For a special semi-continuous 20-year endowment insurance on (70), you are given:

i) The death benefit is 1000

ii) The endowment benefit is 500

iii) Mortality follows the Standard Ultimate Life Table

iv) Deaths are uniformly distributed over each year of age

v) The annual net premium is 35.26

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

Calculate the net premium policy value at the end of year 10 .

• 268
• 272
• 276
• 280
• 284

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

Answer: C

[math]A_{80: 10 \mid}^{1}=A_{80: \overline{10}}-{ }_{10} E_{80}=0.67674-0.33952=0.33722[/math]

[math]\bar{A}_{80: 10 \mathrm{l}}^{1}=\frac{0.05}{\ln (1.05)} 0.33722=0.34559[/math]

EPV future benefits [math]=1000(0.34559)+500(0.33952)=515.35[/math]

EPV future net premiums [math]=\ddot{a}_{80: 10} P=6.7885(35.26)=239.36[/math]

Policy value [math]=515.36-239.36=276[/math]

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