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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Concepts of survival models

Assume a constant force of mortality mu = 0.02 between ages 50 and 52, so that 2p_50 = exp(-0.04). Given l_50 = 100,000, what is the expected number of deaths between exact ages 50 and 52, to the nearest whole number?

Deaths equal l_50 times (1 - exp(-0.04)). Since exp(-0.04) is 0.960789, survivors are about 96,079 and deaths are about 3,921. Simply multiplying the force by two years and the radix overstates deaths because the surviving population shrinks.

  1. A3,921Correct
  2. B3,922
  3. C4,000
  4. D4,081
  5. 3,846

Explanation

l_52 = 100,000 x exp(-0.04) = 100,000 x 0.960789 = 96,078.9. Deaths = 100,000 - 96,078.9 = 3,921.1, so 3,921. Option C uses 100,000 x 0.04 which ignores the compounding of survival. Option D is the result of using exp(0.04) in the wrong direction (100,000 x 0.0408).

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