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
You start with apr. that is how much interest you get in one year. Most loans compound monthly so you divide the apr by 12 and that is your monthly interest rate. But say you compound weekly. You divide the apr by 52 (weeks in a year). That is how much interest you get weekly. Daily would be apr divided by 356.
But if you want to compound continuously you can’t divide by infinity. So you get a more complicated equation of Pe^(rt). So you can say apr is r, t is time since the loan started, P is the principal amount, and e is a constant that a very smart mathematician calculated and we accept because it’s just right and we don’t know enough math to disprove. We can use this to calculate the amount of interest at any given point in time.
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