6. (10 points) Imagine that stock A's price will either rise by 25% or fall by 20% over the next six months. The stock A is now selling for $100 per share. Suppose that you own a one-year American put option on stock A with exercise price of $100. The interest rate is 7% each six months. a. What is the probability that the stock price will rise? (3 points) b. Would you ever want to exercise the put early? Why? (Explain the reason by some calculation.) (4 points) c. Calculate the value of the put. (3 points)