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

For a life aged x, the discount rate is d = 0.05, the temporary annuity-due ä_{x:10} = 7.80 and the pure endowment factor 10E_x = 0.55. What is the value of the 10-year term assurance A^1_{x:10} (sum assured 1, paid at the end of the year of death)?

The 10-year endowment assurance is 1 minus d·ä, which is 1 - 0.05 × 7.80 = 0.61. Subtracting the pure endowment factor 0.55 leaves the term assurance value of 0.06. Quoting 0.61 would include the survival benefit.

  1. A0.06Correct
  2. B0.16
  3. C0.39
  4. D0.61
  5. 1.16

Explanation

The endowment assurance is A_{x:10} = 1 - d·ä_{x:10} = 1 - 0.39 = 0.61. The term assurance is this minus the pure endowment: 0.61 - 0.55 = 0.06. Stopping at 0.61 treats the endowment assurance as the term assurance, which is wrong.

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