SOLUTION: How long (in years) would $11,000 have to be invested at 7% compounded continuously to earn $4,609.74 interest?. It would have to be invested for ____ years. (Round to 2 decimal

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Question 1166448: How long (in years) would $11,000 have to be invested at 7% compounded continuously to earn $4,609.74 interest?.
It would have to be invested for ____ years. (Round to 2 decimal places.)
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


Continuous compound interest formula:

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

t (years) is the unknown
r (interest rate) is 7% = .07
P is the principal, $11,000
A is the amount you want to have -- the $11,000 principal, plus $4,609.74 interest = $15,609.74

15609.74+=+11000e%5E%28.07t%29 [1]

The unknown is in the exponent, so use logarithms.

15609.74%2F11000+=+e%5E%28.07t%29
ln%2815609.74%2F11000%29+=+.07t
t+=+%28ln%2815609.74%2F11000%29%29%2F.07

Use a calculator....

Or solve the equation [1] with a graphing calculator by graphing the two expressions and find their point of intersection.