Answer
$\$12,910.62$.
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:
$P=\$15000$
$t=3$years
$r=5\%=0.05$
Substitute these values into the formula above to obtain:
$\$15000=A \cdot e^{0.05\cdot3}\\A=\frac{\$15000}{e^{0.05\cdot3}}\\A=\frac{\$15000}{e^{0.15}}\approx\$12,910.62$.
