Revision as of 01:31, 20 January 2024 by Admin (Created page with "For a fully discrete whole life insurance of 100 on <math>(x)</math>, you are given: (i) <math>\quad q_{x+15}=0.10</math> (ii) Deaths are uniformly distributed over each year of age (iii) <math>\quad i=0.05</math> (iv) <math>{ }_{t} V</math> denotes the net premium policy value at time <math>t</math> (v) <math>{ }_{16} V=49.78</math> Calculate <math>{ }_{15.6} \mathrm{~V}</math>. <ul class="mw-excansopts"><li> 49.7</li><li> 50.0</li><li> 50.3</li><li> 50.6</li><li...")
ABy Admin
Jan 20'24
Exercise
For a fully discrete whole life insurance of 100 on [math](x)[/math], you are given:
(i) [math]\quad q_{x+15}=0.10[/math]
(ii) Deaths are uniformly distributed over each year of age
(iii) [math]\quad i=0.05[/math]
(iv) [math]{ }_{t} V[/math] denotes the net premium policy value at time [math]t[/math]
(v) [math]{ }_{16} V=49.78[/math]
Calculate [math]{ }_{15.6} \mathrm{~V}[/math].
- 49.7
- 50.0
- 50.3
- 50.6
- 50.9
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Jan 20'24
Answer: E
[[math]]
\begin{aligned}
& { }_{15.6} V(1+i)^{0.4}={ }_{0.4} p_{x+15.6} \quad{ }_{16} V+{ }_{0.4} q_{x+15.6} 100 \\
& { }_{15.6} V(1.05)^{0.4}=0.957447(49.78)+0.042553(100) \\
& { }_{15.6} V=50.91
\end{aligned}
[[/math]]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.