Question

Suppose that $16,000 is deposited for five years at 4% APR. Calculate the interest earned if interest iscompounded semiannually. Round your answer to the nearest cent.

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 compound interest

`\begin{gathered} A = P(1 + (r)/(n))^(nt) \\ \\ Interest=Amount-Principal \end{gathered}`

Where

A =final 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} P=16000 \\ r=(4)/(100)=0.04 \\ n=2\text{ since it is being compounded twice in a year} \\ t=5 \end{gathered}`

STEP 3: Calculate the compounded Amount

`\begin{gathered} \text{By substitution,} \\ A=16000*(1+(0.04)/(2))^(2*5) \\ A=16000*(1+0.02)^(10) \\ A=16000*1.02^(10) \\ A=16000*1.21899442 \\ A=19503.91072 \end{gathered}`

STEP 4: Calculate the interest earned

`\begin{gathered} From\text{ the formula in step 1;} \\ Interest=19503.91072-16000 \\ Interest=3503.91072 \\ Interest\approx3503.91 \end{gathered}`

Hence, the interest earned after 5 years is $3503.91