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
The more frequently you compound interest, the less you compound each time. Still, more compounding events gives you a bit more money relative to doing it less frequently at the same interest rate. If you calculate the difference between compounding every year, every month, every day, even every second, you’ll notice that each one is higher but eventually the differences become smaller and smaller.
This is because they are converging on a theoretical maximum that you can never get higher than no matter how frequently you compound an increasingly tiny amount.
You can use calculus to calculate this theoretical maximum, and continuously compounding interest means that the person paying you interest is just giving you that theoretical maximum which is usually fractions of a percent more than compounding ever day or week.
Put another way, if you take the expression (1+1/x)^x and plug in numbers for x, you will notice that you will start to approach but never reach 2.718, no matter how large of a number you choose for x. This is e, and since that is the general expression for interest we can substitute e and say it’s equivalent to using the largest possible x, which is the frequency of compounding.
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