The futures price of crude oil is $72.45. Future contracts are for 1000 barrel of crude, and the margin requirement (Good faith deposit) is $8,000 a contract. The maintenance margin requirement is $6,000. You expect the price of crude oil to go down; therefore, you short one crude oil future contract at the prevailing price of $72.45.

1. How much must you initially remit in order to be able to short one crude future? (5 points)
2. Assume you have shorted at $72.45, estimate your profit or loss both in dollar and in percent if future crude oil price goes up to $76.50 (10 points)
3. Assume you have shorted at $72.45, estimate your profit or loss both in dollar and in percent if future crude oil price goes down to $66.00 (10 points)
4. If spot price of crude is $70.00 and risk-free rate is 4 percent. What should be a future contract on crude oil that expires in three months? (10 points)