Question

Gary deposited $1490 into a savings account in which interest is compounded weekly at a rate of 2.15%. Assuming he makes no other deposits or withdrawals, how much will be in his account after 3 years?

Answer 1

keeping in mind that there are 52 weeks in a year.

`\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 &\$1490\\ r=rate\to r\%\to (r)/(100)\dotfill &0.0215\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus fifty two} \end{array}\dotfill &52\\ t=years\dotfill &3 \end{cases}`

`\bf A=1490\left(1+(0.0215)/(52)\right)^(52\cdot 3)\implies A\approx 1490(1.000413)^(156)\implies A\approx 1589.25`