IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Means and variances of assurance and annuity payments
For a life aged 40, ä_40 = 16.00 at an effective annual interest rate of 5%. Using A_x = 1 − d·ä_x, what is A_40 to two decimal places?
A_40 is approximately 0.24. The discount rate is 0.05/1.05 = 0.047619, so d times the annuity value of 16 is 0.7619, and subtracting from 1 gives 0.2381, which rounds to 0.24 at two decimal places.
- A0.24Correct
- B0.16
- C0.20
- D0.76
- 0.30
Explanation
d = i/(1+i) = 0.05/1.05 = 0.047619. d·ä = 0.047619 × 16 = 0.761905. A_40 = 1 − 0.761905 = 0.238095, which is 0.24. Using i = 0.05 instead of d gives 0.20, which is wrong.
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