Question 30099: an extra credit for my honors math class. i cant figure it out for the life of me...
derive the formula A=Pe^rt from the general formula for compounding interestL A=P(1+r/n)^n*t
Answer by Fermat(136)   (Show Source):
You can put this solution on YOUR website!  - interest compounded periodically
 ------- interest compounded continuously
When interest is compounded continously, this means letting the number of periods in a year increase without bound.
In other words, we find the limit, as n tends to infinity of
Binomial theorem
Applying the Binomial theorem to  , we get
as  ,  , giving
and the above is the Maclaurin series for 
i.e.  as
We wanted to find the limit, as n tends to infinity of and we have the limit, as n tends to infinity, of which is . We substitute for .
So for continuous compounding we can write,
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