Suppose that you own an American put option on a non-dividend paying stock with a strike price of $50 that will expire in six months. The current stock price is $1, and the six-month risk- free rate of interest is 5% with continuous compounding

(a) If you exercise the put today and invest the proceeds, how much will you have in six-months?

(b) What is the maximum payoff you can obtain if you keep the option until expiration? Explain.