Find the present value and the amount of interest earned. Use the present value of a dollar table.
\begin{tabular}{|c|c|c|c|c|c|}
\hline Amount Needed & \begin{tabular}{c}
Time \\
(Years)
\end{tabular} & Interest & Compounded & \begin{tabular}{c}
Present \\
Value
\end{tabular} & \begin{tabular}{c}
Interest \\
Earned
\end{tabular} \\
\hline$\$ 11,600$ & 10 & $4 \%$ & semiannually & $\$$ \\
\hline
\end{tabular}

Click here to view periods $1-25$ of the present value of a dollar table.
Click here to view periods $26-49$ of the present value of a dollar table.

What is the present value?
$5 \square$ (Round to the nearest cent as needed.)
What is the amount of interest eamed?
\$ (Round to the nearest cent as needed.)

Step 1 ：Given in the problem: Future Value (FV) = $11,600, annual interest rate (r) = 4% = 0.04, number of times that interest is compounded per year (n) = 2, and time the money is invested for in years (t) = 10 years.

Step 2 ：The formula for the present value of a future amount is: \(PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}\)

Step 3 ：Substitute the given values into the formula: \(PV = \frac{$11,600}{(1 + \frac{0.04}{2})^{2*10}}\)

Step 4 ：Calculate the rate per period: \(0.04/2 = 0.02\)

Step 5 ：Calculate the total number of periods: \(2*10 = 20\)

Step 6 ：Calculate the factor \((1 + rate)^{periods}\): \((1 + 0.02)^{20} \approx 1.48595\)

Step 7 ：Divide the future value by this factor: \($11,600 / 1.48595 \approx $7803.64\)

Step 8 ：\(\boxed{PV \approx $7803.64}\)

Step 9 ：The amount of interest earned is the difference between the future value and the present value: \(Interest Earned = FV - PV = $11,600 - $7803.64 = $3796.36\)

Step 10 ：\(\boxed{Interest Earned \approx $3796.36}\)