For a whole life insurance of 10,000 on [math](x)[/math], you are given:

(i) Death benefits are payable at the end of the year of death

(ii) A premium of 30 is payable at the start of each month

(iii) Commissions are [math]5 \%[/math] of each premium

(iv) Expenses of 100 are payable at the start of each year

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

(vi) [math]\quad 1000 A_{x+10}=400[/math]

(vii) [math]{ }_{10} \mathrm{~V}[/math] is the gross premium policy value at the end of year 10 for this insurance Calculate [math]{ }_{10} V[/math] using the two-term Woolhouse formula for annuities.

• 950
• 980
• 1010
• 1110
• 1140

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

Answer: D

[[math]] \begin{aligned} & \ddot{a}_{x+10}=\left(1-A_{x+10}\right) / d=(1-0.4) /(0.05 / 1.05)=12.6 \\ & \ddot{a}_{x+10}^{(12)} \approx 12.6-11 / 24=12.142 \\ & { }_{10} V=10,000 A_{x+10}+100 \ddot{a}_{x+10}-12 \ddot{a}_{x+10}^{(12)}(30)(1-0.05) \\ & { }_{10} V=10,000(0.4)+100(12.6)-12(12.142)(28.50) \\ & { }_{10} V=1107 \end{aligned} [[/math]]

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