SOLUTION: an account pays 5% interest, compounded continuously. how long will it take for the investment to double?

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Question 892534: an account pays 5% interest, compounded continuously. how long will it take for the investment to double?
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
We start with the formula A = P*e^(r*t)

We have some unknown investment P and we want it to double to 2P (in t years). So A = 2P.

The interest rate is 5% so r = 0.05

We use this info to solve for t

A = P*e^(r*t)

2P = P*e^(r*t)

2 = e^(r*t)

2 = e^(0.05*t)

ln(2) = ln( e^(0.05*t) )

ln(2) = 0.05*t*ln( e )

ln(2) = 0.05*t*1

ln(2) = 0.05*t

ln(2)/0.05 = t

13.862943611199 = t ... you need a calculator for this step

t = 13.862943611199

It takes roughly 13.862943611199 years for the investment to double.