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

A 3-year term assurance pays Rs 100,000 at the end of the year of death. Annual premiums of Rs 1,500 are payable in advance for up to 3 years. Expenses are Rs 2,000 at issue and Rs 100 at the start of each of years 2 and 3, if the policy is in force. The interest rate is 5% per year. Conditional probabilities of death are 0.01 in year 1, 0.02 in year 2 and 0.03 in year 3. What is the expected value of the gross future loss at issue?

The expected loss is Rs 3,210.59. Value the expected benefit at 5,262.59 and the expected premiums at 4,234.29, using survival probabilities. Add expected expenses of 2,182.29. Treating the premiums or renewal expenses as certain, or dropping expenses, gives different and incorrect results.

  1. ARs 1,028.30
  2. BRs 3,228.30
  3. CRs 3,155.77
  4. DRs 1,210.59
  5. Rs 3,210.59Correct

Explanation

The death probabilities are 0.01, 0.0198 and 0.029106, so A = 0.0526259 and S×A = 5,262.59. The annuity-due is ä = 1 + 0.99/1.05 + 0.9702/1.1025 = 2.822857, so premiums are 4,234.29. Expenses are 2,000 + 100 × 1.822857 = 2,182.29. E[L] = 5,262.59 - 4,234.29 + 2,182.29 = 3,210.59. Ignoring expenses gives 1,028.30, and treating the premium annuity as certain gives 3,155.77.

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