A European up-and-in call has strike price K-$21 and barrier B=$25. The values of the call's underlying asset, S(n,j), at different times n and states j are: S(0,0) = 22, S(1,0) = 16.92, S(1,1)= 28.60, S(2,0) = 13.02, S(2,1)= 22, and S(2,2) = 37.18. (a) On the binomial pricing tree shown above, draw a line indicating the barrier B. (b) Which paths on the binomial pricing tree will lead to a call with zero value at maturity? Explain your answers. (c) At which node will the up-and-in call have two possible values? (d) Calculate the premium of this up-and-in call, given that the return over one time step is R=1.035 and the risk neutral probability is = 0.5. (e) How does the premium calculated in (d) compare to the premium of a vanilla European call with the same strike price and maturity? Explain your answer by discussing all possible maturity payoffs for the two calls. You do not need to calculate the premium of the vanilla call.)