For a fully discrete, 5-payment 10 -year term insurance of 200,000 on (30), you are given:

(i) Mortality follows the Standard Ultimate Life Table

(ii) The following expenses are incurred at the beginning of each respective year:

	Year 1		Years 2-10
	Percent of Premium	Per Policy	Percent of Premium	Per Policy
Taxes	5%	0	5%	0
Commissions	30%	0	10%	0
Maintenance	0%	8	0%	4

(iii) [math]\quad i=0.05[/math]

(iv) [math]\quad \ddot{a}_{30: 5}=4.5431[/math]

Calculate the annual gross premium using the equivalence principle.

• 150
• 160
• 170
• 180
• 190

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Answer: C

[[math]] \begin{aligned} & A P V(\text { expenses })=0.35 G+8+0.15 G a_{30: 4 \mid}+4 a_{30: 9]} \\ & =0.20 G+4+0.15 G \ddot{a}_{30: 51}+4 \ddot{a}_{30: 10} \end{aligned} [[/math]]

[math]G \ddot{a}_{30: 51}=0.20 G+4+0.15 G \ddot{a}_{30: 5]}+4 \ddot{a}_{30: 10 \mid}+200,000 A_{30: 10}^{1}[/math]

[math]G=\frac{200,000 A_{30: \overline{10}}^{1}+4+4 \ddot{a}_{30: \overline{10}}}{0.85 \ddot{a}_{30: 5 \mid}-0.20}[/math]

[math]200,000 A_{30: 10 \mid}^{1}=200,000\left[A_{30: 10 \mid}-{ }_{10} E_{30}\right][/math]

[math]=200,000(0.61447-0.61152)=590[/math]

[math]G=\frac{590+4+4(8.0961)}{0.85(4.5431)-0.20}=171.07[/math]

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.