Question

Suppose that $15,000 is deposited for five years at 3% APR. Calculate the interest earned if interest is compounded semiannually. Round your answer to the nearest cent.

Answer 1

Step 1

State the formula for compound interest

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

where;

$\begin{gathered} P=15000 \\ r=\frac{3}{100}=0.03 \\ n=2 \\ t=5 \end{gathered}$

Step 2

Find the interest earned if the interest is compounded semiannually.

$\begin{gathered} A=15000(1+\frac{0.03}{2})^{2\times5} \\ A=15000(1.015)^{10} \\ A=15000(1.160540825) \\ A=\text{ \ }17408.11238\text{ } \end{gathered}$

The Amount(A)=Interest(I) +Principal(P)

Therefore;

$\begin{gathered} 17408.11238=I\text{ +15000} \\ I=\text{ \ }2408.112375 \\ I=\text{ \ 2408.11} \end{gathered}$

Answer; Interest=$2408.11