For a special whole life policy on (48), you are given:

(i) The policy pays 5000 if the insured's death is before the median curtate future lifetime at issue and 10,000 if death is after the median curtate future lifetime at issue

(ii) Mortality follows the Standard Ultimate Life Table

(iii) Death benefits are paid at the end of the year of death

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

Calculate the actuarial present value of benefits for this policy.

• 1130
• 1160
• 1190
• 1220
• 1250

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

Answer: A

The median of [math]K_{48}[/math] is the integer [math]m[/math] for which

[[math]] P\left(K_{48} \lt m\right) \leq 0.5 \text { and } P\left(K_{48} \gt m\right) \leq 0.5 \text {. } [[/math]]

This is equivalent to finding [math]m[/math] for which

[[math]] \frac{l_{48+m}}{l_{48}} \geq 0.5 \text { and } \frac{l_{48+m+1}}{l_{48}} \leq 0.5 [[/math]]

Based on the SULT and [math]l_{48}(0.5)=(98,783.9)(0.5)=49,391.95[/math], we have [math]m=40[/math] since [math]l_{88} \geq 49,391.95[/math] and [math]l_{89} \leq 49,391.95[/math].

So: [math]A P V=5000 A_{48}+5000_{40} E_{48} A_{88}=5000 A_{48}+5000 \cdot{ }_{20} E_{48}{ }_{20} E_{68} \cdot A_{88}[/math] [math]=5000(0.17330)+5000(0.35370)(0.20343)(0.72349)=1126.79[/math]

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