Question

If $300 is invested at a rate of 5% per year and is compounded quarterly, how much will the investment be worth in 15 years?

Answer 1

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 300\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &15 \end{cases} \\\\\\ A=300\left(1+\frac{0.05}{4}\right)^{4\cdot 15}\implies A=300(1.0125)^{60}\implies A\approx 632.15$