For a special fully discrete 10 -year deferred whole life insurance of 100 on (50), you are given:

(i) Premiums are payable annually, at the beginning of each year, only during the deferral period

(ii) For deaths during the deferral period, the benefit is equal to the return of all premiums paid, without interest

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

(iv) [math]\quad \ddot{a}_{50}=17.0[/math]

(v) [math]\quad \ddot{a}_{60}=15.0[/math]

(vi) [math]{ }_{10} E_{50}=0.60[/math]

(vii) [math]\quad(I A)_{50: 101}^{1}=0.15[/math]

Calculate the annual net premium for this insurance.

• 1.3
• 1.6
• 1.9
• 2.2
• 2.5

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

Answer: D

Let [math]P[/math] be the premium per 1 of insurance.

[[math]] \begin{aligned} & P \ddot{a}_{50: \overline{10}}=P(I A)_{50: 10}^{1}+{ }_{10} E_{50} A_{60} \\ & \ddot{a}_{50: 10 \mid}=\ddot{a}_{50}-{ }_{10} E_{50} \ddot{a}_{60}=17.0-0.60 \times 15.0=8 \\ & A_{60}=1-d \ddot{a}_{60}=1-\left(\frac{0.05}{1.05}\right) 15=0.285714 \\ & P\left(\ddot{a}_{50: \overline{10}}-(I A)_{50: 10}^{1}\right)={ }_{10} E_{50} A_{60} \\ & P=\frac{10}{\ddot{a}_{50: \overline{10}}-(I A)_{50: 10}^{1}}=\frac{0.6 \times 0.285714}{8-0.15}=0.021838 \\ & 100 P=2.18 \end{aligned} [[/math]]

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