Answer
Approximately 14.6 years
Work Step by Step
Continous Compounding: $Pe^{rt}$ where $P$ is the Principal, $r$ is the rate of compounding interest, and $t$ is the time in years. Since we're asked to find the time $t$ it takes to $triple$ the principal at a 7.5% rate: $$3P = Pe^{(0.075)t}$$ $$3 = e^{0.075t}$$ $$0.075t = \ln 3$$ $$t = \frac{\ln 3}{0.075} \approx 14.6$$
