[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$1850\\ P=\textit{original amount deposited}\dotfill & \$231.25\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &8 \end{cases}[/tex]
[tex]1850=231.25e^{\frac{r}{100}\cdot 8}\implies \cfrac{1850}{231.25}=e^{\frac{2r}{25}}\implies 8=e^{\frac{2r}{25}} \\\\\\ \log_e(8)=\log_e\left( e^{\frac{2r}{25}} \right)\implies \ln(8)=\cfrac{2r}{25}\implies 25\ln(8)=2r \\\\\\ \cfrac{25\ln(8)}{2}=r\implies \stackrel{\%}{25.99}\approx r[/tex]
