Question

Find the future value and interest earned if $8704.56 is invested for 9 years at 4% compounded (a) semiannually and (b) continuously.
intorntic compounded semiannually is approximately

Answer 1

a) The future value if the interest is compounded semiannually = $12432

b) The future value if the interest is compounded annually = $12389

The future value for compound interest is given as:

$FV=P(1+\frac{r}{n})^{nt}$

The amount invested is the principal

The principal, P = $8704.56

The rate, r = 4% = 0.04

The interest is compounded semiannually

n = 2

Time, t = 9 years

Substitute these parameters into the equation above

$FV=8704.56(1+\frac{0.04}{2})^{2(9)}\\\\FV=8704.56(1.02)^{18}\\\\FV=\ 12432$

b) The future value if the interest is compounded annually

n = 1

$FV=8704.56(1+\frac{0.04}{1})^{1(9)}\\\\FV=8704.56(1.04)^{9}\\\\FV=\ 12432\\\\FV=\ 12389$

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