Question

Pam opened a savings account 8 years ago. The account earns 2% interest, compounded

monthly. If the current balance is $400.00, how much did she deposit initially

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$400\\ P=\textit{original amount deposited}\\ 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 &8 \end{cases}`

`400=P\left(1+(0.02)/(12)\right)^(12\cdot 8)\implies 400=P\left( (601)/(600) \right)^(96) \\\\\\ \cfrac{400}{ ~~ \left( (601)/(600) \right)^(96) ~~ }=P\implies 340.90\approx P`