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Nov 20'23
Exercise
A five-year 1000 face amount bond with 10% annual coupons is purchased at time of issue for 1216.47 based on an annual effective interest rate of 5%.
Calculate the Macaulay duration
- 2.9
- 3.2
- 3.7
- 4.1
- 4.3
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Nov 20'23
Solution: E
Macaulay duration at an interest rate of [math]5 \%[/math] is
[[math]]
\begin{aligned}
& \frac{100(I a)_5+5000 v^5}{100 a_5+1000 v^5} \\
& =\frac{100(12.56639)+3917.63}{100(4.32947)+783.53}=4.2535
\end{aligned}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.