Answer
$15.27$ years
Work Step by Step
The formula for continuous compounding where $r$ is the rate of interest, $t$ is the time in years is, $P$ is the principal, $A$ is the amount you get back after $t$ years:
$A=Pe^{rt}$
Here we have:
$A=\$25000$
$P=\$10000$
$r=6\%=0.06$
Substitute these values into the formula above to obtain:
\begin{align*}
\$25000&=\$10000 \cdot e^{0.06t}\\
\frac{\$25000}{\$10000}&=e^{0.06t}\\
2.5&=e^{0.06t}\\
\ln{2.5}&=\ln{(e^{0.06t})}\\
\ln{2.5}&=0.06t\\
\frac{\ln{2.5}}{0.06}&=\frac{0.06t}{0.06}\\
15.2715122&=t\end{align*}
Hence, $t\approx15.27$ years.
