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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 level annual premium P payable in advance. Expenses are Rs 1,500 at issue plus 2% of every premium, including the first. Given A_x = 0.32 and the annuity-due value ä_x = 14, what is P under the equivalence principle?

The premium is Rs 2,441.69. Equating expected premiums net of the 2% premium expense to the expected benefit plus the Rs 1,500 initial expense gives 0.98 × 14 × P = 33,500. Dividing 33,500 by 13.72 gives the premium.

  1. ARs 2,441.69Correct
  2. BRs 2,392.86
  3. CRs 2,332.36
  4. DRs 2,438.14
  5. Rs 2,345.94

Explanation

Setting E[L] = 0 gives P ä = 100,000 × 0.32 + 1,500 + 0.02 P ä. So P × 0.98 × 14 = 33,500 and P = 33,500/13.72 = 2,441.69. Ignoring the percentage expense gives 2,392.86, which is too low. Omitting the initial expense gives 2,332.36.

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