ABy Admin
Jan 19'24
Exercise
For a fully discrete 5 -payment whole life insurance of 1000 on (40), you are given:
(i) Expenses incurred at the beginning of the first five policy years are as follows:
| Year 1 | Years 2-5 | |||
|---|---|---|---|---|
| Percent of Premium | Per Policy | Percent of Premium | Per Policy | |
| Sales Commission | 20% | 0 | 5% | 0 |
| Policy Maintenance | 0% | 10 | 0% | 5 |
(ii) No expenses are incurred after Year 5
(iii) Mortality follows the Standard Ultimate Life Table
(iv) [math]\quad i=0.05[/math]
Calculate the gross premium using the equivalence principle.
- 31
- 36
- 41
- 46
- 51
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Jan 19'24
Answer: B
[[math]]
\begin{aligned}
& G \ddot{a}_{40: 5 \mid}=1000 A_{40}+0.15 G+0.05 G \ddot{a}_{40: 51}+5+5 \ddot{a}_{40: 51} \\
& \ddot{a}_{40: 5 \mid}=\ddot{a}_{40}-{ }_{5} E_{40} \bullet \ddot{a}_{45}=18.4578-(0.78113)(17.8162)=4.5410 \\
& G=\frac{121.06+5+5(4.5410)}{-0.15+0.95(4.5410)}=35.73
\end{aligned}
[[/math]]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.