Question

A couple deposits $20,000 into an account earning 7% annual interest for 20 years. Calculate thefuture value of the investment if the interest is compounded semiannually. Round your answer to thenearest cent.

Answer 1

Given

$\begin{gathered} Principal(P)=20,000 \\ r=7\%=\frac{7}{100}=0.07 \\ t=20 \end{gathered}$

To Determine: The future value of the investment

Solution

It can be observed that the deposit is compouned semi-annually

Step 1: Write out the formula

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=future\text{ value} \\ n=2(i.e.\text{ semi-annually means twice a year\rparen} \end{gathered}$

Step 2: SUbstitute the given into the formula

$\begin{gathered} A=20000(1+\frac{0.07}{2})^{2\times20} \\ A=20000(1+0.035)^{40} \end{gathered}$$\begin{gathered} A=20000(1.035)^{40} \\ A=20000(3.95925972117) \\ A=79185.19444 \\ A\approx79,185.19(nearest\text{ cent\rparen} \end{gathered}$

Hence, the future value of the investment is $79,185.19