Consider an at-the-money 6-month American put options on a non-dividend-paying stock. The price of the stock is $72 now and it can move up by 25% or down by 20% each of 3-month period for the next 6 months. The risk-free interest rate in this world is zero with continuous compounding.

1. Determine the value of the American put by constructing a binomial tree showing the stock price and options value at each node of the binomial tree.

Show all necessary workings. (20 marks)