Interest is the cost of borrowing money. Simple interest is interest we
earn on the initial investment only. Compound interest is the interest
Present value tells us the value today of receiving some larger amount in the future. The discount
Initial
investment
Annual
rate
Interest
compounded
Period
invested
Future
Value
$15,000 9% Annually 6 years $25,156.50a
Appendix C
Time Value of Money
REVIEW QUESTIONS
Question C-1 (LO C-1)
Question C-2 (LO C-2)
To compute a future value, you need to know three amounts: (1) initial investment, (2) the interest
Question C-3 (LO C-2)
Question C-4 (LO C-3)
Annuities represent cash payments of equal amounts over equal time intervals.
Question C-5 (LO C-3)
The present value of an annuity is the sum of the present values of a series of cash payments.
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
Brief Exercise C-2 (LO C-2)
Initial
investment
Annual
rate
Interest
compounded
Period
invested
Future
Value
$27,000 7% Annually 2 years $30,912.30a
Arnold and Helene will not be able to pay for their trip.
Initial
investment
Annual
rate
Interest
compounded
Period
invested
Future
Value
1. $8,000 10% Annually 7 years $15,589.74a
2. 6,000 12 Semiannually 4 years 9,563.09b
3. 9,000 8 Quarterly 3 years 11,414.18c
a $8,000 × Future value of $1; n = 7; i = 10%
Future
value
Annual
Rate
Interest
compounded
Period
invested
Present
Value
$6,000 8% Annually 5 years $4,083.50a
Future
value
Annual
Rate
Interest
compounded
Period
invested
Present
Value
$55,000 6% Annually 3 years $46,179.06a
Dusty will have enough to buy a car with the Turbo engine.
Brief Exercise C-3 (LO C-2)
Brief Exercise C-4 (LO C-2)
Brief Exercise C-5 (LO C-2)
Brief Exercise C-6 (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
3. 6,000 12 Quarterly 4 years 3,739.00c
a $10,000 × Present value of $1; n = 5; i = 6%
Annuity
payment
Annual
Rate
Interest
compounded
Period
invested
Future value
of annuity
$4,000 8% Annually 7 years $35,691.21a
Annuity
payment
Annual
Rate
Interest
compounded
Period
invested
Future value
of annuity
$3,000 10% Semiannually 5 years $37,733.68a
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 8 Semiannually Nine years 153,872.48b
3. 5,000 12 Quarterly Five years 134,351.87c
a $3,000 × Future value of annuity; n = 6; i = 7%
Brief Exercise C-7 (LO C-2)
Brief Exercise C-8 (LO C-3)
Tom and Suri will reach their goal.
Brief Exercise C-9 (LO C-3)
Brief Exercise C-10 (LO C-3)
c $5,000 × Future value of annuity; n = 20; i = 3%
Annuity
Paymen
t
Annual
Rate
Interest
compounded
Period
invested
Present value
of annuity
$8,000 6% Annually Four years $27,720.88a
The four $8,000 payments (a total of $32,000 received) are worth $27,720.88 today.
Annuity
Paymen
t
Annual
Rate
Interest
compounded
Period
invested
Present value
of annuity
$5,000 10% Annually Ten years $30,722.84a
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.
Annuity
Paymen
t
Annual
rate
Interest
compounded
Period
invested
Present value
of annuity
1. $4,000 7% Annually Five years $16,400.79a
2. 9,000 8 Semiannually Three years 47,179.23b
3. 3,000 8 Quarterly Two years 21,976.44c
a $4,000 × Present value of annuity; n = 5; i = 7%
Brief Exercise C-11 (LO C-3)
Brief Exercise C-12 (LO C-3)
Brief Exercise C-13 (LO C-3)
EXERCISES
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
George 23,000 8 Annually 6 years 36,498.11c
Kramer 19,000 10 Annually 6 years 33,659.66d
a $13,000 × Future value of $1; n = 24; i = 3%
b $16,000 × Future value of $1; n = 12; i = 3%
George will have the greatest investment accumulation.
Initial
investment
Annual
rate
Interest
compounded
Period
invested
Future
Value
$2,000 13% Annually 30 years $78,231.80a
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
Meredith 500,000 9 Annually Today 500,000.00c
George 500,000 9 Annually 1 year 458,715.60d
a $600,000 × Present value of $1; n = 2; i = 9%
b $640,000 × Present value of $1; n = 3; i = 9%
Derek is being paid the most in present value terms.
Purchase
amount
Discount
rate Compounding
Period
due
Present
Value
Exercise C-1 (LO C-2)
Exercise C-2 (LO C-2)
Exercise C-3 (LO C-2)
Exercise C-4 (LO C-2)
Store 1 $3,500 9% Annually Today $3,500.00a
Store 2 3,700 9 Annually One year 3,394.50b
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 74,324.32b75,000 149,324.32
Option 3 172,500 11 Annually 155,405.41c0155,405.41
a $0 × Present value of $1; n = 1; i = 11%
d Total present value (or total cost) = present value of payment in one year + payment
today
Option 2 has the lowest total cost in present value terms.
Annuity
payment
Annual
Rate
Interest
compounded
Period
invested
Future value
of annuity
$60,000 7% Annually 3 years $192,894.00a
60,000 9 Annually 3 years 196,686.00b
60,000 11 Annually 3 years 200,526.00c
a $60,000 × Future value of annuity; n = 3; i = 7%
Ray and Rachel should buy their ovens from Store 2.
Exercise C-5 (LO C-2)
Exercise C-6 (LO C-3)