Question

Use the appropriate compound interest formula to compute the balance in the account after the stated period of time$7,000 is invested for 16 years with an APR of 5% and monthly compounding.The balance in the account after 16 years is $Round to the nearest cent as needed.)

Answer 1

SOLUTION

We will use the formula

$\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ where \\ P=money\text{ invested = \ 7,000} \\ r=APR=5\%=\frac{5}{100}=0.05 \\ t=time\text{ in years = 16} \\ n=number\text{ of compoundings = monthly =12} \\ A=amount=balance\text{ in the account after t years } \end{gathered}$

Applying we have

$\begin{gathered} A=7,000(1+\frac{0.05}{12})^{12\times16} \\ A=7,000(1+0.0041667)^^{192} \\ A=7,000(1.0041667)^{192} \\ A=15,552.92 \end{gathered}$

Hence the answer is $15,552.92