SOLUTION: 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

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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