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

At an effective annual interest rate of 5%, a whole life annuity-due of 1 per annum for a life aged x has expected present value ä_x = 15. What is the expected present value of a whole life assurance of 1 payable at the end of the year of death, A_x?

A_x equals 1 minus d times ä_x. With d = 0.05/1.05 and ä_x = 15, d·ä_x is 0.7143, so A_x is about 0.29. Using the interest rate i instead of the discount rate d would wrongly give 0.25.

  1. A0.25
  2. B0.29Correct
  3. C0.33
  4. D0.71
  5. 0.75

Explanation

Use A_x = 1 - d·ä_x. Here d = 0.05/1.05 = 0.047619, so d·ä_x = 0.714286 and A_x = 0.285714, which is 0.29. Using i in place of d gives 1 - 0.75 = 0.25, which is wrong because the relationship applies to the discount rate d.

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