For a 3-year term insurance of 1000 on (70), you are given:

(i) [math]\quad q_{70+k}^{\text {SULT }}[/math] is the mortality rate from the Standard Ultimate Life Table, for [math]k=0,1,2[/math]

(ii) [math]\quad q_{70+k}[/math] is the mortality rate used to price this insurance, for [math]k=0,1,2[/math]

(iii) [math]\quad q_{70+k}=(0.95)^{k} q_{70+k}^{S U L T}[/math], for [math]k=0,1,2[/math]

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

Calculate the single net premium.

• 29.05
• 29.85
• 30.65
• 31.45
• 32.25

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

Answer: B

Time	Age	[math]q_{x}^{ ext {SULT }}[/math]	Improvement Factor	[math]q_{x}[/math]
0	70	0.010413	[math]100.00 \%[/math]	0.010413
1	71	0.011670	[math]95.00 \%[/math]	0.011087
2	72	0.013081	[math]90.25 \%[/math]	0.011806

[math]v=1 / 1.05=0.952381[/math]

[[math]] \begin{aligned} E P V & =1,000\left[0.010413 v+0.989587(0.011087) v^{2}+0.989587(0.988913)(0.011806) v^{3}\right] \\ & =29.85 \end{aligned} [[/math]]

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