What you may not know is that $e$ is defined as $$\lim_{x \to \infty} (1+1/x)^x$$ from which it follows (by a little bit of limit manipulation) that $$\lim_{x \to \infty} (1+r/x)^x=e^r$$ The formula you are asking about can be explained from this; see Christopher Wong's comment above.

What you may not know is that $e$ can be defined as $$\lim_{x \to \infty} (1+1/x)^x$$ from which it follows (by a little bit of limit manipulation) that $$\lim_{x \to \infty} (1+r/x)^x=e^r$$ The formula you are asking about can be explained from this; see Christopher Wong's comment above.