For a fully discrete 10 -payment whole life insurance of [math]H[/math] on (45), you are given:

(i) Expenses payable at the beginning of each year are as follows:

Expense Type	First Year	Years 2-10	Years 11+
Per policy	100	20	10
[math]\%[/math] of Premium	[math]105 \%[/math]	[math]5 \%[/math]	[math]0 \%[/math]

(ii) Mortality follows the Standard Ultimate Life Table

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

(iv) The gross annual premium, calculated using the equivalence principle, is of the form [math]G=g H+f[/math], where [math]g[/math] is the premium rate per 1 of insurance and [math]f[/math] is the per policy fee

Calculate [math]f[/math].

• 42.00
• 44.20
• 46.40
• 48.60
• 50.80

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

Answer: E

[[math]] \begin{aligned} & G \ddot{a}_{45: \overline{10}}=H A_{45}+G+0.05 G \ddot{a}_{45: \overline{10}}+80+10 \ddot{a}_{45}+10 \ddot{a}_{45: 10} \\ & G=\frac{H A_{45}+80+10\left(\ddot{a}_{45}+\ddot{a}_{45: 10 \mid}\right)}{0.95 \ddot{a}_{45: 10}-1} \\ & G=\frac{H A_{45}+80+10(17.8162+8.0751)}{(0.95 \times 8.0751)-1} \\ & G=\frac{A_{45}}{(0.95 \times 8.0751)-1} H+\frac{80+10(17.8162+8.0751)}{(0.95 \times 8.0751)-1} \\ & g=\frac{A_{45}}{(0.95 \times 8.0751)-1} \\ & f=\frac{80+10(17.8162+8.0751)}{(0.95 \times 8.0751)-1}=50.80 \end{aligned} [[/math]]

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