Consider the following two-period setting: the price of a stock is $50. Interest rate per period is 2%. After one period, the price of the stock can go up to $55 or drop to $47, and it will pay (in both cases) a dividend yied of 5%. If it goes up in the first period, in the second period it can go up to $57 or down to $48. If it goes down in the first period, in the second period it can go up to $48 or down to $41. Compute the price of an American call option with strike price K = $45 that matures at the end of the second period. Use the snell envelop method. Is the option exercised early? Give the optimal exercise rule. Assume that Delta t = 1. In addition, assume that the option is exercised before dividends are paid off if exercised in the intermediate period. (Note that the rates u and d are different if the stock price goes up or down in the first period.)