For a fully discrete whole life insurance of 1000 on (35), you are given:

(i) First year expenses are [math]30 \%[/math] of the gross premium plus 300

(ii) Renewal expenses are [math]4 \%[/math] of the gross premium plus 30

(iii) All expenses are incurred at the beginning of the policy year

(iv) Gross premiums are calculated using the equivalence principle

(v) The gross premium policy value at the end of the first policy year is [math]R[/math]

(vi) Using the Full Preliminary Term Method, the modified net premium reserve at the end of the first policy year is [math]S[/math]

(vii) Mortality follows the Standard Ultimate Life Table

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

Calculate [math]R-S[/math].

• -280
• -140
• 0
• 140
• 280

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

Answer: A

If [math]G[/math] denotes the gross premium, then

[[math]] G=\frac{1000 A_{35}+30 \ddot{a}_{35}+270}{0.96 \ddot{a}_{35}-0.26}=\frac{1000(0.09653)+30(18.9728)+270}{0.96(18.9728)-0.26}=52.12 [[/math]]

So that,

[[math]] \begin{aligned} & R=1000 A_{36}+(30-0.96 G) \ddot{a}_{36} \\ & \quad=1000(0.10101)+(30-0.96 \times 52.12)(18.8788)=-277.23 \end{aligned} [[/math]]

Note that [math]S=0[/math] as per definition of FPT reserve.

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