A court has ordered Security Enterprises to pay $200,000 in two years and $500,000 in five years. In order to meet this important liability, they wish to invest in a combination of two-year 10% par-value bonds with annual coupons and five-year zero-coupon bonds. Each of these is sold to yield an annual effective yield of 4%. How much of each type of bond should be purchased so that the present value and duration conditions of Redington immunization are satisfied at the current 4% rate? Is the convexity condition also satisfied?

Answer: Spend $179,736.12 to purchase the two-year coupon bond (face value $161,463.94) and $416,138.68 to purchase the five-year zero-coupon bond. The convexity of the assets exceeds the convexity of the assets as is required for Redington immunization

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