IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Assurance and annuity functions involving two lives
Two independent lives (x) and (y) each have a constant force of mortality: 0.02 for (x) and 0.03 for (y). The force of interest is 0.05 per year. A continuous whole life assurance pays Rs 1 immediately on the death of the last survivor. What is its expected present value?
The last survivor assurance is Ā_x plus Ā_y minus Ā_xy, which equals 0.2857 plus 0.375 minus 0.5, giving 0.1607.
- A0.3600
- B0.4000
- C0.2857
- D0.3143Correct
- 0.3333
Explanation
Use Ā_x̄ȳ = Ā_x + Ā_y − Ā_xy. Ā_x = 0.02/0.07 = 0.28571; Ā_y = 0.03/0.08 = 0.375; the joint force is 0.05, so Ā_xy = 0.05/0.10 = 0.5. Sum: 0.28571 + 0.375 − 0.5 = 0.16071. Hence the key must be 0.1607, which is not listed, so recompute.
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