Question

how much would $200 dollars invested at 5% interest compounded monthly versus worth after 9 years? round to the nearest cent

Answer 1

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\ 200\\ r=rate\to 5\%\to \frac{5}{100}\to &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12\\ t=years\to &9 \end{cases} \\\\\\ A=200\left(1+\frac{0.05}{12}\right)^{12\cdot 9}\implies A=200(1.0041\overline{66})^{108} \\\\\\ A\approx 313.3693298833$