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.

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.