[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2543\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]2543=2000e^{\frac{r}{100}\cdot 4}\implies \cfrac{2543}{2000}=e^{\frac{r}{25}}\implies \log_e\left( \cfrac{2543}{2000}\right)=\log_e\left( e^{\frac{r}{25}} \right) \\\\\\ \ln\left( \cfrac{2543}{2000}\right)=\cfrac{r}{25}\implies 25\ln\left( \cfrac{2543}{2000}\right)=r\implies 6\approx r[/tex]
