Question

Kaylee used her saved birthday money to set up a college savings account that earns 4.2% interest compounded weekly. If the original amount deposited was $750, how much interest will she have earned after 10 years?
Total amount of interest rounded to the nearest penny.

Answer 1

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

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 750\\ r=rate\to 4.2\%\to \frac{4.2}{100}\dotfill &0.042\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus fifty-two} \end{array}\dotfill &52\\ t=years\dotfill &10 \end{cases}$

$A=750\left(1+\frac{0.042}{52}\right)^{52\cdot 10}\implies A=750\left( \frac{26021}{26000} \right)^{520} \\\\\\ \stackrel{\textit{\Large Amounts}}{\stackrel{accumulated}{750\left( \frac{26021}{26000} \right)^{520}}~~ - ~~\stackrel{original}{750}} ~~ \approx ~~ \stackrel{earned~interest}{391.28}$