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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Gross random future loss

A whole life policy pays Rs 100,000 at the end of the year of death. Level premiums of Rs 2,000 are payable annually in advance, and there are no expenses. Interest is 5% per annum effective. The policyholder dies during the 10th policy year (K = 9). What is the gross future loss at issue, to two decimal places?

The loss is Rs 45,175.69. The benefit's present value is 100,000 v^10 = 61,391.33, and ten advance premiums are worth 2,000 × 8.107822 = 16,215.64. Subtracting the premium value from the benefit value gives the loss.

  1. ARs 45,947.86
  2. BRs 41,024.43
  3. CRs 46,464.90
  4. DRs 45,175.69Correct
  5. Rs 61,391.33

Explanation

Death in year 10 means the benefit is paid at time 10, so v^10 = 0.613913 and the benefit PV is 61,391.33. Ten premiums are paid, and ä_10 = (1 − v^10)/d = 0.386087/0.047619 = 8.107822, so the premium PV is 16,215.64. Loss = 61,391.33 − 16,215.64 = 45,175.69. Using an annuity-immediate (a_10) gives 45,947.86, which is wrong because premiums are paid in advance.

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