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]

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

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

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

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