For a special fully discrete 15 -year endowment insurance on (75), you are given:

(i) The death benefit is 1000

(ii) The endowment benefit is the sum of the net premiums paid without interest

(iii) [math]\quad d=0.04[/math]

(iv) [math]\quad A_{75: 15}=0.70[/math]

(v) [math]\quad A_{75: 15 \mid}=0.11[/math]

Calculate the annual net premium.

• 80
• 90
• 100
• 110
• 120

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

Answer: C

[math]P \times \ddot{a}_{75: 15 \mid}=1000\left(A_{75: 15 \mid}^{1}+15 \times P \times A_{75: 15}\right) \rightarrow P=\frac{1000 A_{75: 15}^{1}}{\ddot{a}_{75: 15 \mid}-15 \times A_{75: 15}}[/math]

[math]A_{75: 15}^{1}=A_{75: 15}-A_{75: 15}=0.7-0.11=0.59[/math]

[math]\ddot{a}_{75: 15 \mid}=\frac{1-A_{75: 15 \mid}}{d}=(1-0.7) / 0.04=7.5[/math]

So [math]P=\frac{590}{7.5-15(0.11)}=100.85[/math]

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