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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Assurance and annuity functions involving two lives

For two independent lives, A_x = 0.40, A_y = 0.50 and A_{xy} (assurance payable at the end of the year of first death) = 0.65. What is A_{x̄ȳ}, the EPV of 1 payable at the end of the year of the second death?

The first-death and last-death assurances together pay the same as the two single-life assurances, so A_{x̄ȳ} = A_x + A_y − A_{xy} = 0.40 + 0.50 − 0.65 = 0.25.

  1. A0.15
  2. B0.25
  3. C0.35Correct
  4. D0.55
  5. 0.90

Explanation

The relation A_{xy} + A_{x̄ȳ} = A_x + A_y holds because one benefit is paid at the first death and one at the second death. So A_{x̄ȳ} = 0.40 + 0.50 − 0.65 = 0.25. Check: 0.65 + 0.25 = 0.90. Hence 0.25 is correct; 0.35 would require A_{xy} = 0.55.

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