Skip to content

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

For a term policy, the gross premium reserve at the start of a policy year is Rs 2,000 per policy. The gross premium is Rs 1,000 paid at the start of the year, with an expense of Rs 100 incurred at the same time. The sum assured of Rs 50,000 is paid at the end of the year of death, the mortality rate for the year is 0.01 and interest is 5% p.a. What is the reserve at the end of the year for a survivor?

The year-end reserve for a survivor is Rs 2,570.71. Accumulate the reserve plus net income at 5% to give 3,045, deduct the expected death claim of 500, and divide the remainder of 2,545 by the survival probability 0.99.

  1. ARs 2,424.24
  2. BRs 2,570.71Correct
  3. CRs 2,676.77
  4. DRs 3,075.76
  5. Rs 2,545.00

Explanation

Recursion: (V + P − e)(1+i) = qS + pV₁. (2,000 + 1,000 − 100) × 1.05 = 3,045. Subtract 0.01 × 50,000 = 500 to get 2,545, then divide by 0.99 to get 2,570.71. Not dividing by the survival probability gives 2,545.

Did you get it right without looking?

One question tells you little. A timed set on Gross random future loss shows your real accuracy, how long you take and where you lose marks.

Practise Gross random future lossFree diagnostic mock

More Gross random future loss questions