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
Continuous compounding will have a “rate/time” value, such as 5% per year. This results in a formula something like Result=Initial*rate^(amount of time periods). A similar formula is involved with half lives.
Using that rate/time value, you can substitute a smaller rate and a smaller time period, such as 2.5% per 6 months (which means more time periods). This ends up increasing the Result, but the rate of that increase is smaller as you decrease the size of the time periods.
Calculus lets us calculate what the rate would be if the time periods were infinitely small (aka the interest happens continuously). This involves the number *e*, which is the result of combining exponents and dividing them against each other (which is what paragraph 2 is doing, and is why it shows up here).
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