For a special 10 -year deferred whole life annuity-due of 50,000 on (62), you are given:

(i) Level annual net premiums are payable for 10 years

(ii) A death benefit, payable at the end of the year of death, is provided only over the deferral period and is the sum of the net premiums paid without interest

(iii) [math]\quad \ddot{a}_{62}=12.2758[/math]

(iv) [math]\quad \ddot{a}_{62: 10 \mid}=7.4574[/math]

(v) [math]\quad A_{62: 10}^{1}=0.0910[/math]

(vi) [math]\quad \sum_{k=1}^{10} A_{62: k}^{1}=0.4891[/math]

Calculate the net premium for this special annuity.

• 34,400
• 34,500
• 34,600
• 34,700
• 34,800

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

Answer: D

Under the Equivalence Principle

[math]P \ddot{a}_{62: 101}=50,000\left(\ddot{a}_{62}-\ddot{a}_{62: 10}\right)+P\left((I A)_{62: 100}^{1}\right)[/math]

where [math](I A)_{62: 10 \mid}^{1}=11 A_{62: 10 \mid}^{1}-\sum_{k=1}^{10} A_{62: k \mid}^{1}=11(0.091)-0.4891=0.5119[/math]

So [math]\quad P=\frac{50,000\left(\ddot{a}_{62}-\ddot{a}_{62: 10}\right)}{\ddot{a}_{62: 10 \mid}-(I A)_{62: 100}^{1}}=\frac{50,000(12.2758-7.4574)}{7.4574-0.5119}=34,687[/math]

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