For a 10 -year deferred whole life annuity-due with payments of 100,000 per year on (70), you are given:
(i) Annual gross premiums of [math]G[/math] are payable for 10 years
(ii) First year expenses are [math]75 \%[/math] of premium
(iii) Renewal expenses for years 2 and later are [math]5 \%[/math] of premium during the premium paying period
(iv) Mortality follows the Standard Ultimate Life Table
(v) [math]\quad i=0.05[/math]
Calculate [math]G[/math] using the equivalence principle.
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Answer: D
[math]G \ddot{a}_{70: \overline{10}}=100,000_{10} E_{70} \ddot{a}_{80}+0.05 G \ddot{a}_{70: \overline{10}}+0.7 G[/math]
[math]7.6491 G=(100,000)(0.50994)(8.5484)+0.05 G(7.6491)+0.7 G[/math]
[math]\Rightarrow G=66,383.54[/math]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.