3. A firms stock starts at $40 and will either go up by 20% or go down by 20% during each of the next three months. The stock pays a fixed dividend of $2.40 next month. Assume the risk-free rate is 12% per annum with continuous compounding.

a) What is the price of an American call option that has a strike price of $40 and expires in three months?

b) What is the price of an American put option that has a strike price of $40 and expires in three months?