SOLUTION: Solve. Where appropriate, include approximations to four decimal places. An investment with interest compounded continuously doubled itself in 16 yr. What is the interest rate?

Question 285204: Solve. Where appropriate, include approximations to four decimal places.
An investment with interest compounded continuously doubled itself in 16 yr. What is the interest rate?
Can someone please help me?
Found 2 solutions by rfer, MathTherapy:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
72/16=4.5%
Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!
This is future value, and the formula for future value, with continuous compounding is: , where A = future value, P = present value, e = continuous compounding factor, or 2.7182818, r = annual interest rate, and t = time, in years = 16.

Let P = P. Then A = 2P, since the initial investment doubled.
would then give us:

---------- Dividing by LCD P
We can rewrite this as

Applying logs, we get: =

, or 4.3322%
Therefore, the rate at which an investment doubles in 16 years, with continuous compounding interest is: %.

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