Revision as of 01:19, 20 November 2023 by Admin (Created page with "An insurer has a liability that is expected to result in the following cash outflows. {| class="table" ! 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. <ul class="mw-excansopts"><li>3.1 years</li><li>3.2 years</li><li>3.4 years</li><li>3.5 years</li><li>3.6 years</li></ul> {{soacopyr...")
Nov 20'23
Exercise
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.
Nov 20'23
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.