Question

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

Answer 1

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \ 400\\ P=\textit{original amount deposited}\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &8 \end{cases}$

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