5. A non-dividend-paying stock (i.e., a stock that doesnt pay dividends over the life of the option) is selling at $40. You buy a call option on the stock for $1. The call has a strike price of $42 and expires in 3 months. From historical returns data on the stock, you know that the mean is 15% and the volatility is 20% per year. Assume that the risk-free rate is 4% per annum.

a) What is the probability that the call will be out-of-the-money at expiration?

b) What is the probability that the call will be in-the-money at expiration?

c) What is the probability that you will at least break even at expiration?

d) What is the probability you will at least double your money at expiration?