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

(i)

	Death Benefit	Annual Premium Rate	Variance of the Present Value of Future Loss at [math]t[/math]
Policy A	1	0.10	0.455
Policy B	2	0.16	-

(ii) [math]\delta=0.06[/math]

Calculate the variance of the present value of future loss at [math]t[/math] for Policy B.

• 0.9
• 1.4
• 2.0
• 2.9
• 3.4

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

Answer: B

[math]L_{A}=v^{T}-0.10 \bar{a}_{\bar{T}}=\left(1+\frac{10}{6}\right) v^{T}-\frac{10}{6}[/math]

[math]\operatorname{Var}\left(L_{A}\right)=\left(1+\frac{10}{6}\right)^{2} \operatorname{Var}\left(v^{T}\right)=0.455 \Rightarrow \operatorname{Var}\left(v^{T}\right)=0.06398[/math]

[math]L_{B}=2 v^{T}-0.16 \bar{a}_{T}=\left(2+\frac{16}{6}\right) v^{T}-\frac{16}{6}[/math]

[math]\operatorname{Var}\left(L_{B}\right)=\left(2+\frac{16}{6}\right)^{2} \operatorname{Var}\left(v^{T}\right)=\left(2+\frac{16}{6}\right)^{2}(0.06398)=1.39[/math]

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