A stock is currently worth 80. Each year it goes up by 50% or down by 25%, with equal probability. The interest rate compounded annually is 5%, i.e., = 1.05. Using the principle of risk-neutrality find the price of a 5-year binary call option with strike price K = 100 and a fixed payment of 1 (i.e. at time T = 5 the option pays 1, if S(5) K = 100, and it pays nothing, if S(5) < K = 100)