IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Key assurance and annuity contracts
For a life aged x, the whole life assurance factor (benefit paid at end of year of death) is A_x = 0.40 at an effective annual interest rate of 5%. What is the whole life annuity-due factor ä_x?
The annuity-due factor is 12.60. It follows from ä_x = (1 - A_x)/d, where d = i/(1+i) = 0.047619, so ä_x = 0.60/0.047619. The denominator must be the discount rate d, not the interest rate i.
- A11.60
- B12.00
- C8.40
- D13.23
- 12.60Correct
Explanation
Use ä_x = (1 - A_x)/d, with d = 0.05/1.05 = 0.047619. So ä_x = 0.60/0.047619 = 12.60. Dividing by i instead of d gives 12.00, which is the wrong denominator for an annuity-due. The figure 11.60 is a_x, the annuity-immediate.
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