A bond is priced at 950, giving an annual effective yield to maturity of 9%. At 9%, the derivative of the price of the bond with respect to the yield rate is -4750 .

Calculate the Macaulay duration of the bond in years.

• 4.59
• 4.62
• 5.00
• 5.41
• 5.45

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

Solution: E

The price is P = 950. The modified duration is

[[math]] \frac{-P'}{P} = \frac{-4750}{950} = 5. [[/math]]

Macaulay duration is (1.09)(5)= 5.45.

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