IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Means and variances of assurance and annuity payments
At 5% effective annual interest, a life aged 70 has p_70 = 0.95 and ä_71 = 8.00. Using the recursion ä_x = 1 + v·p_x·ä_(x+1), what is ä_70 to two decimal places?
ä_70 equals 1 + (0.95/1.05) × 8.00 = 1 + 7.2381 = 8.2381, which rounds to 8.24. The first payment is made immediately, and later payments are discounted and weighted by the probability of surviving one year.
- A8.24Correct
- B8.60
- C8.00
- D7.24
- 9.00
Explanation
v·p = 0.95/1.05 = 0.904762. Multiply by 8.00 to get 7.238095. Add 1 to get 8.238095, which is 8.24. Omitting the survival probability gives 8.62, and forgetting the initial payment gives 7.24.
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