Question

Find the future value of $2000 deposited at 9% for 8 years if the account pays simple interest, and the account pays interest compounded annually.

Answer 1

I think 100000000000

Answer 2

$\bf ~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \ 2000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years\dotfill &8 \end{cases} \\\\\\ A=2000[1+(0.09)(8)]\implies A=2000(1.72)\implies \boxed{A=3440} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 2000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &8 \end{cases} \\\\\\ A=2000\left(1+\frac{0.09}{1}\right)^{1\cdot 8}\implies A=2000(1.09)^8\implies \boxed{A\approx 3985.13}$