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CH 8] Calculating Business 8-27

Homework #8-1
Name: ____________________________
Problems: 1—28

Refer to Page 8-7
A. Calculate (a) the compound amount and (b) the compound interest for each of the
following.
Principal Rate Time Compounded
1. 3,500 9% 4 years Annually
Solution algorithm: NOTE: I am using variable ‘r’ for interest rate; page 7 uses ‘i’.
n
S = (1 + r ) x P r = % / payments per year = 0.09 / 1 = .09
I = S — P n = time x payments per yr = 4 x 1 = 4

4
(a) S = ( 1 + 0.09) x $3,500 = $4,940.54
(b) $4,940.54 — $3,500 = $1,440.54

Principal Rate Time Compounded
2. 6,500 16% 3½ years Semiannually
Solution algorithm: NOTE: I am using variable ‘r’ for interest rate; page 7 uses ‘i’.
n
S = (1 + r ) x P r = % / payments per year = 0.16 / 2 = .08
I = S — P n = time x payments per yr = 3½ x 2 = 7

7
(a) S = ( 1 + 0.08) x $6,500 = $11,139.86
(b) $11,139.86 — $6,500 = $4,639.86
NOTE:
Principal Rate Time Compounded Have learners be
3. 25,000 10% 3 years Quarterly judiciously cautious
Solution algorithm: NOTE: I am using variable ‘r’ for interest rate; page 7 uses ‘i’. with the number of
n
S = (1 + r ) x P r = % / payments per year = 0.10 / 4 = 0.025 times they push the
I = S — P n = time x payments per yr = 3 x 4 = 12 ‘=‘ key button for
exponent value. Too
12
(a) S = (1 + 0.025) x $25,000 = $33,622.22 many pushes yield
(b) $33,622.22 — $25,000 = $8,622.22 the wrong answer.

B. Solve these problems.
4. The sum of $12,000 was invested for 3 years at 9% interest compounded semiannually.
(a) What is the value of the investment at the end of three years? (b) How much more
was earned with compound interest than would have been earned with simple interest?
Solution algorithm: NOTE: I am using variable ‘r’ for interest rate; page 7 uses ‘i’.
(a) Interest Compounded Semiannually
n
S = (1 + r ) x P r = % / payments per year = 0.09 / 2 = 0.045
I = S — P n = time x payments per yr = 3 x 2 = 6

6
(a) S = (1 + .045) x $12,000 = $15,627.12
$15,627.12 — $12,000 = $3,627.12 Interest earned

(b) Simple interest I = P x r x t 8
I = $12,000 x 0.09 x 3 = $3,240.00
Value of Account: P + I = $12,000 + $3,240 = $15,240

Compare Compound interest earnings to Simple interest earnings

Ci — Si = Difference

(b) $3,627.12 — $3, 240.00 = $387.12 difference.
Compounding has the greater value

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