Question

Anne deposited $500 in an account that earns 6% simple annual interest. Shelly deposited $500 in an account that earns 6% annual interest compounded annually. They leave the money in the account for 4 years. How much do Anne and Shelly each have in their accounts at the end of the 4 years?

Answer 1

`~~~~~~ \stackrel{ \textit{\LARGE Anne} }{\textit{Simple Interest Earned Amount}} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 6\%\to (6)/(100)\dotfill &0.06\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 500[1+(0.06)(4)]\implies A=500(1.24) \implies A = 620 \\\\[-0.35em] ~\dotfill`

`~~~~~~ \stackrel{ \textit{\LARGE Shelly} }{\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 &\$500\\ r=rate\to 6\%\to (6)/(100)\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 500\left(1+(0.06)/(1)\right)^(1\cdot 4) \implies A \approx 631.24`