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

A last-survivor assurance pays Rs 1,00,000 at the end of the year of the second death, for two independent lives (x) and (y), for a one-year term only, meaning it pays only if both die within the year. With q_x = 0.02 and q_y = 0.03 and an interest rate of 4%, what is the expected present value, assuming deaths are independent and the benefit is paid at the end of the year?

Both lives must die within the year, which has probability 0.02 x 0.03 = 0.0006. Multiplying by Rs 1,00,000 gives Rs 60, and discounting one year at 4% gives Rs 57.69.

  1. ARs 57.69Correct
  2. BRs 60.00
  3. CRs 5.77
  4. DRs 576.92
  5. Rs 500.00

Explanation

P(both die within the year) = 0.02 x 0.03 = 0.0006. EPV = 100,000 x 0.0006 / 1.04 = 60 / 1.04 = 57.69. Rs 60.00 omits discounting. Rs 576.92 is a factor of ten too large.

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