[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$1500\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &7 \end{cases} \\\\\\ 1500=Pe^{0.05\cdot 7}\implies \cfrac{1500}{e^{0.35}}=P\implies 1057.03\approx P[/tex]
