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

A 20-year-old-premium-term whole life policy (premiums payable annually in advance for at most 20 years) is issued to a life aged x with sum assured ₹10,00,000 payable at the end of the year of death. On the premium basis, A_x = 0.32 and the temporary annuity-due ä_{x:20} = 12.50. Using the equivalence principle, what is the annual net premium?

The net premium is ₹25,600. By the equivalence principle, the premium times the 20-year temporary annuity-due equals the sum assured times the whole life assurance factor, so P = 10,00,000 × 0.32 ÷ 12.50.

  1. A₹21,333.33
  2. B₹25,600.00Correct
  3. C₹27,826.09
  4. D₹32,000.00
  5. ₹2,560.00

Explanation

Equivalence principle: P × ä_{x:20} = 10,00,000 × A_x. P = 10,00,000 × 0.32 / 12.50 = ₹25,600. Dividing by 15 or 11.5 instead uses the wrong annuity, and ₹32,000 comes from dividing by 10; none of these matches the 20-year premium term.

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