In part 1 I showed how the number e arises from a simple compund interest problem. In fact when interest is compounded continuously the number seems to arise out of nowhere. That isn't the end of the story though. By looking more carefully at the limit we found to give the number e, we can produce an even better way of obtaining this mysterious number, and then we can create a nice neat formula for a balance that is subject to continuously compounded interest.
So we now have a rather neat equation for our compound interest problem and we have come up with a really nice way of approximating the number e, in fact we can use the summation formula for e as the very definition of the number! but we haven’t really raised its importance. So what if it is the limit of a compound interest problem? At the moment it is just a curiosity – not that important at all really…
Next time I’ll touch on the real power of e by looking at a bit of calculus and venturing where Euler may have done 300 years ago.
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