I recently had learned about the concept of compounding continuously. How does it work? How is compounding something continuously not infinite? What is e and why is it necessary?
In: Economics
e is magic number, like pi. There is an algorithm to get an exact value of the number e^(x) where x can be any number, positive or negative, whole or a fraction, and the algorithm will just keep giving your digits until you get tired of it. Getting an exact power, like 2^(5.122) is possible using this formula, and adjusting it for the fact that 2 is not e.
Compound interest is usually compounded in increments of whenever interest is paid… usually monthly for some banks accounts, perhaps yearly for some bigger investments, and so on. But mathematically, the shorter the period, the better. If you have 12% interest (for the sake of easy math), but compound monthly, each monthly interest payout is only 1% of your bank account’s total. But doing it that way is still worth more than one interest payout of 12% at the end of the year because the interest is compounding month to month.
“Continuous compounding” takes it to the mathematical extreme. Oh, and obviously you need to be able to have tiny fractions of a penny in your bank account to work like this but… What if interest was paid every minute? Every second? Every millisecond? What happens if the interval becomes effectively 0? Now you have continuous compounding, and the extreme limit. You’ll need to use e to get the value.
I’m not aware of anyone actually *doing* this. Few banks want to give their customers more money, ya know?
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