How long will it take $200 to triple itself if it is invested at 8% interest compounded continuously? Please round the answer to the nearest tenth.
A) 12.7 years
B) 14.2 years
C) 16.7 years
D) 14.7 years
E) 13.7 years

Question

Quizplus · Accepted Answer

To find the time it takes for an investment to triple with continuous compounding, use the formula $A = Pe^{rt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time (years). To triple, $A = 3P$. Substituting the given values, $3(200) = 200e^{0.08t}$. Simplifying, $3 = e^{0.08t}$. Taking the natural logarithm of both sides, $\ln(3) = 0.08t$. Solving for $t$, $t = \frac{\ln(3)}{0.08} \approx 13.7$ years.

How Long Will It Take $200 to Triple Itself If