A non-dividend-paying stock is trading at $80. The risk-free interest rate is 6%. Suppose the 3-month European call with a strike price of $90 costs $6.

(1) What can you say about the price of the 3-month European put with a strike price of $90?

(2) What can you say about the price of the 3-month American put with a strike price of $90?

(3) Suppose the 3-month European put with a strike price of $90 actually costs $12. Explain why arbitrage opportunities exist. Describe one arbitrage strategy (What securities do you long? What securities do you short? No need for calculation).

(4) Why is an American put more valuable than a European put (with the same expiration and strike price)? Would you ever exercise an American put early? Explain your intuitions without math.