Question

Leo invests $2,000 at an interest rate of 4%, compounded quarterly.

How much is the investment worth at the end of 3 years?

Answer 1

`~~~~~~ \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}\dotfill &\$2000\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &3 \end{cases} \\\\\\ A=2000\left(1+(0.04)/(4)\right)^(4\cdot 3)\implies A=2000(1.01)^(12)\implies A\approx 2253.65`