Question

before leaving for a 3 year trip overseas, I deposited a sum of money in an account that pays 6% interest compunded quarterly. When i return from my trip, the amount in my account stands at $9564.95. How much interest has been added since I have been away?

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 9564.95\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to (6)/(100)\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &3 \end{cases}`

`9564.95 = P\left(1+(0.06)/(4)\right)^(4\cdot 3) \implies 9564.95=P(1.015)^(12)\implies \cfrac{9564.95}{(1.015)^(12)}=P \\\\\\ 8000\approx P\hspace{9em}\stackrel{\textit{interest added}}{9564.95~~ - ~~8000} ~~ \approx ~~ \text{\LARGE 1564.95}`