Revision as of 00:22, 19 January 2024 by Admin (Created page with "For a fully discrete 10 -year term life insurance policy on <math>(x)</math>, you are given: (i) Death benefits are 100,000 plus the return of all gross premiums paid without interest (ii) Expenses are <math>50 \%</math> of the first year's gross premium, <math>5 \%</math> of renewal gross premiums and 200 per policy expenses each year (iii) Expenses are payable at the beginning of the year (iv) <math>A_{x: 10}^{1}=0.17094</math> (v) <math>\quad(I A)_{x: 10 \mid}^{1...")
ABy Admin
Jan 19'24
Exercise
For a fully discrete 10 -year term life insurance policy on [math](x)[/math], you are given:
(i) Death benefits are 100,000 plus the return of all gross premiums paid without interest
(ii) Expenses are [math]50 \%[/math] of the first year's gross premium, [math]5 \%[/math] of renewal gross premiums and 200 per policy expenses each year
(iii) Expenses are payable at the beginning of the year
(iv) [math]A_{x: 10}^{1}=0.17094[/math]
(v) [math]\quad(I A)_{x: 10 \mid}^{1}=0.96728[/math]
(vi) [math]\quad \ddot{a}_{x: 100}=6.8865[/math]
Calculate the gross premium using the equivalence principle.
- 3200
- 3300
- 3400
- 3500
- 3600
ABy Admin
Jan 19'24
Answer: E
[[math]]
\begin{aligned}
& G \ddot{a}_{x: \overline{10}}=100,000 A_{x: 10 \mid}^{1}+G(I A)_{x: 10 \mid}^{1}+0.45 G+0.05 G \ddot{a}_{x: 10 \mid}+200 \ddot{a}_{x: \overline{10}} \\
& G=\frac{(100,000)(0.17094)+200(6.8865)}{(1-0.05)(6.8865)-0.96728-0.45}=3604.23
\end{aligned}
[[/math]]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.