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
Question C-2 (LO C-2)
Question C-3 (LO C-2)
Question C-4 (LO C-3)
An annuity represents cash payments of equal amounts over time periods of equal length.
Question C-5 (LO C-3)
The present value of an annuity is the sum of the present values of the single payments that make
BRIEF EXERCISES
Brief Exercise C-1 (LO C-1)
Oprah should choose the second option, the investment on which interest is
Brief Exercise C-2 (LO C-2)
Initial
investment
Annual
rate
Interest
compounded
Period
invested
$15,000
9%
Annually
6 years
Brief Exercise C-3 (LO C-2)
Initial
investment
Annual
rate
Interest
compounded
Period
invested
$27,000
7%
Annually
2 years
Brief Exercise C-4 (LO C-2)
Initial
investment
Annual
rate
Interest
compounded
Period
invested
1.
$8,000
10%
Annually
7 years
2.
4 years
3.
3 years
Brief Exercise C-5 (LO C-2)
Future
value
Annual
Rate
Interest
compounded
Period
invested
8%
Annually
Brief Exercise C-6 (LO C-2)
Future
value
Annual
Rate
Interest
compounded
Period
invested
$55,000
6%
Annually
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
2.
7,000
8
Semiannually
8 years
3,737.36b
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
a $3,000 × Future value of annuity; n = 10; i = 5%
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
2.
6,000
Semiannually
Brief Exercise C-11 (LO C-3)
Annuity
Payment
Annual
Rate
Interest
compounded
Period
invested
Present value
of annuity
$8,000
Annually
Brief Exercise C-12 (LO C-3)
Annuity
Payment
Annual
Rate
Interest
compounded
Period
invested
Present value
of annuity
$5,000
Annually
Since the present value of revenue expected to be received ($30,722.84) is less than
the cost today ($35,000), Monroe should not make the purchase.
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
2.
Semiannually
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
Kramer
Annually
6 years
Exercise C-2 (LO C-2)
Initial
investment
Annual
rate
Interest
compounded
Period
invested
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
Annually
3 years
Meredith
500,000
Annually
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
Store 2
Annually
One year
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
Annually
Option 3
Annually
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
Annually
11
Annually
Exercise C-7 (LO C-3)
Annuity
payment
Annual
Rate
Interest
compounded
Period
invested
Future value
of annuity
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
Option 2
12%
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
Daniel
45
$11,000
William
35
$11,000
Stephen
$11,000
Problem C-2A (LO C-2, C-3)
Annuity
payment
Discount
Rate
Interest
compounded
Period
invested
Present value
of annuity
Years 1-6
Annually
Future
value
Discount
rate
Interest
compounded
Period
invested
Present
Value
Year 7
$110,000
11%
Annually
7 years
$ 52,982.43a
Year 8
11%
Annually
8 years
Year 9
11%
Annually
9 years
Year 10
11%
Annually
Bruce should purchase the restaurant. With a discount rate of 11%, the current cost of
the restaurant ($1,000,000) is less than the present value of future cash flows
($1,086,073.27).
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
Annually
Future
value
Discount
rate
Interest
compounded
Period
invested
Present
Value
Year 8
9%
Annually
8 years
+
Camera 2:
Future
payment
Discount
rate
Interest
compounded
Period
invested
Present
Value
Year 3
$ 900
9%
Annually
3 years
$ 694.97a
Year 5
9%
Annually
5 years
Year 7
9%
Annually
7 years
By comparing the total cost of camera 1 ($7,509.89) to the total cost of camera 2
($7,326.94), Hollywood Tabloid should purchase camera 2.
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%
$65,945.72
Elle
$6,000
Stocks
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
If Woody wants to make at least 9% on his investment, the most he would pay for the
toy store is $654,771.27, the total present value of future cash flows.
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
8%
Option 3:
Annuity
payment
Discount
Rate
Interest
compounded
Period
invested
Present value
of annuity
Annually
Option 4:
Future
payment
Discount
rate
Interest
compounded
Period
invested
Present
Value
Year 5
$2,300,000
8%
Annually
5 years
$1,565,341.35a