Question

You put $113 into a savings account that has an interest rate of 6% compounded every week.

a. How much money is in your account after 4 years?

How much interest did you earn in those 4 years?
b.

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 &\$113\\ r=rate\to 6\%\to (6)/(100)\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus 52} \end{array}\dotfill &52\\ t=years\dotfill &4 \end{cases}`

`A = 113\left(1+(0.06)/(52)\right)^(52\cdot 4) \implies \boxed{A \approx 143.63}\hspace{5em}\underset{ earned~interest }{\stackrel{ 143.63~~ - ~~113 }{\boxed{\approx 30.63}}}`