For a fully discrete 20 -year endowment insurance of 100,000 on (30), you are given:

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

(ii) Expenses, payable at the beginning of each year, are:

	First Year		Renewal Years
	Percent of Premium	Per Policy	Percent of Premium	Per Policy
Taxes	4%	0	4%	0
Sales Commission	35%	0	2%	0
Policy Maintenance	0%	250	0%	50

(iii) The net premium is 2143

Calculate the gross premium using the equivalence principle.

• 2410
• 2530
• 2800
• 3130
• 3280

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

Answer: A

[math]P_{30: 20 \mid}=\frac{1}{\ddot{a}_{30: \overline{20}}}-d \Rightarrow \frac{2,143}{100,000}+0.05=\frac{1}{\ddot{a}_{30: \overline{20}}} \Rightarrow \ddot{a}_{30: 20}=14[/math]

[math]A_{30: \overline{20}}=1-d \ddot{a}_{30: \overline{20}}=1-0.05(14)=0.3[/math]

[math]G \ddot{a}_{30: \overline{20}}=100,000 A_{30: \overline{20}}+\left(200+50 \ddot{a}_{30: \overline{20}}\right)+\left(0.33 G+0.06 G \ddot{a}_{30: \overline{20}}\right)[/math]

[math]14 G=100,000(0.3)+[200+50(14)]+(0.33 G+0.84 G)[/math]

[math]12.83 G=30,900[/math]

[math]G=2408[/math]

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