For fully discrete whole life insurances of 1 issued on lives age 50 , the annual net premium, [math]P[/math], was calculated using the following:

(i) [math]\quad q_{50}=0.0048[/math]

(ii) [math]\quad i=0.04[/math]

(iii) [math]\quad A_{51}=0.39788[/math]

A particular life has a first-year mortality rate 10 times the rate used to calculate [math]P[/math]. The mortality rates for all other years are the same as the ones used to calculate [math]P[/math].

Calculate the expected present value of the loss at issue random variable for this life, based on the premium [math]P[/math].

• 0.025
• 0.033
• 0.041
• 0.049
• 0.057

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

Answer: C

For calculating [math]P[/math]

[math]A_{50}=v q_{50}+v p_{50} A_{51}=v(0.0048)+v(1-0.0048)(0.39788)=0.38536[/math]

[math]\ddot{a}_{50}=\left(1-A_{50}\right) / d=15.981[/math]

[math]P=A_{50} / \ddot{a}_{50}=0.02411[/math]

For this particular life,

[math]A_{50}^{\prime}=v q_{50}^{\prime}+v p_{50}^{\prime} A_{51}=v(0.048)+(1-0.048)(0.39788)=0.41037[/math]

[math]\ddot{a}_{50}^{\prime}=\left(1-A_{50}^{\prime}\right) / d=15.330[/math]

Expected PV of loss [math]=A_{50}^{\prime}-P \ddot{a}_{50}^{\prime}=0.41037-0.02411(15.330)=0.0408[/math]

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