The modified duration of a ten-year zero-coupon bond with an annual effective yield rate of i is 9.26 years. Based on an annual effective interest rate of i, the Macaulay duration of a ten-year annuity- immediate with level annual payments is D.

Calculate D.

• 4.05
• 4.37
• 4.51
• 4.87
• 4.96

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

Solution: D

[[math]] \begin{aligned} & 9.26=\frac{10}{1+i} \\ & i=0.079914 \\ & \bar{d}=\frac{(I a)_{\overline{10}|}}{a_{\overline{10}|}}=\frac{32.70395}{6.71270}=4.8720 . \end{aligned} [[/math]]

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