A company must pay liabilities of 1000 at the end of year 1 and X at the end of year 2. The only investments available are:

1. One-year zero-coupon bonds with an annual effective yield of 5%
2. Two-year bonds with a par value of 1000 and 10% annual coupons, with an annual effective yield of 6%

The company constructed a portfolio that creates an exact cash flow matching strategy for these liabilities. The total purchase price of this portfolio is 1783.76.

Calculate the amount invested in the one-year zero-coupon bonds.

• 784
• 831
• 871
• 915
• 935

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

Solution: B

The company must purchase 4000 in one-year bonds and 6000 in two-year bonds. The total purchase price is 4000 /1.08 + 6000 /1.11²= 8573.

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