Skip to content

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

A whole life policy was issued at age x with sum assured Rs 200,000 and level annual premium Rs 2,500 payable in advance. Some years later the life, now aged x+t, is still alive. Valuation values are A_x = 0.45, A_{x+t} = 0.50 and ä_{x+t} = 13.0. What is the expected future loss at that time, given survival?

The expected future loss is Rs 67,500. At duration t the benefit value uses age x+t: 200,000 × 0.50 = 100,000, less the premium value 2,500 × 13.0 = 32,500. The issue-age assurance value of 0.45 must not be used.

  1. ARs 67,500Correct
  2. BRs 70,000
  3. CRs -67,500
  4. DRs 100,000
  5. Rs 57,500

Explanation

The future loss at duration t must use the values at age x+t. E[Lt] = 200,000 × 0.50 - 2,500 × 13.0 = 100,000 - 32,500 = 67,500. Using A_x = 0.45 gives 57,500, which is the wrong age. Using ä - 1 gives 70,000, which wrongly drops the premium due now.

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