[BrenBarn]

> None of these topics (calculus, complex analysis, and trigonometry) require prior knowledge about specifically, so why bring it up using compound interest?

This seems like kind of a silly question. The reason is that e is usually introduced before you learn about calculus. You might learn about complex numbers before e, but not in any way that would make "e^i*pi = -1" understandable or even interesting. And you'll certainly learn about e before learning what it means for a function to be periodic in the complex plane.

The reason to start with compound interest isn't that these other topics require prior knowledge of e, it's that they require prior knowledge of those topics. The compound interest explanation doesn't require prior knowledge of anything, because you can build it from the ground up in explaining the concept of compound interest and exponential growth. It's also an explanation with obvious practical relevance. There's still a bit of a leap of faith in assuming anyone will find it interesting that that limit converges to this one particular number, but it's a smaller leap than is required to get people to care about anything involving complex numbers.

[nh23423fefe]

Probably the most important thing about the interest introduction is that its computable by hand. You can see the value "converge" in a few approximations