Question

You+deposit+$500+in+an+account+that+pays+5%+interest+compounded+yearly. +how+much+money+is+in+the+account+after+4+years?

Answer 1

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 500\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A=500\left(1+\frac{0.05}{1}\right)^{1\cdot 4}\implies A=500(1.05)^4\implies A\approx 607.75$