A stock price is currently $80. Over each of the next two 6-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a 1-year European put option with a strike price of $80? What would be the value if it was an American call option instead of European option? Also draw the binomial tree to illustrate your answer.