[Chinjut]

A lot of the commentary suggests that this motivation for e in terms of continuously compounded interest is introduced for misguidedly contrived pedagogical reasons. But this is historically the way e was first discovered. e was first discovered precisely through Jacob Bernoulli wanting to understand continuously compounded interest.

Of course, the arithmetic laws of exponential growth of money are exactly the same as the arithmetic laws of exponential growth of anything else. And there is no reason that, just because a topic is historically discovered in some fashion, that must be the way it is taught, or even is a good way to teach it.

But it's not some made up conceit by teachers to connect e and continuously compounded interest. That is historically how e came to be investigated.