(50) just had surgery to remove a life-threatening tumor and is purchasing a 3 -year term life insurance policy with a face amount of 100,000. You are given:

i) The probability of (50) surviving the first year after surgery is [math]55 \%[/math] of the Standard Ultimate Life Table survival probability

ii) If (50) survives the first year, subsequent mortality follows the Standard Ultimate Life Table

iii) Benefits are payable at the end of the year of death

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

Calculate the expected present value of the death benefit.

• 43,000
• 44,000
• 45,000
• 46,000
• 47,000

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

Answer: A

Probability (50) survives one year under Standard Ultimate Life Table [math]=1-0.001209=[/math] 0.998791

Probability (50) survives one year following surgery [math]=0.55 \times 0.998791=0.5493=p_{50}[/math]

[[math]] \begin{aligned} q_{50}= & 1-p_{50}=0.4507 \\ A_{50: 31} & =q_{50}\left(\frac{1}{1.05}\right)+p_{50} q_{51}\left(\frac{1}{1.05^{2}}\right)+p_{50} p_{51} q_{52}\left(\frac{1}{1.05^{3}}\right) \\ & =(0.4507)\left(\frac{1}{1.05}\right)+(0.5493)(0.001331)\left(\frac{1}{1.05^{2}}\right)+(0.5493)(0.99867)(0.001469)\left(\frac{1}{1.05^{3}}\right) \\ & =0.4306 \end{aligned} [[/math]]

Therefore, answer [math]=100,000 \times 0.4306 \approx 43,000[/math]

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