Question

For 7 years, Sheri deposits $3350 at the end of each year into an account that earns 19.7% per year compounded annually. Determine the interest earned.

Answer 1

$\bf ~~~~~~~~~~~~\textit{Future Value of an ordinary annuity}\\ ~~~~~~~~~~~~(\textit{payments at the end of the period}) \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\ ~~~~~~ \begin{cases} A=\textit{accumulated amount}\\ pymnt=\textit{periodic payments}\to &3350\\ r=rate\to 19.7\%\to \frac{19.7}{100}\to &0.197\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &7 \end{cases}$

$\bf A=3350\left[ \cfrac{\left( 1+\frac{0.197}{1} \right)^{1\cdot 7}-1}{\frac{0.197}{1}} \right]\implies A=3350\left[\cfrac{1.197^7-1}{0.197} \right] \\\\\\ A\approx 3350(12.7966673797946)\implies A\approx 42868.8357223119$

now, for 7 years she has been depositing $3350, so the amount that she put out of her pocket is 7*3350.

and we know the compounded amount is A, so the interest is just their difference.

42868.8357223119 - (7 * 3350).