IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Means and variances of assurance and annuity payments
At 6% effective annual interest, the recursion A_x = v·q_x + v·p_x·A_(x+1) is used. If q_60 = 0.02 and A_61 = 0.50, what is A_60 to two decimal places?
Computation gives A_60 = (0.02 + 0.98×0.50)/1.06 = 0.51/1.06 = 0.4811, which is about 0.48.
- A0.49Correct
- B0.47
- C0.52
- D0.51
- 0.50
Explanation
v = 1/1.06 = 0.943396. p_60 = 0.98. A_60 = 0.943396 × (0.02 + 0.98 × 0.50) = 0.943396 × 0.51 = 0.481132, which is 0.48. Check: 0.51/1.06 = 0.4811. So the answer is 0.48, not any listed value except none...
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