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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?

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    $\begingroup$ Because it is easy and convenient to manipulate mathematically, and because any non-continuously compounded return can be turned into a continuously compounded one. $\endgroup$ May 14 at 19:18
  • $\begingroup$ @rubikscube09 is there any toy example to back up your answer? $\endgroup$
    – Eiffelbear
    May 14 at 19:20
  • $\begingroup$ 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). $\endgroup$
    – noob2
    May 14 at 20:02
  • $\begingroup$ Dupliacte which was in turn closed because it is a basic financial question. Reading it will "back" up how they are related though. $\endgroup$
    – AKdemy
    May 14 at 20:06
  • $\begingroup$ @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. $\endgroup$
    – Eiffelbear
    May 14 at 20:10
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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).

If you refer to a toy example for convenient manipulation; it's because you can use calculus.

Edit: A differentiable function must be continuous.

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  • $\begingroup$ Can you also briefly talk about why it should be continuous variable, rather than discrete numbers, to apply calculus on? In retrospect, all the calculus exercises that I have dealt with, are based on continuous numbers. Why no calculus on discrete numbers? $\endgroup$
    – Eiffelbear
    May 14 at 20:50
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    $\begingroup$ Because calculus uses limits - and put rather simply, limits are most effective when used with the real number system (continuum) $\endgroup$ May 15 at 3:25

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