You manage a pension fund, and your liabilities consist of two payments as follows:

(Time : Payments)

10 years : $20M

30 years : $30M

Your assets are $18 million. The term structure is currently flat at 5%.

1. Compute the present value of your liabilities. (Note: Your answer should be expressed in units of millions of dollars.)
2. Compute modified duration of your liabilities.
3. Compute an approximate change in the present value of your liabilities, using duration, when interest rates fall by 0.25%. (Note: Your answer should be expressed in units of millions of dollars.)
4. Suppose that you invest the $18 million in 1-year Treasury bills (i.e., 1-year zero-coupon bond) and in a Treasury bond with modified duration of 20. How would you allocate your assets to avoid interest rate risk of your portfolio, which includes both assets and liabilities? (Note: Your answers should be expressed in units of millions of dollars.)
5. Amount invested in Treasury bills?
6. Amount invested in the Treasury bond?