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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Means and variances of assurance and annuity payments

For a life aged x, the expected present value of a whole life assurance of 1 payable at the end of the year of death is A_x = 0.40. The effective annual interest rate is 5%. What is the expected present value of a whole life annuity-due of 1 per annum, ä_x?

The expected annuity-due value is 12.60. The relationship A_x = 1 − d·ä_x gives ä_x = (1 − 0.40)/d, and d = 0.05/1.05 = 0.047619, so ä_x = 0.60/0.047619 = 12.60. Using i in place of d would give 12.00.

  1. A8.40
  2. B11.60
  3. C12.00
  4. D12.60Correct
  5. 13.23

Explanation

Use A_x = 1 − d·ä_x. With d = 0.05/1.05 = 0.047619, ä_x = 0.60/0.047619 = 12.60. Dividing by i = 0.05 gives 12.00, which wrongly uses i instead of d. Using A_x = 0.40 in the numerator gives 8.40, which forgets the 1 − A_x step.

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