Revision as of 01:35, 20 January 2024 by Admin (Created page with "For two fully discrete whole life insurance policies on <math>(x)</math>, you are given: (i) {| class="table table-bordered" ! !! 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>. <ul class="mw-excansopts"><li> 30.8</li><li> 38.5</li><li> 46.2...")
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ABy Admin
Jan 20'24

Exercise

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.

ABy Admin
Jan 20'24

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.

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