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

A whole life policy with sum assured Rs 100,000 payable at the end of the year of death has an annual gross premium of Rs 2,800 payable in advance. Renewal expenses are 2% of each gross premium, incurred when each premium is paid. At the valuation date, just before a premium is due, A = 0.40 and the annuity-due value is 12 for the life aged x+t. What is the gross premium reserve per policy?

The reserve is Rs 7,072.00. Expected present value of benefits is 40,000, expected present value of expenses is 672, and expected present value of premiums is 33,600. Reserve equals benefits plus expenses minus premiums, so 40,000 + 672 − 33,600 = 7,072.

  1. ARs 5,728.00
  2. BRs 6,400.00
  3. CRs 7,072.00Correct
  4. DRs 9,872.00
  5. Rs 73,600.00

Explanation

Benefits: 100,000 × 0.40 = 40,000. Expenses: 0.02 × 2,800 × 12 = 672. Premiums: 2,800 × 12 = 33,600. Reserve = 40,000 + 672 − 33,600 = 7,072. Omitting expenses gives 6,400, and subtracting expenses gives 5,728.

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