Question

You deposit $3000 in an account earning 5% interest compounded monthly. How much will you have in the account in 15 years? Round to the nearest cent.

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}`

`A = 3000\left(1+(0.05)/(12)\right)^(12\cdot 15) \implies A = 3000( 1.0041\overline{66})^(180)\implies A \approx 6341.11`