Question

Erin deposited $400 in a saving account earning 3% yearly compound interest. write an equation to represent how much money (y) Erin would have after (x) years. use your equation to determine how much money Erin would have in the account after 15 years.

Answer 1

$~~~~~~ \textit{Compound Interest Earned Amount \underline{in 15 years}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 400\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yeary, thus once} \end{array}\dotfill &1\\ t=years\dotfill &15 \end{cases}$

$A=400\left(1+\frac{0.03}{1}\right)^{1\cdot 15}\implies A=400(1.03)^{15}\implies A\approx 623.19 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=400(1.03)^x~\hfill$