An insurer issues a 30-year term insurance policy on (40). You are given:

i) Net premiums of 750 are payable quarterly

ii) The death benefit, payable at the end of the quarter of death, is [math]1,000,000[/math]

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

iv) [math]10.5^{V}=10,000[/math] v) [math]q_{50}=0.01[/math]

vi) Mortality is uniformly distributed over each year of age

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

Calculate [math]{ }_{10.75} V[/math].

• 8,360
• 8,370
• 8,380
• 8,390
• 8,400

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

Answer: D

[[math]] \begin{aligned} & \left({ }_{10.5} V+P\right)(1+i)^{0.25}=1,000,000 \times{ }_{0.25} q_{50.5}+{ }_{0.25} p_{50.5} \times{ }_{50.75} V \\ & (10,000+750)(1+0.05)^{0.25}=1,000,000 \times\left(1-\frac{(1-0.75 \times 0.01)}{(1-0.5 \times 0.01)}\right)+\left(\frac{(1-0.75 \times 0.01)}{(1-0.5 \times 0.01)}\right) \times{ }_{50.75} V \\ & { }_{50.75} V=8,390 \end{aligned} [[/math]]

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