For a fully discrete whole life insurance of 1000 on (30), you are given:

(i) Mortality follows the Standard Ultimate Life Table

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

(iii) The premium is the net premium

Calculate the first year for which the expected present value at issue of that year's premium is less than the expected present value at issue of that year's benefit.

• 21
• 25
• 29
• 33
• 37

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

Answer: D

Let [math]k[/math] be the policy year, so that the mortality rate during that year is [math]q_{30+k-1}[/math]. The objective is to determine the smallest value of [math]k[/math] such that

[math]v^{k-1}\left({ }_{k-1} p_{30}\right)\left(1000 P_{30}\right) \lt v^{k}\left({ }_{k-1} p_{30}\right) q_{30+k-1}(1000)[/math]

[math]P_{30} \lt v q_{30+k-1}[/math]

[math]\frac{0.07698}{19.3834}\lt\frac{q_{29+k}}{1.05}[/math]

[math]q_{29+k}\gt0.00417[/math]

[math]29+k\gt61 \Rightarrow k\gt32[/math]

Therefore, the smallest value that meets the condition is 33 .

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