Respuesta :
Answer:
$4,167.27
Explanation:
The amount, A(n) in an account for a Principal invested at compound interest is calculated using the formula:
[tex]\begin{gathered} A(n)=P(1+\frac{r}{k})^{nk}\text{ }where=\begin{cases}P=Prin\text{cipal} \\ r=\text{Annual Interest Rate} \\ k=\text{Compounding Period}\end{cases} \\ n=nu\text{mber of years} \end{gathered}[/tex]In the given problem:
• P = $11,000.00
,• r=11% = 0.11
,• n= 3 years
,• k=2 (semi-annual)
Substitute these into the formula:
[tex]\begin{gathered} A(n)=11,000(1+\frac{0.11}{2})^{2\times3} \\ =11,000(1+0.055)^6 \\ =11,000(1.055)^6 \\ =\$15,167.27 \end{gathered}[/tex]Next, we find the interest earned.
[tex]\begin{gathered} \text{Interest}=\text{Amount}-\text{Prncipal} \\ =15167.27-11000 \\ =\$4,167.27 \end{gathered}[/tex]You would earn $4,167.27 in interest (rounded to 2 decimal places).
