Please answer all the questions listed, thanks.

5) A stock is currently traded at 80. In a binomial world it can only go up to 10% with 65% probability or come down 10% with 35% probability. The risk free interest rate is 2% (continuous compounding). (1) What is the value of a 1 year European put option with strike = 82? Present your answer in both single step and two step binomial tree. (2) What if the put is American? Price it using a two step binomial tree. 5) A stock is currently traded at 80. In a binomial world it can only go up to 10% with 65% probability or come down 10% with 35% probability. The risk free interest rate is 2% (continuous compounding). (1) What is the value of a 1 year European put option with strike = 82? Present your answer in both single step and two step binomial tree. (2) What if the put is American? Price it using a two step binomial tree