Question

You deposit $3000 each year into an account earning 5% interest compounded annually. How much will you have in the account in 30 years?

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{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &30 \end{cases} \\\\\\ A=3000\left(1+(0.05)/(1)\right)^(1\cdot 30) \implies a=3000(1.05)^(30)\implies A \approx 12965.83`