For a special fully discrete whole life insurance on (40), you are given:

(i) The death benefit is 1000 during the first 11 years and 5000 thereafter

(ii) Expenses, payable at the beginning of the year, are 100 in year 1 and 10 in years 2 and later

(iii) [math]\pi[/math] is the level annual premium, determined using the equivalence principle

(iv) [math]G=1.02 \times \pi[/math] is the level annual gross premium

(v) Mortality follows the Standard Ultimate Life Table

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

(vii) [math]{ }_{11} E_{40}=0.57949[/math]

Calculate the gross premium policy value at the end of year 1 for this insurance.

• -82
• -74
• -66
• -58
• -50

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

Answer: B

EPV of benefits at issue [math]=1000 A_{40}+4_{11} E_{40}\left(1000 A_{51}\right)[/math]

[[math]] =121.06+(4)(0.57949)(197.80)=579.55 [[/math]]

EPV of expenses at issue [math]=100+10\left(\ddot{a}_{40}-1\right)=100+10(17.4578)=274.58[/math]

[math]\pi=(579.55+274.58) / \ddot{a}_{40}=854.13 / 18.4578=46.27[/math]

[math]G=1.02 \pi=47.20[/math]

EPV of benefits at time [math]1=1000 A_{41}+4_{10} E_{41} \times 1000 A_{51}[/math]

[[math]] =126.65+(4)(0.60879)(197.80)=608.32 [[/math]]

EPV of expenses at time [math]1=10\left(\ddot{a}_{41}\right)=10(18.3403)=183.40[/math]

Gross Prem Policy Value [math]=608.32+183.40-G \ddot{a}_{41}=791.72-47.20(18.3403)=-73.94[/math]

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