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.

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.