XYZ Insurance writes 10,000 fully discrete whole life insurance policies of 1000 on lives age 40 and an additional 10,000 fully discrete whole life policies of 1000 on lives age 80 . [math]\mathrm{XYZ}[/math] used the following assumptions to determine the net premiums for these policies:

(i) Mortality follows the Standard Ultimate Life Table

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

During the first ten years, mortality did follow the Standard Ultimate Life Table.

Calculate the average net premium per policy in force received at the beginning of the eleventh year.

• 29
• 32
• 35
• 38
• 41

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

Answer: A

Premium at issue for (40): [math]\frac{1000 A_{40}}{\ddot{a}_{40}}=\frac{121.06}{18.4578}=6.5587[/math]

Premium at issue for (80): [math]\frac{1000 A_{80}}{\ddot{a}_{80}}=\frac{592.93}{8.5484}=69.3615[/math]

Lives in force after ten years:

Issued at age [math]40: 10,000_{10} p_{40}=10,000 \times \frac{98,576.4}{99,338.3}=9923.30[/math]

Issued at age [math]80: 10,000_{10} p_{80}=10,000 \times \frac{41,841.1}{75,657.2}=5530.35[/math]

The total number of lives after ten years is therefore: [math]9923.30+5530.35=15,453.65[/math]

The average premium after ten years is therefore:

[math]\frac{(6.5587 \times 9923.30)+(69.3615 \times 5530.35)}{15,453.65}=29.03[/math]

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