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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Valuing cashflows contingent on multiple transition events

Two independent lives have constant forces of mortality 0.03 and 0.05, and the force of interest is 0.04. A sum assured of Rs 90,000 is payable immediately on the second death (the last survivor). What is the EPV?

The EPV is Rs 28,571.43. The last-survivor assurance factor equals the sum of the two single-life factors (0.428571 + 0.555556) less the first-death factor (0.666667), which gives 0.317460. Multiplying by Rs 90,000 gives Rs 28,571.43.

  1. ARs 60,000.00
  2. BRs 38,571.43
  3. CRs 28,571.43Correct
  4. DRs 30,000.00
  5. Rs 55,555.56

Explanation

For the last-survivor assurance, Abar = Abar_x + Abar_y - Abar_first. Abar_x = 0.03/0.07 = 0.428571 and Abar_y = 0.05/0.09 = 0.555556. Abar_first = 0.08/0.12 = 0.666667. The result is 0.317460, and 0.317460 x 90,000 = Rs 28,571.43. Rs 60,000 is the first-death assurance.

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