An insurer issues a special 20 payment insurance policy on (45) with the following benefits: - A death benefit of 1000 , payable at the end of year of death, provided death occurs before age 65 ; and - An annuity benefit that pays 2500 at the start of each year, starting at age 65

You are given:

i) Level annual premiums of [math]P[/math] are paid at the beginning of each year

ii) Premiums are calculated based on the equivalence principle

iii) Mortality follows the Standard Ultimate Life Table

iv) [math]i=0.05[/math]

Calculate [math]P[/math].

• 872
• 896
• 920
• 944
• 968

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

Answer: D

EPV(benefits [math])=1000 \times A_{45: 20 \mid}^{1}+2500 \times{ }_{20} \ddot{a}_{45}[/math]

[[math]] =1000(0.15161-0.35994 \times 0.35477)+2500 \times 0.35994 \times 13.5498=12,216.7 [[/math]]

[math]\mathrm{EPV}([/math] premiums [math])=P \times(17.8161-0.35994 \times 13.5498)=P \times 12.9391[/math]

[[math]] P=\frac{12216.7}{12.9391}=944.17 [[/math]]

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