We want to price options using the binomial lattice. The current stock price is 54 and the strike price is 50. Assume that the stock up-trend rate is u = 1.2 with probability p = 0.4 and the down-trend rate is d = 0.8 with probability 1 -p = 0.6. The annual risk-free rate is r = 0.005 with discrete compounding. Assume that the length of a period is one month. Using a binomial lattice find the price of a 5-month American put option.