SOLUTION: how long will it take for an investment to double in value if it earns 5.25% compound continuously?

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Question 471981: how long will it take for an investment to double in value if it earns 5.25% compound continuously?
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
If the interest is compounded continuously, we use this formula to determine the future value:
FV+=+Pe%5EYr where P = the initial principal, Y = the number of years, r = interest rate
If the investment doubles, FV = 2P, so we can write
2P+=+Pe%5EYr
2+=+e%5E%280.0525Y%29
Take the natural log of both sides to get rid of the exponential, and solve for y:
ln+2+=+0.0525Y
Y+=+ln+2%2F0.0525
This gives Y = 13.203 years