Use a four-period binomial model to value an American put option with a $55 strike price and two months remaining to maturity. The underlying stock does not pay any dividend and is currently selling for $50 per share. The risk-free rate is 3% per annum, compounded continuously. The stock return volatility is 30%. What if the option is European? Use the same binomial tree to value the European put. Show all calculations at every node of the binomial tree.