An insurer has a liability that is expected to result in the following cash outflows.

End of Year	Cash Outflow
1	10
2	12
3	15
4	20
5	30

The insurer uses an 8% annual effective interest rate to discount future cash flows.

Calculate the Macaulay duration of this liability.

• 3.1 years
• 3.2 years
• 3.4 years
• 3.5 years
• 3.6 years

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

Solution: C

Using the general Macaulay duration formula:

[[math]] \frac{\sum R_tv_t t}{\sum R_t v^t} [[/math]]

where R is the cashflow:

Period	Cashflow	PV at 8%	Period ×PV
1	10	9.26	9.26
2	12	10.29	20.58
3	15	11.91	35.73
4	20	14.70	58.80
5	30	20.42	102.10
Total	66.58	226.47

Macaulay duration = 226.47/66.58 = 3.401472 years

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