(20 marks) Question 4 Pension funds pay lifetime annuities to recipients. If a firm remains in business indefinitely. the pension obligation will resemble a perpetuity. Suppose that you are managing a pension fund with obligations to make perpetual payments of $3 million per year to beneficiaries. The yield to maturity on all bonds is 10%. To fully fund and immunize the obligations, you want to set up an immunization strategy using the following two high-grade corporate bonds. Delta Bond A 4-year maturity bond has a 7% coupon rate, paid annually. : A 30-year maturity bond has a 3% coupon rate, paid semi-annually. It sells today for $337.47. The Macaulay duration of this bond is 12.17 Gamma Bond : years. Required: Determine the number of each of these corporate bonds you will want to hold to both fully fund and immunize the obligations (20 marks)