An insurer issues a 20-year deferred whole life annuity due on [45]. You are given:

i) Net premiums of 20,000 are payable at the beginning of each year during the deferral period

ii) There is no benefit paid upon death during the deferral period

iii) [math]V[/math] denotes the net premium policy value at time [math]t, t \geq 0[/math]

iv) [math]{ }_{19} V=575,000[/math] v) [math]q_{[45]+18}=0.023044[/math]

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

Calculate [math]{ }_{18} V[/math].

• 495,000
• 505,000
• 515,000
• 525,000
• 535,000

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

Answer: C

[math]\left({ }_{18} V+P\right)(1+i)=p_{[45]+18} \times{ }_{19} V[/math]

[math]{ }_{18} V=0.976956 \times 575,000 / 1.05-20,000=515,000[/math]

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