For two fully discrete whole life insurance policies on [math](x)[/math], you are given:

(i)

	Death Benefit	Annual Net Premium	Variance of Loss at Issue
Policy 1	8	1.250	20.55
Policy 2	12	1.875	[math]W[/math]

(ii) [math]\quad i=0.06[/math]

(iii) The two policies are priced using the same mortality table.

Calculate [math]W[/math].

• 30.8
• 38.5
• 46.2
• 53.9
• 61.6

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

Answer: C

[[math]] \begin{aligned} & V\left[L_{0} \# 1\right]=\left(B_{1}+\frac{P_{1}}{d}\right)^{2}\left({ }^{2} A_{x}-A_{x}^{2}\right)=20.55==\gt\left(8+\frac{1.25(1.06)}{0.06}\right)^{2}\left({ }^{2} A_{x}-A_{x}^{2}\right)=20.55 \\ & { }^{2} A_{x}-A_{x}^{2}=\frac{20.55}{\left(8+\frac{1.25(1.06)}{0.06}\right)^{2}}=0.0227 \\ & V\left[L_{0} \# 2\right]=\left(12+\frac{1.875(1.06)}{0.06}\right)^{2}\left({ }^{2} A_{x}-A_{x}^{2}\right)=\left(12+\frac{1.875(1.06)}{0.06}\right)^{2}(0.0227)=46.24 \end{aligned} [[/math]]

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