Question 644477: 7000 is compounded continuously at 6% interest, what is the amount after 2 years?
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! I think that compunding continuously at p percent per year (expressed as a decimal) has the factor
(1) e^p, where e = 2.71828... an irrational number named after Euler, a famous Swiss mathematician, 1707-1783.
The balance, B, of account starting with principal, P, earning p percent per year for n years is
(2) B = P*(e^p)^n
For this example we have
(3) B = 7000*(e^.06)^2
Using a calculator with the e^x key we get
(4) B = 7892.478
The answer to the nearest cent is $7892.48.
If you did not compound continuously but only yearly you would have
(5) By = 7000*(1.06)^2 or
(6) By = 7865.20
Giving $27.28 less.
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