Henry is investing at a continuously compounded annual interest rate of 4.5%. How many years will it take for the balance to triple?.

Answer 1

Hi Lari. You will need to use the formula for continuously compounded interest to solve this problem. The formula is

A = Pe^rt

when P is the starting balance, r is the annual interest rate as a decimal, t is the amount of time passed in year, and A is the balance after t years.

For this problem, you are trying to find the time t when the balance A is three times the starting balance P. Using variables, you want to know t when A = 3P. You are told that r is 0.045.

You can plug the value for r and the expression for A into the formula.

3P = P e^0.045t

From here, you can solve the rest of the equation like this:

3 = e^0.045t

ln(3) = ln(e^0.045t)

ln(3) = 0.045t•ln(e)

ln(3) = 0.045t

t = ln(3)/0.045

The answer is t = 24.4 years. In other words, it will take 24.4 years for the balance to triple.