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

A policy is in its final year, with no further premiums. At the end of the year it pays 50,000 on death, 10,000 on withdrawal and 20,000 on survival to maturity. The dependent probabilities of exit during the year are 0.02 for death and 0.08 for withdrawal. Benefits are paid at the end of the year, and interest is 5% per annum effective. What is the reserve at the start of the year?

The reserve is 18,857.14. The expected end-year payment is 1,000 from deaths, 800 from withdrawals and 18,000 from the 90% who survive, totalling 19,800. Since all benefits fall due at the end of one year, this is discounted once at 5%.

  1. A19,619.05
  2. B18,857.14Correct
  3. C19,800.00
  4. D17,959.18
  5. 20,380.95

Explanation

The survival probability is 1 − 0.02 − 0.08 = 0.90. Expected benefit = 50,000 × 0.02 + 10,000 × 0.08 + 20,000 × 0.90 = 1,000 + 800 + 18,000 = 19,800. Discounting one year gives 19,800/1.05 = 18,857.14. Discounting for two years gives 17,959.18, and omitting discounting gives 19,800.

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