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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Key assurance and annuity contracts

A whole life policy with sum assured Rs 1,00,000 pays the benefit at the end of the year of death. The valuation rate is 5% per annum effective. The life, aged x, dies during the third policy year, so the curtate future lifetime K_x = 2. What is the present value of the benefit payment at issue?

The present value is Rs 86,383.76. Death in the third year means K_x = 2, and the benefit is paid at the end of that year, at time 3. Discounting Rs 1,00,000 for three years at 5% gives 100000/1.157625.

  1. ARs 90,702.95
  2. BRs 86,383.76Correct
  3. CRs 82,270.25
  4. DRs 95,238.10
  5. Rs 1,00,000.00

Explanation

Death in the third year gives K_x = 2, so the benefit is paid at time K_x + 1 = 3. PV = 100000 × 1.05^-3 = 100000/1.157625 = 86,383.76. Using time 2 would give 90,702.95, which is wrong because the payment is made at the end of the year of death.

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