For the country of Bienna, you are given:

(i) Bienna publishes mortality rates in biennial form, that is, mortality rates are of the form:

[[math]] { }_{2} q_{2 x}, \text { for } x=0,1,2, \ldots [[/math]]

(ii) Deaths are assumed to be uniformly distributed between ages [math]2 x[/math] and [math]2 x+2[/math], for [math]x=0,1,2, \ldots[/math]

(iii) [math]{ }_{2} q_{50}=0.02[/math]

(iv) [math]{ }_{2} q_{52}=0.04[/math]

Calculate the probability that (50) dies during the next 2.5 years.

• 0.02
• 0.03
• 0.04
• 0.05
• 0.06

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Answer: B

[math]{ }_{2.5} q_{50}={ }_{2} q_{50}+{ }_{2} p_{50}{ }_{0.5} q_{52}=0.02+(0.98)\left(\frac{0.5}{2}\right)(0.04)=0.0298[/math]