For a fully discrete 20 -year term insurance of 100,000 on (50), you are given:

(i) Gross premiums are payable for 10 years

(ii) Mortality follows the Standard Ultimate Life Table

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

(iv) Expenses are incurred at the beginning of each year as follows:

	Year 1	Years 2-10	Years 11-20
Commission as % of premium	[math]40 \%[/math]	[math]10 \%[/math]	Not applicable
Premium taxes as % of premium	[math]2 \%[/math]	[math]2 \%[/math]	Not applicable
Maintenance expenses	75	25	25

(v) Gross premiums are calculated using the equivalence principle

Calculate the gross premium for this insurance.

• 617
• 627
• 637
• 647
• 657

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

Answer: D

[math]\ddot{a}_{50: 10}=8.0550[/math]

[[math]] \begin{aligned} & A_{50: \overline{20}}^{1}=A_{50: 20 \mid}-{ }_{20} E_{50}=0.38844-0.34824=0.04020 \\ & \ddot{a}_{50: \overline{20}}=12.8428 \end{aligned} [[/math]]

APV of Premiums [math]=[/math] APV Death Benefit + APV Commission and Taxes + APV Maintenance [math]G \ddot{a}_{50: 10 \mathrm{io}}=100,000 A_{50: 20}^{1}+0.12 G \ddot{a}_{50: 101}+0.3 G+25 \ddot{a}_{50: 20}+50[/math]

[math]8.0550 G=4020+1.2666 G+371.07[/math]

[math]6.7883 G=4391.07[/math]

[[math]] \Rightarrow G=646.86 [[/math]]

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