(a)The option pricing model based on binomial tree is used to price unusual feature of options. In considerations of following scenario. The price of stock can go up by 25% or go down by 15% in 90 days considering the price of stock S80. The scenario has the risk-free rate of 9%. A European call option with expiration in 90 days has exercise price Of $76. The agreement has been made between options parties; however, the maximum limit of the payoff is $42. Find the value of option under European and American settings. What value added exist in European settings. In current setting would your answers be change if there is no limit to pay off?