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15. 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 $4 million per year to beneficiaries. The yield to maturity on all bonds is 10%. a) Assume that the duration of 5-year maturity bonds with coupon rates of 12% (paid annually) is 4 years, and the duration of 20-year maturity bonds with coupon rates of 6% (paid annually) is 14 years. Calculate how much of each of these two coupon bonds (in market value) you will want to hold in order to both fully fund and immunize your obligation. (2 marks) b) Calculate the total par value of your holdings in the 20-year coupon bond. (1 mark)