The risk free rate is 5%, the price of the underlying stock is $50, the underlying stock can increase or decrease by 30% each year, the underlying stock is set to pay a dividend of $5 just before T=2. Consider the exotic American option with two years until expiration and the following payoff function:

where t is the amount of time that has passed since the "initial date" in years, i.e. (t=0 today, t=1 one year from today, and t =T=2 two years from today). Therefore, the time to expiration at time t is (T-t).

Price this exotic security using the two-period binomial model.