SOLUTION: You are investing money at 8.5 percent annual interest, compounded continuously. It will take you how many years to double your investment.

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Question 593328: You are investing money at 8.5 percent annual interest, compounded continuously. It will take you how many years to double your investment.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let P be the amount initially invested. Since we want this investment to double, the final amount is A = 2P

One other thing to keep in mind is that the rate 8.5% means r = 0.085


So plug A = 2P and r = 0.085 into A+=+Pe%5E%28rt%29 and then solve for t


A+=+Pe%5E%28rt%29

2P+=+P%2Ae%5E%280.085t%29

2P%2FP+=+e%5E%280.085t%29

2+=+e%5E%280.085t%29

ln%282%29+=+ln%28e%5E%280.085t%29%29

ln%282%29+=+0.085t%2Aln%28e%29

ln%282%29+=+0.085t%2A%281%29

ln%282%29+=+0.085t

ln%282%29%2F0.085+=+t

0.693147180559945%2F0.085+=+t

8.15467271246994+=+t

t+=+8.15467271246994

So it will take you roughly 8.15 years to double your investment.

If your answer must be a whole number of years, then round up to 9 years.