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

In a service table, the only two decrements are death and withdrawal, with constant forces of decrement of 0.02 and 0.08 per year respectively. Of 1,000 lives all in service at the start of the year, what is the expected number who leave by withdrawal during the year?

The expected number of withdrawals is 76.13. With a total force of 0.10, the probability of leaving by withdrawal is the share 0.08/0.10 of the total exit probability 1 - e^-0.10, which is 0.0761 per life, so 76.13 per 1,000 lives.

  1. A80.00
  2. B76.88
  3. C76.13Correct
  4. D95.16
  5. 19.03

Explanation

The total force is 0.10. The probability of leaving by withdrawal is (0.08/0.10)(1 - e^-0.10) = 0.8 x 0.0951626 = 0.07613, so about 76.13 of 1,000 lives. 76.88 uses only the withdrawal force in the exponent, ignoring the death decrement. 80.00 ignores the competing death decrement entirely.

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