Question

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

Answer 1

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+(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=(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+(0.06)/(2))^(2*5) \\ A=\text{\$}45000(1+0.03)^1 \\ A=\text{\$}45000(1.03)^(10) \\ A=\text{\$}45000*1.343916379 \\ 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