Question

Suppose $2000 is deposited in an account paying 3.5% interest compounded quarterly. What will the account balance be after 14 years?

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 &\$2000\\ r=rate\to 3.5\%\to (3.5)/(100)\to &0.035\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\to &4\\ t=years\to &14 \end{cases} \\\\\\ A=2000\left(1+(0.035)/(4)\right)^(4\cdot 14)\implies A=2000(1.00875)^(56) \\\\\\ A\approx 3257.681852590698`