Question: 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

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 are satisfied at the current 4% rate?

Is the convexity condition also satisfied?

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