Below, we consider a forward contract for one share of a stock. The current price (at t = 0) of the stock is S0 = 50. The observed price of a forward contract whose expiration date is 6 months from now (T = 0.5) is 51.10. The risk-free interest rate is r = 0.06 and the dividend rate is = 0.02, both compounded continuously. (a) Calculate the theoretical price of the forward contract. Use only two decimal places in your answer. Show your work. (b) You notice that the theoretical and observed prices of the forward contract are not equal. To make use of the resulting arbitrage opportunity, what should an investor do now (at time t = 0), in terms of buying or selling some or all of the following: a forward contract, the stock, and a bond (whose interest rate is r, compounded continuously). (Buying a bond amounts to investing money, selling a bond amounts to taking a loan.) State whether an asset is bought or sold, and in which amount the asset is bought or sold (assuming that the amount for the forward contract, whether long or short, is for one share), all at t = 0. We assume that fractional shares can be bought or shorted and that the amount in the bond can be any real number. (c) Explain what is done at time t = T to change everything to cash, and state the amount of profit at time t = T. Show your work.