Question

Find compound interest:$12,300 at 2% compounded semiannually for 4 years

Answer 1

Given:

$12,300 at 2% compounded semiannually for 4 years

So, P = 12300

r = 2% = 0.02

compounded semiannually ⇒ n = 2

Time = t = 4 years

We will find the compound interest I, we will use the following formula:

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

Substitute with the given values:

$\begin{gathered} I=12300\cdot(1+\frac{0.02}{2})^{2\cdot4}-12300 \\ I=12300\cdot1.01^8-12300 \\ I=12300\cdot(1.01^8-1)\approx1019.1375 \end{gathered}$

Rounding to the nearest cent

So, the answer will be the compound interest = $1,019.14