I have attached the problem & the answer. Please provide the work. Thank you very much in advance.

8. A stock price is currently trading at 40. Paul Tripp, CFA wants to value one-year index option using the single-period binomial model. The stock will either increase in value by 20% with probability of 40% or fall in value by 30% with probability of 60%. The annual risk-free interest rate is 2%. No dividends are paid on any of the underlying securities in the index. a. Calculate the value of a European call option on the index with an exercise price of 40 b. Combine the call options from question a with T-bills and the underlying stock in the way that the payoff of the resulting portfolio becomes the same as a payoff of a long straddle with the call option from question a. Find the position in each security in this portfolio. Cu(1 - d+ r) + Ca(u-1-) C= (u - d)(1+rs) where Cu = 40 x 1.2 - 40 = 8, Ca=0, u = 1.2, d=0.7. b. Buy two call options, short stock and lend $39.22