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.

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 960\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases}$

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