Question

You deposit $5000 in an account earning 8% interest compounded monthly. How much will you have in the account in 15 years?

Answer 1

`\bf ~~~~~~ \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 &\$5000\\ r=rate\to 8\%\to (8)/(100)\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}`

`\bf A=5000\left(1+(0.08)/(12)\right)^(12\cdot 15)\implies A=5000(1.00\overline{66})^(180)\implies A\approx 16534.61`