Someone help me with these 3 problems

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SAMPLE PROBLEM SET 1 - FUTURES AND OPTIONS FIN 436 1. You have opened a futures account with a cash deposit of $10,000.00. You decide to sell 8 October contracts of bean meal at 305.4. Contract specs are as follows: CONTRACT QUOTE TIC SIZE CONTRACT MOS. INITIAL MAINT UNIT UNITS MARGIN MARGIN 100 TONS US$ AND 0.10/TON = Jan, Mar, May, Jul, $1,122/ $1,020/ CENTS/TON $10.00 Sep, Oct, Dec CONTRACT CONTRACT If soybean oil drops $.10, what is the equity of the account when marked-to-market? 2. You are day-trading the S&P E-Mini contract with $3,250.00 of equity in your account. Contract specs are as follows: CONTRACT QUOTE TIC SIZE CONTRACT MOS. INITIAL MAINT UNIT UNITS MARGIN MARGIN $50 x S&P US$ AND 0.25 INDEX $907.50/ $825/ 500 INDEX CENTS/TIC PTS = Mar, Jun, Sep, Dec CONTRACT CONTRACT $12.50 (DAY-TRADE) DAY- TRADE) Based on your new sophisticated algorithm, there is an 85% chance that the S & P will fall over the next half hour, so you go all in by selling 6 June contracts. The market rises 5 tics, and then plunges 50 tics when you flatten your position (buy to close them all). What was your gross profit or loss for the day? 3. After the trade in Problem 2, you decide to buy October gold futures. Contract specs are as follows: CONTRACT QUOTE TIC SIZE CONTRACT MOS. INITIAL MAINT UNIT UNITS MARGIN MARGIN 100 TROY US$ AND 0.10/TrOZ = 3 NEAREST MOS. + $6,250/ $5,000/ OUNCES CENTS/TroZ $10.00 Feb, Apr, Aug, Oct CONTRACT CONTRACT a. How many contracts can you (safely) buy? b. If gold then declines $3.65 per troy ounce, what is the market-to-market equity in the account? 4. You are a trading associate at a major bank. Your supervisor assigns you with an assignment to hedge against increases in future interest rates the bank's inventory of two-year notes. You have these alternatives: I. Sell the necessary (optimal) amount of 2-year treasury futures, longest delivery date. II. Sell the necessary (optimal) amount of 2-year treasury futures, shortest delivery date. Ill. Buy necessary (optimal) amount of 2-year treasury futures puts, shortest delivery date. IV. Buy necessary (optimal) amount of 2-year treasury futures puts, shortest delivery date. V. Buy necessary (optimal) amount of 2-year treasury futures calls, shortest delivery date. What do you do? a. Either I. or III. b. Either I., Ill., or V. C. Either I., II., III., or IV. d. Only V. 5. Silver futures and spot silver have a correlation factor of 0.97. If the standard deviation for the futures contract is 2.98 and the standard deviation for the spot is 1.87, what is the optimum hedge ratio