Please show your work

1. Suppose a bank has an asset duration of 4 years and a liability duration of 2.75 years. This bank has $1,050 million in assets and $780 million in liabilities. They are planning on trading in a Treasury bond future which has a duration of 7.5 years and which is selling right now for $98,500 for a $100,000 contract. How many futures contracts does this bank need to fully hedge itself against interest rate risk?

2. Suppose a Eurodollar time deposit futures contract has a duration of .6 years and has a current market price of $965,000. Market interest rates are 7.5 percent and are expected to fall to 6.5 percent. What is the change in this futures contract's market price from this change in interest rates?

3. An investor purchases one September T-bond futures contract at 116-210. The settlement price for the contract on next day is 118-120. What is the marked-to-market gain/loss for the investor?

4. Suppose a $100,000 T-Bond futures contract whose underlying bonds duration is 6 years and has a current market price of $98,765. Market interest rates are 3 percent today but are expected to rise to 4 percent. What is the expected change in this futures contract's market price as a result of this change in interest rates?

5. ABC Banks asset portfolio has an average duration of 4 years and its liability portfolio has an average duration of 3 years. The bank has $500 million in total assets and $400 million in liabilities. ABC Bank is thinking about hedging its risk by using a Treasury bond futures contract whose underlyings duration is 5 years and has a price of $97,650. How many futures contracts will it need to hedge its risk?