Question

A principal of $3200 is invested at 7.75% interest, compounded annually. How much will the investment be worth after 13 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 &\$3200\\ r=rate\to 7.75\%\to (7.75)/(100)\dotfill &0.0775\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &13 \end{cases} \\\\\\ A=3200\left(1+(0.0775)/(1)\right)^(1\cdot 13)\implies A=3200(1.0775)^(13)\implies A\approx 8444.51`