SOLUTION: How long​ (in years and​ months) will it take for an investment to double at 9 9​% compounded​ monthly?

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Question 1103814:
How long​ (in years and​ months) will it take for an investment to double at
9
9​% compounded​ monthly?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The annual interest rate is 9%, or 0.09; the monthly interest rate is 0.09/12 = 0.0075. The monthly growth factor is then 1+.0075 = 1.0075.

We want to know how many months it takes for the overall growth factor to be 2, so that the original investment doubles.

%281.0075%29%5En+=+2
n%2Alog%281.0075%29+=+log%282%29
n+=+log%282%29%2Flog%281.0075%29+=+92.77

It will take 93 months for the investment to double in value; or, in years and months, 7 years and 9 months.