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Where does the continuous compounding formula come from?

Assume the limit exists, and call it L, then:

So

If we are allowed ...

Now, log of a product is the sum of the logs ...

Use log rules:

But as *m* gets large, so
gets really small, so can use the
log approximation
,
to get

Cancel to get

Now **exp** both sides to get

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*Richard Waterman*

*1999-05-14*