Let a two-period binomial tree be given with the following parameters: S = $100, u = 1.10, d = 0.90, and rf = 5 percent. Consider a two-period American put option with a strike of $90. Note that this put is quite deep out-of-the-money at inception. b. Suppose a dividend of $4 is paid at the end of the first period. What is the new price of the put?

Currently I have

Puu= Max{90-(100-4*1.10*1.10),0}=0

Pud=Max{90-(100-4*1.10*.9),0}=0

Pdd=Max{90-(100-4*.9*.9),0}=12.24

But where do I go from here?

p=.[1/1.05][.75(0)+.25(12.24)] ????