A stock currently trades at $52. It is expected that dividends of $1.00/share will be paid to owners of the stock at 1 month and at 4 months from the current date. Consider these dates as ex-dividend dates as well. The continuously compounded risk free rate is 5%. European call and put options on the stock with exercise prices of $50 and 6 months to the expiration date are currently trading

a) If the European call option has a market price (premium) of $2.00, based on put-call parity, what should be the price of a European put on the stock with the same exercise price and time to expiration? (

b) Calculate the lower bound for the value of an American call option on the stock with an exercise price of $50 and a time to expiration of 6 months.