Question

A couple deposits $21,000 into an account earning 7% annual interest for 20 years. Calculate the future value of the investment if the interest is compounded monthly
Round your answer to the nearest cent.

Answer 1

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 21000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}$

$A=21000\left(1+\frac{0.07}{12}\right)^{12\cdot 20}\implies A=21000\left( \frac{1207}{1200} \right)^{240}\implies A\approx 84813.52$