4. Suppose the S&P 500 index is currently 950 and the initial margin is 10%. And the maintenance margin is 75% of the initial margin. You wish to enter into 10 S&P 500 futures contracts. Each contract permits delivery of 250 units of the index exactly 3 months from now. a. Suppose you earn a continuously compounded rate of 6% on your margin balance, your position is marked to market weekly. What is your margin balance in 1 week, if the future price drop to $945? b. Calculate the amount of this margin call. c. If the future price decreases, what's the effect to your total profit compared to forward contract with forward price drop? d. If the future price at week 2 rise to 947, what's your margin balance? (You need week 1's balance to do this question)