Question

Find compound interest:$45,000 at 6% compounded semiannually for 5 years

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the formula for calculating compounded Amount

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

Where A = final compounded amount

P=initial principal balance

r=interest rate

n=number of times interest applied per time period

t=number of time periods elapsed

STEP 2: Write the given parameters

$\begin{gathered} \text{compunded semi-annually means that it is compounded twice in a years, this implies that:} \\ n=2 \\ P=45000,t=5,r=\frac{6}{100}=0.06 \end{gathered}$

STEP 3: Substitute the values into the formula to get the compound Amount

$\begin{gathered} A=\text{\ }45000(1+\frac{0.06}{2})^{2\times5} \\ A=\text{\ }45000(1+0.03)^1 \\ A=\text{\ }45000(1.03)^{10} \\ A=\text{\ }45000\times1.343916379 \\ A=\text{\ }60476.23707 \\ A\approx\text{\ }60476.24\text{ to the nearest cents} \end{gathered}$

STEP 4: Calculate the compound interest

$\begin{gathered} \text{Compound interest= Compound Amount-Principal} \\ \text{Compound interest=\ }60476.24-\text{\ }45000 \\ \text{Compound interest}=\text{\ }15476.24 \end{gathered}$

Hence, the compound interest is approximately $15476.24 to the nearest cents