How long will it take an investment to triple if it is continuously compounded at 15% per year? Select the correct answer rounded to the nearest year.

Question

Quizplus · Accepted Answer

The formula for continuous compounding is: 
A = Pe^(rt) 
where A is the amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), and t is the time (in years).

We want to find the time it takes for the investment to triple, so we need to solve for t: 
3P = Pe^(0.15t) 
Divide both sides by P: 
3 = e^(0.15t)

Take the natural logarithm of both sides: 
ln(3) = 0.15t 
t = ln(3)/0.15

Using a calculator, we get t ≈ 7.27 years. Rounded to the nearest year, the answer is 7 years. Therefore, the best choice is C.

How Long Will It Take an Investment to Triple If