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Nov 20'23
Exercise
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.
Nov 20'23
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.