The table below defines available zero-coupon bonds and their prices:

Years to Maturity	Bond Price Per Bond	Redemption Value Per Bond
1	961.54	1,000
2	966.14	1,050
3	878.41	1,000

A company chooses to purchase 15 one-year zero-coupon bonds; 20 two-year zero- coupon bonds; and 30 three-year zero-coupon bonds.

Calculate the Macaulay duration of this portfolio

• 1.97
• 2.11
• 2.16
• 2.20
• 2.23

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

Solution: D

(15(961.54)(1) +20(966.14)(2)+ 30(878.41)(3))/(15(961.54) +20(966.14) + 30(878.41)) = 2.198495.

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