An insurance company wants to match liabilities of 25,000 payable in one year and 20,000 payable in two years with specific assets. The following assets are currently available

• One-year bond with an annual coupon of 6.75% at par
• Two-year bond with annual coupons of 4.50% at par
• Two-year zero-coupon bond yielding 5.00% annual effective

Calculate the smallest amount the company needs to disburse today to purchase assets that will exactly match these liabilities.

• 41,220
• 41,390
• 41,560
• 41,660
• 41,750

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

Solution: C

The strategy is to use the two highest yielding assets: the one-year bond and the two-year zero- coupon bond. The cost of these bonds is 25, 000 /1.0675 + 20, 000 /1.05² =41,560.

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