A special fully discrete 10 -payment 10 -year deferred whole life annuity-due on (55) of 1000 per year provides for a return of premiums without interest in the event of death within the first 10 years. You are given:

(i) Annual net premiums are level

(ii) Mortality follows the Standard Ultimate Life Table

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

(iv) [math]\quad(I A)_{55: 10}^{1}=0.14743[/math]

Calculate [math]{ }_{9} V[/math], the net premium policy value at the end of year 9 .

• 11,540
• 11,650
• 11,760
• 11,870
• 11,980

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

Answer: D

[math]\pi=\frac{1000{ }_{10} \mid \ddot{a}_{55}}{\ddot{a}_{55: \overline{10}}-(I A)_{55: \overline{10}}^{1}}=\frac{1000(0.59342)(13.5498)}{8.0192-0.14743}=1021.46[/math]

[math]{ }_{9} V=1000 \quad{ }_{1} \mid \ddot{a}_{64}+10 \pi A_{64: 1}^{1}-\pi \ddot{a}_{64: 1}[/math]

[math]=1000 \frac{1}{1.05}\left(\frac{94,579.7}{95,082.5}\right) 13.5498+10(1021.46) \frac{1}{1.05}(0.005288)-1021.46[/math]

[math]=11,866[/math]

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