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

At 5% effective annual interest, ä_x = 12.00 and ä_{x+1} = 12.60. Using the recursion linking annuity-due values at successive ages, what is q_x?

From ä_x = 1 + v·p_x·ä_{x+1}, we get 11 = p_x × 12.6/1.05 = 12 p_x. So p_x = 11/12 and q_x = 1/12, which is about 0.08. Ignoring discounting would give 0.13.

  1. A0.00
  2. B0.05
  3. C0.08Correct
  4. D0.13
  5. 0.17

Explanation

The recursion is ä_x = 1 + v·p_x·ä_{x+1}. So 11 = p_x × 12.60/1.05 = 12 p_x, giving p_x = 11/12 and q_x = 1/12 = 0.08. Omitting v gives p_x = 11/12.6 and q_x = 0.13, while multiplying by v instead of dividing gives 0.17.

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