Question

17. Sally put $960 in a savings account that earns 7% interest compounded quarterly. How much interest will she earn at the end of the thrid quarter? What will be her account balance at that time?​

Answer 1

well, one quarter of a year is 3 months, so at the end of third quarter, 9 months have passed, and since a year has 12 months, 9 months are simply 9/12 of a year.

`~~~~~~ \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 &\$960\\ r=rate\to 7\%\to (7)/(100)\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\to (9)/(12)\dotfill &(3)/(4) \end{cases}`

`A=960\left(1+(0.07)/(4)\right)^{4\cdot (3)/(4)}\implies A=960(1.0175)^3\implies A\approx 1011.29`