2) 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%. a) 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? ( 5 points). b) What is the par value of your holdings in the twenty-year bond? ( 5 points)