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

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\ 500\\ r=rate\to 7\%\to \frac{7}{100}\to &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\to &4\\ t=years\to &1 \end{cases} \\\\\\ A=500\left(1+\frac{0.07}{4}\right)^{4\cdot 1}\implies A=500(1.0175)^4\implies A\approx 535.92951564$