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

$\bf ~~~~~~ \stackrel{Sheldon}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\ 15000\\ r=rate\to 3\%\to \frac{3}{100}\to &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &12 \end{cases} \\\\\\ A=15000\left(1+\frac{0.03}{1}\right)^{1\cdot 12}\implies A=15000(1.03)^{12}\implies A\approx 21386.41$

$\bf -------------------------------\\\\ ~~~~~~ \stackrel{Howard}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\ 15000\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &5 \end{cases}$

$\bf A=15000\left(1+\frac{0.06}{1}\right)^{1\cdot 5}\implies A=15000(1.06)^5\implies A\approx 20073.38$

compare them away.