Black-Scholes formula

The Black-Scholes model is as follows:

$$V_{call} = SN(d_{1}) - E^{-r(T-t)}N(d_{2})$$ (1)

where

$$d_{1,2} = \frac{ln(S/E) + (r - D \pm \frac{\sigma^{2}}{2})(T - t)}{\sigma\sqrt{T - t}}$$ (2)

The derivation of Black-Scholes is rather complex. I will not be studying the theoretical validity of this model; rather, I will look at whether it accurates prices options in the real market. If one is interested in the derivation of the Black-Scholes formula, see http://www.lifelong-learners.com/opt/SYL/s4node10.php3