For a special whole life insurance of 100,000 on (40), you are given:

(i) The death benefit is payable at the moment of death

(ii) Level gross premiums are payable monthly for a maximum of 20 years

(iii) Mortality follows the Standard Ultimate Life Table

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

(v) Deaths are uniformly distributed over each year of age

(vi) Initial expenses are 200

(vii) Renewal expenses are [math]4 \%[/math] of each premium including the first (viii) Gross premiums are calculated using the equivalence principle Calculate the monthly gross premium.

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

Answer: C

[[math]] \begin{aligned} & G \ddot{a}_{40: 20}^{(12)}=100,000\left(\frac{i}{\delta}\right) A_{40}+200+0.04 G \ddot{a}_{40: 20}^{(12)} \\ & \ddot{a}_{40: 20}^{(12)}=\alpha(12) \ddot{a}_{40: 20}-\left(1-{ }_{20} E_{40}\right) \beta(12) \\ & \quad=1.00020 \cdot 12.9935-(1-0.36663) \cdot 0.46651=12.700625 \\ & G=\frac{(100,000)(1.02480)(0.12106)+200}{0.96 \times 12.700625}=1033.92 \\ & \Rightarrow \mathrm{G} / 12=86.16 \end{aligned} [[/math]]

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