You manage a pension fund that will provide retired workers with lifetime annuities. You determine that the payouts of the fund are essentially going to resemble level perpetuities of $ 1million per annum. The interest rate is 10%. You pan to fully fund the obligation using five-year and 20-year maturity zero-coupon bonds.

a. how much market value of each of the zeros will be necessary to fund the plan if you desire an immunised position?

b. what must be the face value of the two zeros to fund the plan?