Question

harriet has deposited $693 in a savings account that earns interest at a rate of 4.6% compounded monthly .what will the account balance be in thirteen years

Answer 1

`\bf ~~~~~~ \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 &\$693\\ r=rate\to 4.6\%\to (4.6)/(100)\dotfill &0.046\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &13 \end{cases}`

`\bf A=693\left(1+(0.046)/(12)\right)^(12\cdot 13)\implies A=693(1.0038\overline{3})^(156)\implies A\approx 1160.68`