Question

Emma and Paul each invest $2,000 into accounts that earn 6% interest. If Emma’s account earns simple interest and Paul’s account earns compound interest, which is the value of each person’s account after 8 years?

a. Emma - $2,960; Paul - $1,187. 70


b. Emma - $960; Paul - $1,187. 70


c. Emma - $2,960; Paul - $3,187. 70


d. Emma - $960; Paul - $3,187. 70

Answer 1

`~~~~~~ \stackrel{\textit{\Large Emma}}{\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 6\%\to (6)/(100)\dotfill &0.06\\ t=years\dotfill &8 \end{cases} \\\\\\ A=2000[1+(0.06)(8)]\implies A=2000(1.48)\implies \boxed{A=2960} \\\\[-0.35em] ~\dotfill`

`~~~~~~ \stackrel{\textit{\Large Paul}}{\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 6\%\to (6)/(100)\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &8 \end{cases}`

`A=2000\left(1+(0.06)/(1)\right)^(1\cdot 8)\implies A=2000(1.06)^8\implies \boxed{A\approx 3187.70}`