Revision as of 01:30, 20 January 2024 by Admin (Created page with "For a fully discrete whole life insurance of 100,000 on (45), you are given: (i) The gross premium policy value at duration 5 is 5500 and at duration 6 is 7100 (ii) <math>\quad q_{50}=0.009</math> (iii) <math>\quad i=0.05</math> (iv) Renewal expenses at the start of each year are 50 plus <math>4 \%</math> of the gross premium. (v) Claim expenses are 200. Calculate the gross premium. <ul class="mw-excansopts"><li> 2200</li><li> 2250</li><li> 2300</li><li> 2350</li>...")
ABy Admin
Jan 20'24
Exercise
For a fully discrete whole life insurance of 100,000 on (45), you are given:
(i) The gross premium policy value at duration 5 is 5500 and at duration 6 is 7100
(ii) [math]\quad q_{50}=0.009[/math]
(iii) [math]\quad i=0.05[/math]
(iv) Renewal expenses at the start of each year are 50 plus [math]4 \%[/math] of the gross premium.
(v) Claim expenses are 200.
Calculate the gross premium.
- 2200
- 2250
- 2300
- 2350
- 2400
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Jan 20'24
Answer: A
[[math]]
\begin{aligned}
\left({ }_{5} V+0.96 G-50\right)(1.05) & =q_{50}(100,200)+p_{50}{ }_{6} V \\
(5500+0.96 G-50)(1.05) & =(0.009)(100,200)+(1-0.009)(7100) \\
(1.05)(0.96) G+5722.5 & =7937.9 \\
(1.05)(0.96) G & =2215.4 \\
G & =2197.8
\end{aligned}
[[/math]]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.