Question

Frank deposited $4000 into an account with 3% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in the account after 5 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}\dotfill &\$4000\\ r=rate\to 3\%\to (3)/(100)\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &5 \end{cases} \\\\\\ A=4000\left(1+(0.03)/(2)\right)^(2\cdot 5)\implies A=4000(1.015)^(10)\implies A\approx 4642.16`