The price of a stock, which pays a 2% continuously compounded annual dividend rate, is $50 and the strike price of a one year put option on the stock is $80. The annual risk-free rate is 4% (continuously compounded). Find the lower bound for the option price such that there is no arbitrage opportunity if the market price of the option is above this lower bound. Compute this value if this option is

a) European, and b) American.