Question

Bill invests $2,977 in a retirement account

Answer 1

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 2977\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &13 \end{cases} \\\\\\ A=2977\left(1+\frac{0.06}{4}\right)^{4\cdot 13}\implies A=2977(1.015)^{52}\implies A\approx 6456.74$