S&P 500 Index futures: Beginning of term $4,465 (09/12/2023), End of term $4,518 (11/14/2023). a. Assume that you purchased an S&P 500 futures contract at the beginning of the school term, with the first settlement date being beyond the end of the school term. Also assume that you sold an S&P 500 futures contract with this same settlement date at the end of the school term. Given that this contract has a value of the futures price times $250, determine the difference between the dollar value of the contract you sold and the dollar amount of the contract you purchased.\ \ b. Assume that you invested an initial margin of 20 percent of the amount that you would owe to purchase the S&P 500 index at the settlement date. Measure your return from taking a position in the S&P 500 index futures as follows. Take the difference determined in part (a) (which represents the dollar amount of the gain on the futures position) and divide it by the amount you originally invested (the amount you originally invested is 20 percent of the dollar value of the futures contract that you purchased).\ \ c. The return that you just derived in part (b) is not annualized. To annualize your return, multiply it by 12/m, where m is the number of months in your school term.\ \ d. Apply the concepts discussed in Chapter 13 to explain why your return on your S&P 500 index futures position was low or high over the school term.