[tex]\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}\\\\
-------------------------------[/tex]
[tex]\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}[/tex]
compare the amounts.
