SOLUTION: You are investing money at 9.5 percent annual interest, compounded continuously. It will take you {insert here} years to double your investment.

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Question 1198969: You are investing money at 9.5 percent annual interest, compounded continuously. It will take you {insert here} years to double your investment.
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for continuous compounding is P%2Ae%5E%28rt%29, where P is the principal, e is Euler's number, r is the interest rate, and t is the number of years.
We are trying to find t in the equation 2P=P%2Ae%5E%28rt%29. Since we know that the interest rate is 0.095, we can put that into the equation to get 2P=P%2Ae%5E%280.095%2At%29. Dividing both sides by P, we get e%5E%280.095%2At%29=2. Taking the natural log of both sides, we get 0.095%2At=ln%282%29. Finally, dividing both sides by 0.095 gives us t=ln%282%29%2F0.095. Plugging into a calculator, we get that t is approximately highlight%287.296%29 years.