Consider the American put with a strike price of $50 and expiring in one year, written on ZZR stock. ZZR does not pay dividends and trades at $13 in the market. Knowing that the interest rate is 10%, and that it is optimal to exercise this option early:

(a) What is the price of the put with the same characteristics but a strike price of $55?

(b) What is the maximum price of the call with an exercise price of $50?