For a fully discrete 5-payment whole life insurance of 1000 on (80), you are given:
(i) The gross premium is 130
(ii) [math]\quad q_{80+k}=0.01(k+1), \quad k=0,1,2, . ., 5[/math]
(iii) [math]\quad v=0.95[/math]
(iv) [math]\quad 1000 A_{86}=683[/math]
(v) [math]{ }_{3} L[/math] is the prospective loss random variable at time 3, based on the gross premium
Calculate [math]E\left[{ }_{3} L\right][/math].
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Answer: D
APV future benefits [math]=1000\left[0.04 v+0.05 \times 0.96 v^{2}+0.96 \times 0.95 \times(0.06+0.94 \times 0.683) v^{3}\right]=630.25[/math]
APV future premiums [math]=130(1+0.96 v)=248.56[/math]
[math]E\left[{ }_{3} L\right]=630.25-248.56=381.69[/math]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.