For a special fully discrete 2 -year term insurance on [math](x)[/math], you are given:

(i) [math]q_{x}=0.01[/math]

(ii) [math]\quad q_{x+1}=0.02[/math]

(iii) [math]\quad i=0.05[/math]

(iv) The death benefit in the first year is 100,000

(v) Both the benefits and premiums increase by [math]1 \%[/math] in the second year Calculate the annual net premium in the first year.

• 1410
• 1417
• 1424
• 1431
• 1438

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

Answer: B

Let [math]P[/math] be the net premium for year 1 .

Then:

[[math]] \begin{aligned} & P+1.01 P v p_{x}=100,000 v q_{x}+(1.01)(100,000) v^{2} p_{x} q_{x+1} \\ & P\left[1+\frac{1.01}{1.05} 0.99\right]=100,000\left(\frac{0.01}{1.05}+\frac{(1.01)(0.99)(0.02)}{(1.05)^{2}}\right) \Rightarrow P=1416.93 \end{aligned} [[/math]]

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