# Calculating present value using Euler's number

So I was reading here where they calculate the expected value of an option at present given the expected value of the option in a year by calculating

$$C_0 = C_1 e^{(-r)}$$

where r is the interest rate. But where does e come from here? Shouldn't present value just be calculated using

$$C_0 = C_1 / (1 + r)$$

What am I missing?

$$e^{-rt}$$ is the continuous discounting factor while $$(1 + r)^{-t}$$ is its discrete counterpart.
Identically/equivalently, there is the continuous manner of computing factors of variation, e.g. $$1 + \ln \frac{x_{0+t}}{x_0}$$, and its discrete counterpart $$\frac{x_{0+t}}{x_0}$$.