Who told you we don’t need to remember the BSM model? Reading 41, learning objectives G-K all scream “MEMORIZE BSM!”. You need to know what every term means (e.g. N(d2) is the probability of the option expiring in the money, N(d1) is the hedge ratio, x is the strike price, e-rt is the discount term, ergo you need to know the formulas).

Thanks for the response. I got a $0.10 difference. Could that be a rounding error? C_{0} = S_{0}N(d_{1}) – e^{–rT}XN(d_{2}) C_{0} = PV {S_{0}e^{rT}N(d_{1}) – XN(d_{2})}. Co = [$50* (.779)] - [(e ^-.03*.5)* ($45)* (.723)] = 6.8994 Co = [$50* (e ^.03 * .5)] * [(.779) - $45 * (.723)] / 1.03 = 6.7997