For a special fully discrete 5 -year deferred 3 -year term insurance of 100,000 on [math](x)[/math] you are given:

(i) There are two premium payments, each equal to [math]P[/math]. The first is paid at the beginning of the first year and the second is paid at the end of the 5 -year deferral period

(ii) The following probabilities:

(iii) [math]{ }_{5} p_{x}=0.95[/math]

(iv) [math]q_{x+5}=0.02, \quad q_{x+6}=0.03, \quad q_{x+7}=0.04[/math]

(v) [math]\quad i=0.06[/math]

Calculate [math]P[/math] using the equivalence principle.

• 3195
• 3345
• 3495
• 3645
• 3895

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

Answer: A

Actuarial present value of insured benefits:

[math]100,000\left[\frac{0.95 \times 0.02}{1.06^{6}}+\frac{0.95 \times 0.98 \times 0.03}{1.06^{7}}+\frac{0.95 \times 0.98 \times 0.97 \times 0.04}{1.06^{8}}\right]=5,463.32[/math]

[math]\Rightarrow P\left(1+\frac{0.95}{1.06^{5}}\right)=5,463.32 \Rightarrow P=3,195.12[/math]

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