so, the principal is 25,000, when it double then, the accumulated amount is 50,000.
[tex]\bf \qquad \textit{Continuously Compounding Interest Earned Amount}\\\\
A=Pe^{rt}\qquad
\begin{cases}
A=\textit{accumulated amount}\to &\$50000\\
P=\textit{original amount deposited}\to& \$25000\\
r=rate\to 5.3\%\to \frac{5.3}{100}\to &0.053\\
t=years
\end{cases}
\\\\\\
50000=25000e^{0.053t}\implies \cfrac{50000}{25000}=e^{0.053t}\implies 2=e^{0.053t}
\\\\\\
ln(2)=ln(e^{0.053t})\implies ln(2)=0.053t\implies \cfrac{ln(2)}{0.053}=t
\\\\\\
13.0782486898102888\approx t\implies 13.08\approx t[/tex]
