For a special fully discrete 3 -year term insurance on (75), you are given:

(i) The death benefit during the first two years is the sum of the net premiums paid without interest

(ii) The death benefit in the third year is 10,000

(iii)

[math]x[/math]	[math]p_{x}[/math]
75	0.90
76	0.88
77	0.85

(iv) [math]\quad i=0.04[/math]

Calculate the annual net premium.

• 449
• 459
• 469
• 479
• 489

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

Answer: B

[math]\mathrm{EPV}([/math] premiums [math])=\mathrm{EPV}([/math] benefits [math])[/math]

[math]P\left(1+v p_{x}+v_{2}^{2} p_{x}\right)=P\left(v q_{x}+2 v^{2} p_{x} q_{x+1}\right)+10000\left(v^{3}{ }_{2} p_{x} q_{x+2}\right)[/math]

[math]P\left(1+\frac{0.9}{1.04}+\frac{0.9 \times 0.88}{1.04^{2}}\right)=P\left(\frac{0.1}{1.04}+\frac{2 \times 0.9 \times 0.12}{1.04^{2}}\right)+10000\left(\frac{0.9 \times 0.88 \times 0.15}{1.04^{3}}\right)[/math]

[math]2.5976 P=0.29588 P+1056.13[/math]

[math]P=459[/math]

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