SOLUTION: Crystal has $750 to invest at 8% annual interest compounded continuously. How long will it take for her investment to double? Round to the nearesthundredth of a year.

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Question 1158423: Crystal has $750 to invest at 8% annual interest compounded continuously. How long will it take for her investment to double? Round to the nearesthundredth of a year.
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for continuous compounding is FV=Pe%5E%28Yr%29, where e=2.71828... and P is the amount you invest at the beginning. So we have 1500=750%2Ae%5E%280.08Y%29. e%5E%280.08Y%29=2. Taking the natural logarithm of both sides gives ln%28e%5E%280.08Y%29%29=ln%282%29 0.08Y=ln%282%29. Y=ln%282%29%2F0.08. Using a calculator to approximate, we have Y=8.66. It will take about 8.66 years for the investment to double.