Joe must pay liabilities of 1,000 due 6 months from now and another 1,000 due one year from now. There are two available investments:

Bond I: A 6-month bond with face amount of 1,000, an 8% nominal annual coupon rate convertible semiannually, and a 6% nominal annual yield rate convertible semiannually;

Bond II: A one-year bond with face amount of 1,000, a 5% nominal annual coupon rate convertible semiannually, and a 7% nominal annual yield rate convertible semiannually.

Calculate the amount of each bond that Joe should purchase to exactly match the liabilities.

• Bond I – 1, Bond II – 0.97561
• Bond I – 0.93809, Bond II – 1
• Bond I – 0.97561, Bond II – 0.94293
• Bond I – 0.93809, Bond II – 0.97561
• Bond I – 0.98345, Bond II – 0.97561

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: D

Because only Bond II provides a cash flow at time 1, it must be considered first. The bond provides 1025 at time 1 and thus 1000/1025 = 0.97561 units of this bond provides the required cash. This bond then also provides 0.97561(25) = 24.39025 at time 0.5. Thus Bond I must provide 1000 – 24.39025 = 975.60975 at time 0.5. The bond provides 1040 and thus 975.60975/1040 = 0.93809 units must be purchased.

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.