For a 2 -year deferred, 2 -year term insurance of 2000 on [65], you are given:

(i) The following select and ultimate mortality table with a 3-year select period:

[math]x[/math]	[math]q_{[x]}[/math]	[math]q_{[x]+1}[/math]	[math]q_{[x]+2}[/math]	[math]q_{x+3}[/math]	[math]x+3[/math]
65	0.08	0.10	0.12	0.14	68
66	0.09	0.11	0.13	0.15	69
67	0.10	0.12	0.14	0.16	70
68	0.11	0.13	0.15	0.17	71
69	0.12	0.14	0.16	0.18	72

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

(iii) The death benefit is payable at the end of the year of death Calculate the actuarial present value of this insurance.

• 260
• 290
• 350
• 370
• 410

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

Answer: C

[[math]] \begin{aligned} { }_{2 \mid 2} A_{65}= & \underbrace{v^{3}}_{\text {payment year } 3} \underbrace{p_{[65]}}_{\text {Lives } 2 \text { years }} \times \underbrace{q_{[65]+2}}_{\text {Die year } 3} \\ & +\underbrace{v^{4}}_{\text {payment year } 4} \underbrace{3 p_{[65]}}_{\text {Lives 3 years }} \times \underbrace{q_{65+3}}_{\text {Die year 4 }} \\ = & \left(\frac{1}{1.04}\right)^{3}(0.92)(0.9)(0.12) \\ & +\left(\frac{1}{1.04}\right)^{4}(0.92)(0.9)(0.88)(0.14) \\ = & 0.088+0.087=0.176 \end{aligned} [[/math]]

The actuarial present value of this insurance is therefore [math]2000 \times 0.176=352[/math].