Here is more about this, contributed by a colleague:

Annual interest for 3 years (1+.04)³
Compounded quarterly (1 + .04/4)^3·4 = (1 + 1/{4/.04})^{{4/.04}·3·.04}
In symbols (1 + r/k)^n·k=(1 + 1/{k/r})^{k/r}·n·r where k is the frequency of compounding, r is the rate, n is years.
let m = k/r to get (1 + {1/m})^m·n·r which in the limit as k, i.e. m goes to infinity, becomes e^n·r

Maintained by greenfie@math.rutgers.edu and last modified 9/17/2004.