please answer the question attached. this is all that is provided by the professor.

3. (30 points) Consider a pension fund with liabilities valued at $500 million today. The Macaulay duration of these liabilities is 8. The yield curve is flat at 3%. The fund is 3 currently fully funded with assets also valued at $500 million. You are being asked to design a bond portfolio to invest the $500 million in assets. You are restricted as follows: Of the $500 million you have, you must keep $100 million in cash with a duration of O. The remaining $400 million to be invested is to be split between 3-year and 15)-year zero coupon bonds. (a) (10 points) You are to spit the $400 million between the 3-year and 15-year bonds to protect the portfolio from parallel shifts in the yield curve. What amount of money would you put in the two bonds? (b) (5 points) Suppose that interest rates decline to 2%. Using duration alone what would you predicted for the changes in the dollar value of the assets? For the liabilities? (c) (10 points) If interest rates do decline to 2% from the original 3%, what would be the actual value of the assets? Is this larger or smaller than your answer to part 3b? What explains the difference?