For a given population with two subgroups, you are given:

i) Subgroup [math]\mathrm{X}[/math] represents 80% of the total population and is subject to a constant annual force of mortality of 0.01

ii) Subgroup [math]\mathrm{Y}[/math] represents 20% of the total population and is subject to a constant annual force of mortality of 0.02

Calculate the proportion of the population 15 years from now that is part of subgroup [math]\mathrm{X}[/math].

• 80.0%
• 81.1%
• 82.3%
• 83.4%
• 84.6%

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

Answer: C

	[math]{ }_{15} p[/math]	Alive at time 0	Alive at time 15
[math]\mathrm{A}[/math]	[math]e^{-15(0.01)}=0.8607[/math]	8,000	6,885.66
[math]\mathrm{B}[/math]	[math]e^{-15(0.02)}=0.7409[/math]	2,000	1,481.64
Total		10,000	8,367.30

Fraction [math]A=\frac{6,885.66}{8,367.30}=0.823[/math]