Question

I put $500 in a saving account that warns 7% interest compounded quarterly. How much will be in the account after 1 year? Rounded to the nearest hundredth.

Answer 1

`\bf ~~~~~~ \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}\to &\$500\\ r=rate\to 7\%\to (7)/(100)\to &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\to &4\\ t=years\to &1 \end{cases} \\\\\\ A=500\left(1+(0.07)/(4)\right)^(4\cdot 1)\implies A=500(1.0175)^4\implies A\approx 535.92951564`