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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Gross premiums and reserves

A one-year term assurance has sum assured Rs 2,00,000 payable at the end of the year of death. The mortality rate is 0.01 and interest is 6% per annum. A single premium is paid at the start. Expenses are 5% of the premium plus Rs 100 per policy, both incurred at the start. What is the gross premium on the equivalence principle?

The gross premium is Rs 2,091.36. The discounted expected claim of Rs 1,886.79 plus the Rs 100 fixed expense equals 95% of the premium, because 5% of the premium is absorbed by the percentage expense. Dividing 1,986.79 by 0.95 gives the premium.

  1. ARs 2,086.09
  2. BRs 2,091.36Correct
  3. CRs 2,086.13
  4. DRs 2,210.53
  5. Rs 1,986.79

Explanation

The benefit PV is 2,000/1.06 = 1,886.79, and adding the Rs 100 expense gives 1,986.79. The premium net of the 5% loading must cover this, so G = 1,986.79/0.95 = 2,091.36. Multiplying by 1.05 instead gives 2,086.13, which is wrong because the loading is a percentage of the gross premium, not of the net cost.

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