Ok, so I understand $e$ is just $\lim\limits_{n\to \infty}(1 + \frac{1}{n})^n$, and ends up being $2.71828\ldots$
It assumes the annual return you are getting is $100\%$ and is continuously compounded.
I don't understand how if you take $e$ to some power like $r$ or $t$, it flows through into the equation. For example, when you take $e^r$, that changes the return to whatever $r$ is. I assume (probably am thinking about this wrong) that $e^r$ is equivalent to:
$$\lim_{n\to\infty}\left(\left(1 + \frac{1}{n}\right)^n\right)^r$$
How does the $r$ flow through so that it changes the $1$ in $\frac{1}{n}$ to a different rate of return? For example, $e^{0.05}$ means a continuously compounded rate of return of $0.05$ for a year.
Also, how does $t$ cause the same effect?
