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.
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.