A stock price is currently $12. Over each of the next two three- month periods it is expected to go up by 6% or down by 5%. The risk- free interest rate is 5% per annum with continuous compounding. Suppose this option has a strike price of $16. If that option is an American put, what is the value of this six-month American put option? Would it ever be optimal to exercise it early ? Write down the binominal tree to indicate if the early exercise is optimal or not.