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

[tex]~~~~~~ \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 \frac{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[/tex]

[tex]~~~~~~ \stackrel{\textit{\Large Paul}}{\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 6\%\to \frac{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}[/tex]

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

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O D. 2001
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