Question

R 4 You Invest

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Initial $100 in an account that has an annual interest rate of 3%, compounded quarterly. How much money will you have in the account after 20 years? Round your answer to the nearest whole

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 &\$100\\ r=rate\to 3\%\to (3)/(100)\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &20 \end{cases} \\\\\\ A=100\left(1+(0.03)/(4)\right)^(4\cdot 20)\implies A=100(1.0075)^(80)\implies A\approx 182`