# Why continuously compounded interest a standard in finance? [closed]

Why is the "continuously compounded interest" the standard in finance? Many finance textbooks use the formula e^rt without justification.

The assumption that the interest frequency is approaching infinity, it is very unrealistic but how did it become a standard in finance?

• Because it is easy and convenient to manipulate mathematically, and because any non-continuously compounded return can be turned into a continuously compounded one. May 14 at 19:18
• @rubikscube09 is there any toy example to back up your answer? May 14 at 19:20
• Simple interest at $r$ per year is equivalent to continuously compounded interest at $\ln 1+r$ per year. For example 5% simple is same as 4.879% continuous. (Take the exponential of 0.04879 to see why). May 14 at 20:02
• Dupliacte which was in turn closed because it is a basic financial question. Reading it will "back" up how they are related though. May 14 at 20:06
• @Akdemy The post that you refer to was a question about the relationship between discrete and continuous interest. It is irrelevant to my question because mine is asking why the continuously compounded interest became standard in finance. May 14 at 20:10

It's a Duplicate which was in turn closed because it is a basic financial question. Reading it will "back" up how they are related: You asked rubikscube09 if he has a toy example to back up his answer. He answered that any non-continuously compounded return can be turned into a continuously compounded one: $$1+r_d = e^{r_c}$$ shows this in the post I refer to (in this case use the natural logarithm to solve for $$r_c$$; or if the other way around, exponential as noob2 pointed out).