# What is continuous compounding?

I understand that compounding is interest multiplied by itself several times depending on the number of compounding periods. But how is it possible to have infinite number of compounding periods? I can seem to make sense of it. If it is infinite, therefore, immeasurable, how did they derive the formula? Aside from that, is continuous compounding the same with discrete compounding?

They derived the formula using calculus. It’s the limit of discrete compounding as the number of compounding periods becomes infinite and the length of each compounding period goes to zero.

It’s not much different than daily compounding. The difference between daily compounding and continuous compounding of a 4% nominal rate on \$1,000,000 for one year is \$2.28.

I’ve always just assumed daily compounding too when doing these types of problems. As S2000magician said, the difference is minimal and it’s easier than remembering another formula.

Alright! Thanks guys!

My pleasure.