeanne has just graduated from high school and has received an award for $5,000. She would
like to deposit the money in an interest earning account until she graduates from college (i.e.,
four years from now). In her search for the highest interest earning account, she has narrowed the
list down to the following two accounts: 1) bank A pays 9 percent interest compounded annually,
and 2) bank B pays 8 percent interest compounded semiannually. Which is the better offer, and
how much will Jeanne have upon graduation from college?
Answer: Bank A: n = 4, r = 9%, m = 1
FV = 5,000{[(1.09)4 – 1]/.09} = $7,057
Bank B: n = 4, r = 8%, m = 2
FV = 5,000{[1.04)8 – 1]/.04} = $6,842
Jeanne should deposit her money in Bank A and she will have $7,057 upon her graduation from
college.
Diff: 3
Topic: Nominal and Effective Interest Rates
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
41
Copyright © 2019 Pearson Education, Inc.
23) Assume you have a choice between two deposit accounts. Account X has an annual
percentage rate of 12.25 percent but with interest compounded monthly. Account Y has an
annual percentage rate of 12.20 percent with interest compounded continuously. Which account
provides the highest effective annual return?
Answer: Account X
EAR = [1 + – 1 = 12.96%
Account Y
EAR = – 1 = 12.75%
Choose X
Diff: 2
Topic: Continuous Compounding and Effective Annual Rate
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
24) Carlos is the new assistant branch manager of a larger Florida-based bank and the branch
manager has asked him a question to test his knowledge. The question is which rate should the
bank advertise on monthly-compounded loans, the nominal annual percentage rate or the
effective annual percentage rate? Which rate should the bank advertise on quarterly-compounded
savings accounts? Explain. As a consumer, which would you prefer to see and why?
Answer: A bank would rather advertise the annual percentage rate on loans since this rate
appears to be lower and the effective annual rate. With respect to savings accounts, the bank
would advertise the effective rate since this rate will be higher than the annual percentage
rate(APR). As a consumer, the effective rate is the more important rate since it represents the rate
actually paid or earned.
Diff: 1
Topic: Nominal and Effective Interest Rates
Learning Obj.: LG 5
Learning Outcome: F-03
AACSB: Analytical Thinking
5.6 Special applications of time value
1) In general, with an amortized loan, the payment amount remains constant over the life of the
loan, the principal portion of each payment grows over the life of the loan, and the interest
portion of each payment declines over the life of the loan.
Answer: TRUE
Diff: 1
Topic: Loan Amortization
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
42
Copyright © 2019 Pearson Education, Inc.
2) In general, with an amortized loan, the payment amount remains constant over the life of the
loan, the principal portion of each payment declines over the life of the loan, and the interest
portion of each payment grows over the life of the loan.
Answer: FALSE
Diff: 1
Topic: Loan Amortization
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
3) In general, with an amortized loan, the payment amount remains constant over the life of the
loan, both the principal portion of and the interest portion declines over the life of the loan.
Answer: FALSE
Diff: 1
Topic: Loan Amortization
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
4) In general, with an amortized loan, the payment amount grows over the life of the loan, the
principal portion of each payment grows over the life of the loan, and the interest portion
declines over the life of the loan.
Answer: FALSE
Diff: 1
Topic: Loan Amortization
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
5) When computing an interest or growth rate, the rate will increase with an increase in future
value, holding present value and the number of periods constant.
Answer: TRUE
Diff: 1
Topic: Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
6) When computing an interest or growth rate, the rate will decrease with an increase in future
value, holding present value and the number of periods constant.
Answer: FALSE
Diff: 1
Topic: Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
43
Copyright © 2019 Pearson Education, Inc.
7) When computing an interest or growth rate, the rate will increase with a decrease in future
value, holding present value and the number of periods constant.
Answer: FALSE
Diff: 1
Topic: Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
8) When computing the number of deposits needed to accumulate to a future sum, it will take
longer if the interest rate decreases, holding the future value and deposit size constant.
Answer: TRUE
Diff: 1
Topic: Deposits Needed to Accumulate a Future Sum
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
9) When computing the number of deposits needed to accumulate a future sum, it will take
longer if the interest rates are higher, holding the future value and deposit size constant.
Answer: FALSE
Diff: 1
Topic: Deposits Needed to Accumulate a Future Sum
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
10) The time value concept/calculation used in amortizing a loan is ________.
A) future value of a dollar
B) future value of an annuity
C) present value of a dollar
D) present value of an annuity
Answer: D
Diff: 1
Topic: Loan Amortization
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
44
Copyright © 2019 Pearson Education, Inc.
11) If a United States Savings bond can be purchased for $29.50 and has a maturity value of
$100 at the end of 25 years, what is the annual rate of return on the bond?
A) 5 percent
B) 6 percent
C) 7 percent
D) 8 percent
Answer: A
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
12) If a United States Savings bond can be purchased for $14.60 and has a maturity value at the
end of 25 years of $100, what is the annual rate of return on the bond?
A) 6 percent
B) 7 percent
C) 8 percent
D) 9 percent
Answer: C
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
13) Janice would like to send her parents on a cruise for their 25th wedding anniversary. She has
priced the cruise at $15,000, and she has 5 years to accumulate this money. How much must
Janice deposit annually in an account paying 10 percent interest in order to have enough money
to send her parents on the cruise?
A) $1,862
B) $2,457
C) $3,000
D) $2,234
Answer: B
Diff: 1
Topic: Future Value of an Annuity
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
45
Copyright © 2019 Pearson Education, Inc.
14) Adam borrows $4,500 at 12 percent annually compounded interest to be repaid in four equal
annual installments. The actual end-of-year payment is ________.
A) $942
B) $1,125
C) $1,482
D) $2,641
Answer: C
Diff: 1
Topic: Present Value of an Annuity
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
15) Jia borrows $50,000 at 10 percent annually compounded interest to be repaid in four equal
annual installments. The actual end-of-year loan payment is ________.
A) $10,774
B) $12,500
C) $14,340
D) $15,773
Answer: D
Diff: 1
Topic: Present Value of an Annuity
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
16) Nico makes annual end-of-year payments of $5,043.71 on a four-year loan with an interest
rate of 13 percent. The original principal amount was ________.
A) $24,450
B) $15,000
C) $3,100
D) $20,175
Answer: B
Diff: 1
Topic: Present Value of an Annuity
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
46
Copyright © 2019 Pearson Education, Inc.
17) Hayley makes annual end-of-year payments of $6,260.96 on a five-year loan with an 8
percent interest rate. The original principal amount was ________.
A) $31,000
B) $30,000
C) $25,000
D) $20,000
Answer: C
Diff: 1
Topic: Present Value of an Annuity
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
18) Ashley owns stock in a company which has consistently paid a growing dividend over the
last five years. The first year Ashley owned the stock, she received $1.71 per share and in the
fifth year, she received $2.89 per share. What is the growth rate of the dividends over the last
five years?
A) 7 percent
B) 11 percent
C) 12 percent
D) 5 percent
Answer: B
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
19) Julian was given a gold coin originally purchased for $1 by his great-grandfather 50 years
ago. Today the coin is worth $450. The rate of return realized on the sale of this coin is
approximately equal to ________.
A) 7.5%
B) 13%
C) 9%
D) 18%
Answer: B
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
47
Copyright © 2019 Pearson Education, Inc.
20) Alexis owns stock in a company which has consistently paid a growing dividend over the last
10 years. The first year Alexis owned the stock, she received $4.50 per share and in the 10th
year, she received $4.92 per share. What is the growth rate of the dividends over the last 10
years?
A) 15 percent
B) 14.8 percent
C) 12.2 percent
D) 9.3 percent
Answer: D
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
21) The rate of return earned on an investment of $50,000 today that guarantees an annuity of
$10,489 for six years is approximately ________.
A) 5%
B) 7%
C) 10%
D) 12%
Answer: B
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
22) What is the rate of return on an investment of $16,278 if the company expects to receive
$3,000 per year for the next 10 years?
A) 18 percent
B) 13 percent
C) 8 percent
D) 3 percent
Answer: B
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
48
Copyright © 2019 Pearson Education, Inc.
23) What is the rate of return on an investment of $124,090 if the company expects to receive
$10,000 per year for the next 30 years?
A) 7 percent
B) 4 percent
C) 6 percent
D) 5.5 percent
Answer: A
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
24) A local brokerage firm is offering a zero-coupon certificate of deposit for $10,000. At
maturity, three years from now, the investor will receive $14,000. What is the rate of return on
this investment?
A) 14 percent
B) 13 percent
C) 12 percent
D) 11 percent
Answer: C
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
25) A local bank is offering a zero-coupon certificate of deposit for $25,000. At maturity, three
years from now, the investor will receive $32,000. What is the rate of return on this investment?
A) 3 percent
B) 6 percent
C) 9 percent
D) 12 percent
Answer: C
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
49
Copyright © 2019 Pearson Education, Inc.
26) A ski chalet at Peak n’ Peak now costs $250,000. Inflation is expected to cause this price to
increase at 5 percent per year over the next 10 years before Chris and Julie retire from successful
investment banking careers. How large an equal annual end-of-year deposit must be made into
an account paying an annual rate of interest of 13 percent in order to buy the ski chalet upon
retirement?
A) $8,333
B) $13,572
C) $25,005
D) $22,108
Answer: D
Diff: 2
Topic: Complex Time Value Problems
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
27) A beach house in Southern California now costs $350,000. Inflation is expected to cause this
price to increase at 5 percent per year over the next 20 years before Eric and Karinna retire from
successful careers in commercial art. How large an equal annual end-of-year deposit must be
made into an account paying an annual rate of interest of 13 percent in order to buy the beach
house upon retirement?
A) $11,472
B) $4,323
C) $79,977
D) $17,350
Answer: A
Diff: 2
Topic: Complex Time Value Problems
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
28) Xiao Xin is planning to accumulate $40,000 by the end of 5 years by making 5 equal annual
deposits. If she plans to make her first deposit today and can earn an annual compound rate of 9
percent on her investment, how much must each deposit be in order to accumulate the $40,000?
A) $6,132
B) $6,684
C) $23,844
D) $9,434
Answer: B
Diff: 1
Topic: Future Value of an Annuity
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
50
Copyright © 2019 Pearson Education, Inc.
29) Zheng Sen wishes to accumulate $1 million by the end of 20 years by making equal annual
end-of-year deposits over the next 20 years. If Zheng Sen can earn 10 percent on his investments,
how much must he deposit at the end of each year?
A) $14,900
B) $50,000
C) $117,453
D) $17,460
Answer: D
Diff: 1
Topic: Future Value of an Annuity
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
30) Xiao Li wishes to accumulate $50,000 by the end of 10 years by making equal annual end-
of-year deposits over the next 10 years. If Xiao Li can earn 5 percent on her investments, how
much must she deposit at the end of each year?
A) $3,975
B) $6,475
C) $5,000
D) $4,513
Answer: A
Diff: 1
Topic: Future Value of an Annuity
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Reflective Thinking
31) Dorothy borrows $10,000 from the bank. For a four-year loan, the bank requires annual end-
of-year payments of $3,223.73. The annual interest rate on the loan is ________.
A) 9 percent
B) 10 percent
C) 11 percent
D) 12 percent
Answer: C
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
51
Copyright © 2019 Pearson Education, Inc.
32) Detta borrows $20,000 from the bank. For a five-year loan, the bank requires annual end-of-
year payments of $4,878.05. The annual interest rate on the loan is ________.
A) 6 percent
B) 7 percent
C) 8 percent
D) 9 percent
Answer: B
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
33) Thelma is planning for her son’s college education to begin five years from today. She
estimates the yearly tuition, books, and living expenses to be $5,000 per year for a four-year
degree, assuming the expenses incur only at the end of the year. How much must Thelma deposit
today, at an interest rate of 8 percent, for her son to be able to withdraw $5,000 per year for four
years of college?
A) $20,000
B) $13,620
C) $39,520
D) $11,270
Answer: D
Diff: 3
Topic: Complex Time Value Problems
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Reflective Thinking
34) Otto is planning for his son’s college education to begin ten years from today. He estimates
the end-of-the-year tuition, books, and living expenses to be $10,000 per year for a four-year
degree. How much must Otto deposit today, at an interest rate of 12 percent, for his son to be
able to withdraw $10,000 per year for four years of college?
A) $12,880
B) $9,780
C) $40,000
D) $18,950
Answer: B
Diff: 3
Topic: Complex Time Value Problems
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Reflective Thinking
52
Copyright © 2019 Pearson Education, Inc.
35) Aunt Tilly borrows $3,500 from the bank at 12 percent annually compounded interest to be
repaid in four equal annual installments. The interest paid in the first year is ________.
A) $152
B) $277
C) $420
D) $1,152
Answer: C
Diff: 3
Topic: Loan Amortization
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
36) Danny Joe borrows $10,500 from the bank at 11 percent annually compounded interest to be
repaid in six equal annual installments. The interest paid in the first year is ________.
A) $1,155
B) $2,481
C) $144
D) $1,327
Answer: A
Diff: 3
Topic: Loan Amortization
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
37) Rita borrows $4,500 from the bank at 9 percent annually compounded interest to be repaid in
three equal annual installments. The interest paid in the third year is ________.
A) $277.95
B) $405.00
C) $352.00
D) $147.00
Answer: D
Diff: 3
Topic: Loan Amortization
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Reflective Thinking
53
Copyright © 2019 Pearson Education, Inc.
38) Uncle Butch borrows $19,500 from the bank at 8 percent annually compounded interest to be
repaid in 10 equal annual installments. The interest paid in the third year is ________.
A) $1,336.00
B) $1,560.14
C) $2,906.11
D) $1,947.10
Answer: A
Diff: 3
Topic: Loan Amortization
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Reflective Thinking
39) Entertainer’s Aid plans five annual colossal concerts, each in a different nation’s capital. The
concerts will raise funds for an endowment which would provide the World Wide Hunger Fund
with $3,000,000 per year into perpetuity. The endowment will be given at the end of the fifth
year. The rate of interest is expected to be 9 percent in all future periods. How much must
Entertainer’s Aid deposit each year to accumulate to the required amount?
A) $5,569,749
B) $3,333,333
C) $1,830,275
D) $8,568,980
Answer: A
Diff: 3
Topic: Complex Time Value Problems
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Reflective Thinking
40) A wealthy art collector has decided to endow her favorite art museum by establishing funds
for an endowment which would provide the museum with $1,000,000 per year for acquisitions
into perpetuity. The art collector will give the endowment upon her fiftieth birthday 10 years
from today. She plans to accumulate the endowment by making annual end-of-year deposits into
an account. The rate of interest is expected to be 6 percent in all future periods. How much must
the art collector deposit each year to accumulate to the required amount?
A) $1,575,333
B) $736,000
C) $1,264,466
D) $943,396
Answer: C
Diff: 3
Topic: Complex Time Value Problems
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Reflective Thinking
54
Copyright © 2019 Pearson Education, Inc.
41) How long would it take for you to save an adequate amount for retirement if you deposit
$40,000 per year into an account beginning today that pays 12 percent per year if you wish to
have a total of $1,000,000 at retirement?
A) 12.2 years
B) 10.5 years
C) 14.8 years
D) 11.5 years
Answer: D
Diff: 2
Topic: Finding an Unknown Number of Periods
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
42) How many years would it take for Harry to save an adequate amount for retirement if he
deposits $2,000 per month into an account beginning today that pays 12 percent per year if he
wishes to have a total of $1,000,000 at retirement?
A) 13 years
B) 16 years
C) 15 years
D) 12 years
Answer: C
Diff: 1
Topic: Finding an Unknown Number of Periods
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
43) How long would it take for Nico to save an adequate amount for retirement if he deposits
$40,000 per year into an account beginning one year from today that pays 12 percent per year if
he wishes to have a total of $1,000,000 at retirement?
A) 12.2 years
B) 15.7 years
C) 14.5 years
D) 16.5 years
Answer: A
Diff: 1
Topic: Finding an Unknown Number of Periods
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
55
Copyright © 2019 Pearson Education, Inc.
44) What annual rate of return would Jia need to earn if she deposits $20,000 per year into an
account beginning one year from today in order to have a total of $1,000,000 in 30 years?
A) 2.3%
B) 3.3%
C) 1.3%
D) 4.3%
Answer: B
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
45) What annual rate of return would Grandma Zoe need to earn if she deposits $1,000 per
month into an account beginning one month from today in order to have a total of $1,000,000 in
30 years?
A) 4.55%
B) 5.28%
C) 5.98%
D) 6.23%
Answer: C
Diff: 2
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
46) What effective annual rate of return (EAR) would Rayne need to earn if she deposits $1,000
per month into an account beginning one month from today in order to have a total of $1,000,000
in 30 years?
A) 5.98%
B) 6.55%
C) 4.87%
D) 6.14%
Answer: D
Diff: 2
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Reflective Thinking
56
Copyright © 2019 Pearson Education, Inc.
47) Janice borrows $25,000 from the bank at 15 percent to be repaid in 10 equal annual
installments. Calculate the end-of-year payment.
Answer: Use financial calculator: PV = 25,000, I = 15, FV = 0, N = 10, CPT PMT: $4,981.30
Diff: 1
Topic: Present Value of an Annuity
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
48) The following table presents the Sally’s Silly Service Company’s net earnings for the past six
years. Compute the growth rate in the company’s earnings.
Answer: g = (FV/PV)1/n – 1, n = 5, FV = 2,659, PV = 1,728
g = (2,659/1,728)1/5 – 1 = .09 = 9%
Diff: 2
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Reflective Thinking
49) Marc has purchased a new car for $15,000. He paid $2,500 as down payment and he paid the
balance by a loan from his hometown bank. The loan is to be paid on a monthly basis for two
years charging 12 percent interest. How much are the monthly payments?
Answer: PV = 15,000 – 2,500 = $12,500, r = 12%, n = 2, m = 12
Use financial calculator: PV = 12,500, I = 1, n = 24, FV = 0, CPT PMT: $588.42
Diff: 1
Topic: Present Value of an Annuity
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Reflective Thinking
50) You have been given the opportunity to earn $20,000 five years from now if you invest
$9,524 today. What will be the rate of return to your investment?
Answer: Use financial calculator: PV = -9,524, FV = 20000, PMT = 0, N = 5, CPT I: 16%
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
57
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51) Ten years ago, Tom purchased a painting for $300. The painting is now worth $1,020. Tom
could have deposited $300 in a savings account paying 12 percent interest compounded annually.
Which of these two options would have provided Tom with a higher return?
Answer: Using financial calculator: PV = – $300, FV = $1,020, n = 10, PMT = 0, CPT I: 13%
Painting has a higher return (13 percent) in comparison to the 12 percent rate of return from the
savings account.
Diff: 2
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
52) Find the equal annual end-of-year payment on $50,000, 15 year, and 10 percent loan.
Answer: Using financial calculator: PV = 50,000, FV = 0, N = 15, I = 10, CMP PMT: $6,573.69
Diff: 1
Topic: Present Value of an Annuity
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
53) A firm wishes to establish a fund which, in 10 years, will accumulate to $10,000,000. The
fund will be used to repay an outstanding bond issue. The firm plans to make deposits, which
will earn 12 percent, to this fund at the end of each of the 10 years prior to maturity of the bond.
How large must these deposits be to accumulate to $10,000,000?
Answer: Financial Calculator: PV = 0, FV = 10,000,000, N = 10, I = 12, CPT PMT:
$569,833.04
Diff: 1
Topic: Future Value of an Annuity
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
54) John borrowed $12,000 to buy a new car and expects to pay $564.87 per month for the next
2 years to pay off the loan. What is the loan’s rate of interest?
Answer: Using Financial Calculator: PV = 12,000, FV = 0, N = 24, PMT = -564.87, CPT I:
0.9998 × 12 = 12%
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
58
Copyright © 2019 Pearson Education, Inc.
55) The New York Soccer Association would like to accumulate $10,000 by the end of 4 years
from now to finance a big soccer weekend for its members. The Association currently has $2,500
and wishes to raise the balance by arranging annual fund-raising events. How much money
should they raise at each annual fund-raising event assuming 8 percent rate of interest?
Answer: Using Financial Calculator: PV = -2,500, FV = 10,000, N = 4, I = 8, CPT PMT:
1,464.41
Diff: 3
Topic: Complex Time Value Problems
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
56) Ms. Day needs $20,000 to buy her dream car. In her search for the best (low cost) loan, she
has gathered the following information from three local banks. Which bank would you
recommend Ms. Day borrow from?
Answer: A: Using financial calculator: PV = 20,000, PMT = -8,326.40, N = 3, FV = 0, CPT I =
12%
B: Using financial calculator: PV = 20,000, PMT = -6,309.15, N = 4, FV = 0, CPT I = 10%
C: Using financial calculator: PV = 20,000, PMT = -5,411.25, N = 5, FV = 0, CPT I = 11%
Ms. Day should borrow from Bank B. Bank B has the lowest rate.
Diff: 2
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
57) A deep-discount bond can be purchased for $312 and in 20 years it will be worth $1,000.
What is the rate of interest on the bond?
Answer: Using financial calculator: PV = -312, PMT = 0, N = 20, FV = 1,000, CPT I = 6
percent
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
59
Copyright © 2019 Pearson Education, Inc.
58) Timothy borrows $6,930 from the bank. For a four-year loan, the bank requires annual end-
of-year payments of $2,281.86. Calculate the interest rate on the loan.
Answer: Using financial calculator: PV = 6,930, PMT = -2,281.86, N = 4, FV = 0, CPT I = 12%
Diff: 1
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
59) Tom is evaluating the growth rate in dividends of a company over the past 6 years. What is
the annual compound growth rate if the dividends are as follows:
Answer: ($2.15/$1.38)1/5 – 1 = .0927 = 9.27%
Approximately 9 percent.
Diff: 2
Topic: Finding Interest or Growth Rates
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
60) To expand its operation, the International Tools Inc. (ITI) has applied for a $3,500,000 loan
from the International Bank. According to ITI’s financial manager, the company can only afford
a maximum yearly loan payment of $1,000,000. The bank has offered ITI, 1) a 3-year loan with
a 10 percent interest rate, 2) a 4-year loan with a 11 percent interest rate, or 3) a 5-year loan with
a 12 percent interest rate.
(a) Compute the loan payment under each option.
(b) Which option should the company choose?
Answer:
(a)
1) Using financial calculator: PV = 3,500,000, N = 3, FV = 0, I = 10, CPT PMT = 1,407,402
2) Using financial calculator: PV = 3,500,000, N = 4, FV = 0, I = 11, CPT PMT = $1,128,304.32
3) Using financial calculator: PV = 3,500,000, N = 5, FV = 0, I = 12, CPT PMT = $970,873.79
(b) The company should choose option #3.
Diff: 1
Topic: Present Value of an Annuity
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
60
Copyright © 2019 Pearson Education, Inc.
61) To buy his favorite car, Larry is planning to accumulate money by investing his Christmas
bonuses for the next five years in a security which pays a 10 percent annual rate of return. The
car will cost $20,000 at the end of the fifth year and Larry’s Christmas bonus is $3,000 a year.
Will Larry accumulate enough money to buy the car?
Answer: Using financial calculator: PV = 0, N = 5, PMT = 3,000, I = 10, CPT FV = $18,315
Larry will not have enough money to buy the car. He should either invest more money or deposit
his christmas bonuses in a security paying a higher rate of return.
Diff: 1
Topic: Future Value of an Annuity
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
62) Mr. & Mrs. Pribel wish to purchase a boat in 8 years when they retire. They are planning to
purchase the boat using proceeds from the sale of their property which is currently worth
$90,000 and its value is growing at 7 percent a year. The boat is currently worth $200,000
increasing at 5 percent per year. In addition to the value of their property, how much additional
money should they deposit at the end of each year in an account paying 9 percent annual interest
in order to be able to buy the boat upon retirement?
Answer: Value of the property upon retirement:
PV = $90,000, I = 7, N = 8, PMT = 0
CPT FV = $154,637
Value of the boat upon retirement:
PV = $200,000, I = 5, N = 8, PMT = 0
CPT FV = $295,491
Additional money needed upon retirement:
$295,491 – $154,637 = $140,854
Amount of money needed to deposit at the end of each year:
PV = 0, FV = $140,780, N = 8, I = 9%, PMT = ?
PMT = $12,765.69
Diff: 3
Topic: Complex Time Value Problems
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
61
Copyright © 2019 Pearson Education, Inc.
63) Herbert has opened a retirement fund account which pays 7 percent interest and requires
$5,000 annual deposits. Herbert will retire in 15 years and expects 10 years of retirement life.
What is the maximum annual retirement benefit Herbert can get during his retirement years?
Answer: I = 7%, PMT = $5,000, N = 15, PV = 0
At the beginning of retirement:
CPT FV = $125,645
Annual retirement benefit: i = 7%, n = 10, PV = $125,645, FV = 0
CPT PMT = $17,887.96
Diff: 3
Topic: Complex Time Value Problems
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
64) Brian borrows $5,000 from a bank at 8 percent annually compounded interest to be repaid in
five annual installments. Calculate the principal paid in the third year.
Answer: PV = 5,000, I = 8, N = 3, FV = 0, CPT PMT = $1,252.19
The principal paid in the third year is $993.99.
Diff: 3
Topic: Loan Amortization
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
65) Nancy would like to accumulate $10,000 by the end of 3 years from now to buy a sports car
from her friend, Jim. She has $2,500 now and would like to save equal annual end-of-year
deposits to pay for the car. How much should she deposit at the end of each year in an account
paying 8 percent interest to buy the car?
Answer: Using financial calculator: PV = -2,500, N = 3, I = 8, FV = 10,000, CPT PMT =
2,110.25
Diff: 3
Topic: Complex Time Value Problems
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
62
Copyright © 2019 Pearson Education, Inc.
66) To expand its operation, International Tools Inc. has applied to the International Bank for a
3-year, $3,500,000 loan. Prepare a loan amortization table assuming 10 percent rate of interest.
Answer: PV = 3,500,000, I = 10, N = 3, FV = 0, CPT PMT = $1,407,401.81
Diff: 3
Topic: Loan Amortization
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
67) Ken borrows $15,000 from a bank at 10 percent annually compounded interest to be repaid
in six equal installments. Calculate the interest paid in the second year.
Answer: PPV = 15000, I = 10, N = 2, FV = 0, CPT PMT = $3,444.32
The interest paid in the second year is $1,305.57.
Diff: 3
Topic: Loan Amortization
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking
68) Suzy wants to buy a house but does not want to get a loan. The average price of her dream
house is $500,000 and its price is growing at 5 percent per year. How much should Suzy invest
in a project at the end of each year for the next 5 years in order to accumulate enough money to
buy her dream house with cash at the end of the fifth year? Assume the project pays 12 percent
rate of return.
Answer: FV = 500,000(1.05)5 = $638,141
PV = 0, I = 12, N = 5, FV = 638,141, CPT PMT = $100,450
Diff: 2
Topic: Complex Time Value Problems
Learning Obj.: LG 6
Learning Outcome: F-03
AACSB: Analytical Thinking

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