Question

1 You are put in charge of managing your firm’s working capital. Your firm has $ 100,000 in extra cash on hand and decides to put it in a savings account 7% interest. How much will you have in your account in 15 years under the following compounded periods;

(a) Compounded annually

(b) Compounded monthly

(c) Compounded 5 times per year.

(d) Compounded continuously.

Answer 1

We use the following compound interest formula

$C = P \times (1+\frac{r}{m})^{n \times m}$

Where,
C is the final amount of investment
P is principal
r is annual interest rate
m is the frequency of compounding

We have
P = $100,000
r = 7%
n = 15

a.

Substituting values in the formula,

$C = 100,000 \times (1+\frac{0.07}{1})^{15 \times 1}$

Hence C = 275,903
Hence we would have $275,903 in our account

b.

Substituting values in the formula,

$C = 100,000 \times (1+\frac{0.07}{12})^{15 \times 12}$

Hence C = 284,895
Hence we would have $284,895 in our account

c.

Substituting values in the formula,

$C = 100,000 \times (1+\frac{0.07}{5})^{15 \times 5}$

Hence C = 283,692
Hence we would have $283,692 in our account

d.

For continuous compound using the following formula,

$C = P \times e^{r \times t}$

$C = 100,000 \times e^{0.07 \times 15}$

Hence C = 285,765
Hence we would have $285.765 in our account