Use a four-period binomial model to value an American put option with a $105 strike price and four months remaining to maturity. The underlying stock does not pay any dividend and is currently selling for $100 per share. The risk-free rate is 2% per annum, compounded continuously. The stock return volatility is 40%.

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.