Respuesta :
SOLUTION
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
[tex]\begin{gathered} A = P(1 + \frac{r}{n})^{nt} \\ \\ Interest=Amount-Principal \end{gathered}[/tex]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
[tex]\begin{gathered} P=16000 \\ r=\frac{4}{100}=0.04 \\ n=2\text{ since it is being compounded twice in a year} \\ t=5 \end{gathered}[/tex]STEP 3: Calculate the compounded Amount
[tex]\begin{gathered} \text{By substitution,} \\ A=16000\times(1+\frac{0.04}{2})^{2\times5} \\ A=16000\times(1+0.02)^{10} \\ A=16000\times1.02^{10} \\ A=16000\times1.21899442 \\ A=19503.91072 \end{gathered}[/tex]STEP 4: Calculate the interest earned
[tex]\begin{gathered} From\text{ the formula in step 1;} \\ Interest=19503.91072-16000 \\ Interest=3503.91072 \\ Interest\approx3503.91 \end{gathered}[/tex]Hence, the interest earned after 5 years is $3503.91
