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

A 5-year temporary annuity-due of 1 per annum is payable to a life aged x while alive. The corresponding 5-year endowment assurance (sum assured 1, paid at the end of the year of death) has A = 0.80 and second-moment value 2A = 0.65. The annual effective interest rate is i = 1/24, so that d = 0.04. What is the variance of the present value of the annuity?

The variance is 6.25. For a temporary annuity-due, the variance is (2A − A²)/d² using the endowment assurance values, which gives (0.65 − 0.64)/0.0016 = 6.25. The other options come from using the wrong divisor or numerator.

  1. A6.25Correct
  2. B0.25
  3. C5.76
  4. D406.25
  5. 4.00

Explanation

Var = (2A − A²)/d² = (0.65 − 0.64)/0.0016 = 6.25. Dividing by d instead of d² gives 0.25, and dividing by i² gives 5.76. Using 2A alone as the numerator gives 406.25.

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