A special fully discrete 2 -year endowment insurance with a maturity value of 2000 is issued to (x). The death benefit is 2000 plus the net premium policy value at the end of the year of death. For year 2, the net premium policy value is the net premium policy value just before the maturity benefit is paid.

You are given:

(i) [math]\quad i=0.10[/math]

(ii) [math]\quad q_{x}=0.150[/math] and [math]q_{x+1}=0.165[/math]

Calculate the level annual net premium.

• 1070
• 1110
• 1150
• 1190
• 1230

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

Answer: C

[math]{ }_{0} V=0[/math]

[math]{ }_{2} V=2000[/math]

Year 1: [math]\quad\left({ }_{0} V+P\right)(1+i)=q_{x}\left(2000+{ }_{1} V\right)+p_{x 1} V[/math]

[[math]] P(1.1)=0.15\left(2000+{ }_{1} V\right)+0.85\left({ }_{1} V\right) [[/math]]

[[math]] 1.1 P-300={ }_{1} V [[/math]]

Year 2: [math]\quad\left({ }_{1} V+P\right)(1+i)=q_{x+1}\left(2000+{ }_{2} V\right)+p_{x+1}(2000)[/math]

[[math]] \begin{aligned} & (1.1 P-300+P)(1.1)=0.165(2000+2000)+0.835(2000) \\ & 2.31 P-330=2330 \\ & P=\frac{2330+330}{2.31}=1152 \end{aligned} [[/math]]

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