Pension funds pay lifetime annuities to recipients. Assuming the firm stays in business indefinitely, the cash flow would resemble a perpetuity. You are managing a pension fund that pays $4 million per year to its beneficiaries. The yield-to-maturity of all bonds is 15%.

1) If the duration of a five-year maturity, 12% coupon rate bond (annual payments) is four years and the duration of a twenty-year maturity, 6% coupon rate bond (annual payments) is eight years how much of each bond (in market value) would you need to fully fund and immunize your obligation?

2) What is the par value of your holdings in the twenty-year bond?