### Facts about compound interest and continuous
compounding

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}

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