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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

Category: Finance

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