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...")
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
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]]