For a fully discrete increasing 20-year endowment insurance on (50), you are given:

i) The level annual net premium is 5,808

ii) The net premium policy value at the end of year 15 is 130,580

iii) Mortality after age 60 follows the Standard Ultimate Life Table

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

Calculate the expected present value of future death and endowment benefits at age 65 .

• 156,530
• 156,570
• 156,610
• 156,650
• 156,690

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

Answer: D

[math]\ddot{a}_{65: 5 \mid}=\ddot{a}_{65}-{ }_{5} E_{65} \times \ddot{a}_{70}=13.5498-0.75455(12.0083)=4.4889[/math]

EPV future net premiums [math]=4.4889(5,808)=26,072[/math]

[math]130,580=\mathrm{EPV}[/math] future benefits [math]-\mathrm{EPV}[/math] future net premiums [math]=\mathrm{EPV}[/math] future benefits [math]-26,072[/math] EPV future benefits [math]=156,652[/math]

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