A) Consider an insurance company that needs to pay 10 million in each of the years 3, 4, and 5 from now. The term structure is flat at r=2%. What are the present value and Macaulay duration of the companys liabilities? The company has 28 million in cash that it wants to invest in bonds to immunize its liabilities. How many units of 3-year and 5-year zero-coupon bonds with face value 100 does the company need to buy to immunize its liabilities with respect to interest rate risk?

B) Consider the same insurance company in part A. Determine by how much the net worth of the company changes when the flat term structure shifts from 2% to 1.5% and the company does not immunize its liabilities. Determine by how much the net worth of the company changes for the same change in the term structure when the firm immunizes its liabilities as in part A. In both cases, calculate the exact net worth rather than approximation.