Consider an American put option with time to expiry 15 months, and a strike of 74. The current price of the underlying is 71. Divide the time to expiry into three 5-months intervals. Assume that in each 5-months interval, the price can either rise by 5, or fall by 5, with unknown probability. The risk-free (continuously compounding) rate is 0.042.

a) Using a binomial tree, identify the circumstances under which early exercise would be rational for the holder of this option. Draw the binomial tree and show the necessary calculation and briefly explain the answer.

(Please draw the tree, thank you)