1. What is the intuition behind Blacks pseudo American option pricing model?

2. b) Consider an American call option on a dividend paying stock that matures in 6 months time and has a strike of $42. The stock is currently priced at $45 and a dividend with a present value of $3

   is expected in 4 months. Assume a continuously compounded risk free rate of 6% p.a. and volatility of 30% p.a. Use Blacks pseudo American option pricing model to price the option. Show all workings.