You own a one-year American put option on a stock, with a strike price of $80.00. The stock is not expected to pay dividends over the following year and its current price is $70.00. You know that u = 1.181, where u is one plus the rate of capital 1 gain on the stock per every 6-month period if the price goes up, and d = 0.890 , where d is one plus the rate of capital loss on the stock per every 6-month period if the price goes down. The continuously compounded risk-free interest rate is 5%. Construct the binomial tree model and calculate the current price of the American put. Explain if the option will be exercised before expiration and if so, when.