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

A 5-year term assurance pays Rs 200,000 at the end of the year of death. The annual premium of Rs 10,000 is payable in advance throughout the term. Expenses are Rs 2,000 at the start of the policy and Rs 100 at the start of each later policy year. Interest is 5% per annum effective. The policyholder dies during the third policy year. What is the present value at issue of the gross future loss?

The gross future loss is Rs 146,359.36. It is the discounted benefit of 172,767.52 plus discounted expenses of 2,185.94, less discounted premiums of 28,594.10, with premiums at times 0, 1 and 2 and the benefit at time 3.

  1. ARs 144,173.42
  2. BRs 155,429.65
  3. CRs 154,997.64
  4. DRs 141,987.48
  5. Rs 146,359.36Correct

Explanation

Death in year 3 means the benefit is paid at t=3 and premiums are paid at t=0, 1 and 2. Benefit PV = 200,000 x 1.05^-3 = 172,767.52. Premium PV = 10,000 x 2.859410 = 28,594.10. Expense PV = 2,000 + 100 x 1.859410 = 2,185.94. Loss = 172,767.52 - 28,594.10 + 2,185.94 = 146,359.36. Omitting expenses gives 144,173.42, which is wrong because expenses add to the loss.

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