Question 1198837: Kyle invests in an account earning 4.5% interest compounded continuously. How long will it take to double his investment?
Doubling time in years =
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 2 = e^(.045*t)
take natural log of both sides of the equation to get:
ln(2) = ln(e^(.045*t)
since ln(e^(.045*t) is equal to .045*t * ln(e) and since ln(e) = 1, the equation becomes:
ln(2) = .045*t
solve for t to get:
t = ln(2)/.045 = 15.40327068
that's how many years it will take for the money to double.
to confirm, replace t in the equation to get:
2 = e^(.045*15.40327068)
since e^(.045*15.40327068) = 2, the equation becomes:
2 = 2, confirming the value of t is correct.
your solution is it will take 15.40327068 years for the money to double.
note that e is the scientific constant of 2.718282828.....
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