IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Key assurance and annuity contracts
At 4% effective annual interest, a life aged x has ä_x = 14. An annual premium is payable in advance throughout life for a whole life assurance with sum assured 1,000 payable at the end of the year of death. Using the equivalence principle with no expenses, what is the annual premium (to two decimal places)?
The premium per 1,000 is 1,000 times (1/ä_x minus d). With ä_x = 14 and d = 0.04/1.04, this is 71.43 minus 38.46, giving 32.97. Using i instead of d would understate the premium, and ignoring d would give 71.43.
- A31.43
- B32.97Correct
- C35.50
- D38.46
- 71.43
Explanation
P = 1000(1/ä_x - d). With d = 0.04/1.04 = 0.038462 and 1/14 = 0.071429, P = 1000 × 0.032967 = 32.97. Using i = 0.04 instead of d gives 31.43. Using 1/ä_x alone gives 71.43.
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