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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Projecting and valuing cashflows contingent on multiple decrement events

A population of 1,000 lives is subject to two decrements, death and withdrawal, with constant forces of 0.01 and 0.04 per annum respectively. What is the expected number of withdrawals during the second year of the population's exposure?

The expected number is 37.11. About 951.23 lives survive the first year, and in the second year 80% of all exits, a fraction of 0.8 x 0.048771 = 0.039017 of those survivors, are withdrawals, giving 37.11.

  1. A39.02
  2. B37.30
  3. C37.49
  4. D46.39
  5. 37.11Correct

Explanation

Total force is 0.05, so survivors at time 1 are 1000e^-0.05 = 951.23. The fraction leaving by withdrawal in year 2 is (0.04/0.05)(1 - e^-0.05) = 0.8 x 0.048771 = 0.039017. Withdrawals are 951.23 x 0.039017 = 37.11. The value 39.02 is the year 1 figure, ignoring survivorship, and 46.39 omits the 0.8 share for withdrawal.

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