The price of a stock is currently 100 USD. Assume the price can increase by a factor of 1.10 or fall by a factor of 0.90. The stock pays no dividends and the annual percentage rate (APR) is 2%. Consider an American put option on this stock with a strike price of 95 USD, and with two years to maturity and one-year step length. You are standing at year t = 0 currently. (1) What is the price of this American put option at year t = 0? (2) Suppose the strike price is 95 + x, where x is the day of the month when you were born. What is the price of this American put option at year t = 0? (3) What if the interest rate is doubled? Compare your result with (1). Then, using (2) and (3), explain how strike price and interest rate affect the put option price. The price of a stock is currently 100 USD. Assume the price can increase by a factor of 1.10 or fall by a factor of 0.90. The stock pays no dividends and the annual percentage rate (APR) is 2%. Consider an American put option on this stock with a strike price of 95 USD, and with two years to maturity and one-year step length. You are standing at year t = 0 currently. (1) What is the price of this American put option at year t = 0? (2) Suppose the strike price is 95 + x, where x is the day of the month when you were born. What is the price of this American put option at year t = 0? (3) What if the interest rate is doubled? Compare your result with (1). Then, using (2) and (3), explain how strike price and interest rate affect the put option price