Appendix C

Time Value of Money

REVIEW QUESTIONS

Question C-1 (LO C-1)

Interest is the cost of borrowing money. Simple interest is interest we earn on the initial investment

only. Compound interest is the interest we earn on the initial investment plus previous interest. We

use compound interest in calculating the time value of money.

Question C-2 (LO C-2)

To compute a future value, you need to know three amounts: (1) initial investment, (2) the interest

rate per period and (3) the number of periods.

Question C-3 (LO C-2)

BRIEF EXERCISES

Brief Exercise C-1 (LO C-1)

Oprah should choose the second option, the investment on which interest is

compounded semiannually. The more frequent the rate of compounding, the more

interest we earn on previous interest, resulting in a higher future value.

Brief Exercise C-2 (LO C-2)

Initial

investment

Annual

rate

Interest

compounded

Period

invested

Future

Value

$15,000

9%

Annually

6 years

$25,156.50a

Brief Exercise C-3 (LO C-2)

Initial

investment

Annual

rate

Interest

compounded

Period

invested

Future

Value

$27,000

7%

Annually

2 years

$30,912.30a

Brief Exercise C-4 (LO C-2)

Initial

investment

Annual

rate

Interest

compounded

Period

invested

Future

Value

1.

$8,000

10%

Annually

7 years

$15,589.74a

Brief Exercise C-5 (LO C-2)

Future

value

Annual

Rate

Interest

compounded

Period

invested

Present

Value

$6,000

8%

Annually

5 years

$4,083.50a

Brief Exercise C-6 (LO C-2)

Future

value

Annual

Rate

Interest

compounded

Period

invested

Present

Value

Brief Exercise C-7 (LO C-2)

Future

value

Annual

Rate

Interest

compounded

Period

invested

Present

value

1.

$10,000

6%

Annually

5 years

$7,472.58a

Brief Exercise C-8 (LO C-3)

Annuity

payment

Annual

Rate

Interest

compounded

Period

invested

Future value

of annuity

$4,000

8%

Annually

7 years

$35,691.21a

Brief Exercise C-9 (LO C-3)

Annuity

payment

Annual

Rate

Interest

compounded

Period

invested

Future value

of annuity

$3,000

10%

Semiannually

5 years

$37,733.68a

Brief Exercise C-10 (LO C-3)

Annuity

payment

Annual

Rate

Interest

compounded

Period

invested

Future value

of annuity

1.

$3,000

7%

Annually

Six years

$ 21,459.87a

Brief Exercise C-11 (LO C-3)

Annuity

Payment

Annual

Rate

Interest

compounded

Period

invested

Present value

of annuity

$8,000

6%

Annually

Four years

$27,720.88a

Brief Exercise C-12 (LO C-3)

Annuity

Payment

Annual

Rate

Interest

compounded

Period

invested

Present value

of annuity

$5,000

10%

Annually

Ten years

$30,722.84a

Brief Exercise C-13 (LO C-3)

Annuity

Payment

Annual

rate

Interest

compounded

Period

invested

Present value

of annuity

1.

$4,000

7%

Annually

Five years

$16,400.79a

EXERCISES

Exercise C-1 (LO C-2)

Investment

amount

Interest

rate

Compounding

Period

invested

Future

Value

Jerry

$13,000

12%

Quarterly

6 years

$26,426.32a

Elaine

16,000

6

Semiannually

6 years

22,812.17b

Exercise C-2 (LO C-2)

Initial

investment

Annual

rate

Interest

compounded

Period

invested

Future

Value

$2,000

13%

Annually

30 years

$78,231.80a

Exercise C-3 (LO C-2)

Contract

amount

Discount

rate

Compounding

Period

invested

Present

Value

Derek

$600,000

9%

Annually

2 years

$505,008.00a

Isabel

640,000

9

Annually

3 years

494,197.43b

Exercise C-4 (LO C-2)

Purchase

amount

Discount

rate

Compounding

Period

due

Present

Value

Store 1

$3,500

9%

Annually

Today

$3,500.00a

Exercise C-5 (LO C-2)

Payment

in one

year

Discount

rate

Compounding

Present

value of

payment in

one year

Payment

today

Total

present

value (or

total cost)d

Option 1

$ 0

11%

Annually

$ 0a

$150,000

$150,000.00

Option 2

82,500

11

Annually

74,324.32b

75,000

149,324.32

Exercise C-6 (LO C-3)

Annuity

payment

Annual

Rate

Interest

compounded

Period

invested

Future value

of annuity

$60,000

7%

Annually

3 years

$192,894.00a

Exercise C-7 (LO C-3)

Annuity

payment

Annual

Rate

Interest

compounded

Period

invested

Future value

of annuity

$2,000

13%

Annually

30 years

$586,398.43a

Exercise C-8 (LO C-3)

Annuity

payment

Annual

Rate

Interest

compounded

Period

invested

Present value

of annuity

Option 1

$35,000

12%

Annually

Today

$35,000.00a

PROBLEMS: SET A

Problem C-1A (LO C-2)

Person

Age

Initial

investment

Accumulated

investment by

retirement

(age 65)

Alec

55

$11,000

$28,531.17a

Problem C-2A (LO C-2, C-3)

Annuity

payment

Discount

Rate

Interest

compounded

Period

invested

Present value

of annuity

Years 1-6

$100,000

11%

Annually

6 years

$423,053.79a

Future

value

Discount

rate

Interest

compounded

Period

invested

Present

Value

Year 7

$110,000

11%

Annually

7 years

$ 52,982.43a

Problem C-3A (LO C-2, C-3)

Camera 1:

Annuity

payment

Discount

Rate

Interest

compounded

Period

invested

Present value

of annuity

Years 1-8

$300

9%

Annually

8 years

$1,660.45a

Future

value

Discount

rate

Interest

compounded

Period

invested

Present

Value

Year 8

$300

9%

Annually

8 years

$150.56a

Camera 2:

Future

payment

Discount

rate

Interest

compounded

Period

invested

Present

Value

Year 3

$ 900

9%

Annually

3 years

$ 694.97a

PROBLEMS: SET B

Problem C-1B (LO C-3)

Requirements 1 and 2

Person

Annuity

Payment

Type of

account

Expected

Annual

Return

Four-year

accumulated

investment

Maximum

home

purchasee

Mary Kate

$4,000

Savings

2%

$16,486.43a

$65,945.72

Problem C-2B (LO C-2, C-3)

Annuity

payment

Discount

Rate

Interest

compounded

Period

invested

Present value

of annuity

Future

value

Discount

rate

Interest

compounded

Period

invested

Present

Value

Year 20

$600,000

9%

Annually

20 years

$107,058.53a

Problem C-3B (LO C-2, C-3)

Option 1:

Present value = $1,600,000

Option 2:

Annuity

payment

Discount

Rate

Interest

compounded

Period

invested

Present value

of annuity

Years 1-10

$150,000

8%

Annually

10 years

$1,006,512.21a

Option 3:

Annuity

payment

Discount

Rate

Interest

compounded

Period

invested

Present value

of annuity

Option 4:

Future

payment

Discount

rate

Interest

compounded

Period

invested

Present

Value

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