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

`\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 (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+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 9\%\to (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+(0.09)/(1)\right)^(1\cdot 8)\implies A=2000(1.09)^8\implies \boxed{A\approx 3985.13}`

Answer 2

i think 100000000000