Skip to content

IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Projecting and valuing cashflows contingent on multiple decrement events

An employee aged 55 is subject to two decrements with constant forces: death 0.02 and withdrawal 0.08 per year. What is the probability that the employee leaves the scheme by withdrawal within the next 5 years?

The answer is 0.31. With constant forces, the chance of exiting by withdrawal is the withdrawal share of the total force, 0.8, multiplied by the chance of any exit within 5 years, 1 - e^{-0.5} = 0.3935, which gives 0.3148.

  1. A0.31Correct
  2. B0.39
  3. C0.40
  4. D0.08
  5. 0.33

Explanation

Total force is 0.10. The probability of leaving by withdrawal within 5 years is (0.08/0.10)(1 - e^{-0.5}) = 0.8 x 0.393469 = 0.3148, or 0.31. The option 0.39 is the probability of leaving for any reason and ignores the withdrawal share.

Did you get it right without looking?

One question tells you little. A timed set on Projecting and valuing cashflows contingent on multiple decrement events shows your real accuracy, how long you take and where you lose marks.

Practise Projecting and valuing cashflows contingent on multiple decrement eventsFree diagnostic mock

More Projecting and valuing cashflows contingent on multiple decrement events questions