A firm has a liability cash flow of 100 at the end of year two and a second liability cash flow of 200 at the end of year three. The firm also has asset cash flows of X at the end of years one and five. Using an annual effective interest rate of 10%, calculate the absolute value of the difference between the Macaulay durations of the asset and liability cash flows.

• 0.018
• 0.020
• 0.022
• 0.024
• 0.026

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

Solution: E

[[math]] \begin{array}{l}{{(1+s_{4})^{4}(1+{}_{1}f_{4})=(1+s_{5})^{5}}}\\ {{(1.09)^{4}(1+{}_{1}f_{4})=(1.095)^{5}}}\\ {{1f_{4}=0.1152}}\end{array} [[/math]]

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