Consider a three month futures contract on the S&P 500 index. The value of the index is 1000; the dividend yield is 1% and the three month interest rate is 4% continuously compounded. (a) Explain how to compute the futures price making sure to define all terms and assumptions. In particular carefully explain why the formula holds. Then compute the fair futures price. (b) Suppose the actual futures price is 1010.0. In great detail describe a strategy that creates guaranteed arbitrage free profits. What is the profit and when is it realized.