Question

DJ plans to invest $10,000 into an account offering 2.45% compounded monthly. How much will his investment be worth in 20 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 &\$10000\\ r=rate\to 2.45\%\to (2.45)/(100)\dotfill &0.0245\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}`

`A = 10000\left(1+(0.0245)/(12)\right)^(12\cdot 20) \implies A \approx 10000( 1.0020)^(240)\implies A \approx 16315.01`