Two bonds have the same annual effective yield rate, r, where r > 0. The bonds have Macaulay duration of 5 years and 6 years with respect to r. One of the bonds has modified duration of 5.76 years while the other bond has modified duration of d years.

Calculate d.

• 4.760
• 4.800
• 5.208
• 5.240
• 6.912

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

Solution: B

[[math]] \begin{aligned} & \bar{v}=\frac{\bar{d}}{1+r} \\ & 5.76=\frac{6}{1+r} \\ & r=0.041667 \\ & \bar{v}=\frac{5}{1.041666}=4.8 \end{aligned} [[/math]]

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