Question

If your parents deposit $3600 in to a bank account when you are born paying 2% annual interest compounded monthly, how much money will be in the account when you turn 18? Round to the nearest cent.

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 &\$3600\\ r=rate\to 2\%\to (2)/(100)\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &18 \end{cases}`

`A = 3600\left(1+(0.02)/(12)\right)^(12\cdot 18)\implies A=3600((601)/(600))^(216) \implies A \approx 5158.44`