Question

elizabeth invests $250 at a 1% interest rate compounded continuously. emily invests $200 at a 2% interest rate compounded continuously. who has a higher balance at the end of 20 years? how much more is their balance?

Answer 1

$\bf ~~~~~~ \stackrel{Elizabeth}{\textit{Continuously Compounding Interest Earned Amount}} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to& \ 250\\ r=rate\to 1\%\to \frac{1}{100}\to &0.01\\ t=years\to &20 \end{cases} \\\\\\ A=250e^{0.01\cdot 20}\implies A=250e^{0.2}\\\\ -------------------------------$

$\bf ~~~~~~ \stackrel{Emily}{\textit{Continuously Compounding Interest Earned Amount}} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to& \ 200\\ r=rate\to 2\%\to \frac{2}{100}\to &0.02\\ t=years\to &20 \end{cases} \\\\\\ A=200e^{0.02\cdot 20}\implies A=200e^{0.4}$

compare the amounts.