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

A whole life policy has sum assured Rs 500,000 payable at the end of the year of death, with a claim expense of Rs 1,000 at the time of payment. The gross annual premium is Rs 14,000, payable annually in advance, and renewal expenses are 2% of each premium paid. At the end of 10 years the policyholder is alive, and the actuarial values at that age are A = 0.40 and ä = 12. What is the gross premium reserve per policy in force at that time?

The reserve is Rs 35,760. The expected present value of the benefit plus claim expense is 501,000 × 0.40 = 200,400. The expected present value of premiums net of 2% expense is 14,000 × 0.98 × 12 = 164,640. The reserve is outgo less income.

  1. ARs 35,760Correct
  2. BRs 32,400
  3. CRs 35,360
  4. DRs 29,040
  5. Rs −35,760

Explanation

The reserve is the expected PV of future outgo less future income. Benefit and claim expense: 501,000 × 0.40 = 200,400. Net premiums after the 2% expense: 14,000 × 0.98 × 12 = 164,640. Reserve = 200,400 − 164,640 = 35,760. Ignoring the premium expense gives 32,400, which is wrong because that cost is paid out of each premium.

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