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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Gross random future loss

A 3-year term assurance pays ₹1,00,000 at the end of the year of death. Level annual premiums of ₹2,500 are payable in advance during the term while the life survives. The interest rate is 10% per annum effective, and there are no expenses. The one-year mortality probabilities for the life are q0 = 0.02, q1 = 0.03 and q2 = 0.04 at successive policy years. What is the probability that the future loss is positive?

The probability is 8.74%. Any death during the term gives a positive loss, because the discounted benefit exceeds the premiums paid. Surviving the full term gives a negative loss, as only premiums are paid. So the probability is 1 − 0.98 × 0.97 × 0.96 = 0.0874.

  1. A8.74%Correct
  2. B2.00%
  3. C91.26%
  4. D4.94%
  5. 9.00%

Explanation

If death occurs in year 1, 2 or 3, the loss is 88,409, 77,872 or 68,293 respectively, all positive. If the life survives all 3 years, L = −2500 × 2.7355 = −6,838.84, which is negative. So P(L > 0) = P(death within 3 years) = 1 − 0.98 × 0.97 × 0.96 = 1 − 0.912576 = 0.0874. Adding the q values (9.00%) wrongly ignores the conditioning on survival.

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