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

For an increasing whole life assurance paying k at the end of year k if death occurs in year k, the recursion (IA)_x = v q_x + v p_x [ (IA)_{x+1} + A_{x+1} ] holds. Given q_x = 0.02, A_{x+1} = 0.40, (IA)_{x+1} = 5.00 and i = 5%, what is (IA)_x?

(IA)_x is 5.06. The benefit increase for survivors adds A_{x+1} to (IA)_{x+1}, so the value is [0.02 + 0.98 × 5.40] / 1.05 = 5.312/1.05 = 5.059. Leaving out the A_{x+1} term gives the wrong value 4.69.

  1. A4.69
  2. B5.04
  3. C5.16
  4. D5.31
  5. 5.06Correct

Explanation

Inside the bracket: 0.02 + 0.98 × (5.00 + 0.40) = 0.02 + 5.292 = 5.312. Dividing by 1.05 gives 5.0590, which is 5.06. Omitting A_{x+1} gives 4.69, and omitting the q term gives 5.04.

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