Question

Sheldon invests $15,000 in an account earning 3% interest, compounded annually for 12 years. Seven years after Sheldon's initial investment, Howard invests $15,000 in an account earning 6% interest, compounded annually for 5 years. Given that no additional deposits are made, compare the balances of the two accounts after the interest period ends for each account. (round to the nearest dollar)

Answer 1

`\bf ~~~~~~ \stackrel{Sheldon}{\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}\to &\$15000\\ r=rate\to 3\%\to (3)/(100)\to &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &12 \end{cases} \\\\\\ A=15000\left(1+(0.03)/(1)\right)^(1\cdot 12)\implies A=15000(1.03)^(12)\implies A\approx 21386.41`


`\bf -------------------------------\\\\ ~~~~~~ \stackrel{Howard}{\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}\to &\$15000\\ r=rate\to 6\%\to (6)/(100)\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &5 \end{cases}`


`\bf A=15000\left(1+(0.06)/(1)\right)^(1\cdot 5)\implies A=15000(1.06)^5\implies A\approx 20073.38`

compare them away.