Revision as of 22:48, 18 January 2024 by Admin (Created page with "For a life annuity-due issued to (55), you are given: i) The annuity pays an annual benefit of <math>X</math> through age 64 ii) Beginning at age 65 , the annuity pays <math>75 \%</math> of <math>X</math> iii) The present value of this annuity is 250,000 iv) Mortality follows the Standard Ultimate Life Table v) <math>\quad i=0.05</math> Calculate <math>X</math>. <ul class="mw-excansopts"><li> 17,400</li><li> 17,500</li><li> 17,600</li><li> 17,700</li><li> 17,800</l...")
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AAdmin
Jan 18'24

Exercise

For a life annuity-due issued to (55), you are given:

i) The annuity pays an annual benefit of [math]X[/math] through age 64

ii) Beginning at age 65 , the annuity pays [math]75 \%[/math] of [math]X[/math]

iii) The present value of this annuity is 250,000

iv) Mortality follows the Standard Ultimate Life Table v) [math]\quad i=0.05[/math]

Calculate [math]X[/math].

  • 17,400
  • 17,500
  • 17,600
  • 17,700
  • 17,800

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

AAdmin
Jan 19'24

Answer: E

Any of these ways of viewing the benefit structure would be fine; all give the same answer:

(i) A temporary life annuity-due of [math]X[/math] plus a deferred life annuity-due of [math]0.75 X[/math].

(ii) A whole life annuity-due of [math]0.75 \mathrm{X}[/math] plus a temporary deferred life annuity-due of [math]0.25 \mathrm{X}[/math]

(iii) A whole life annuity-due of [math]X[/math] minus a deferred life annuity-due of [math]0.25 X[/math]

This solution views it the first way.

[math]X \ddot{a}_{55: 10}+0.75 X \ddot{a}_{65}{ }_{10} E_{55}=8.0192 X+(0.75 X)(0.59342)(13.5498)=14.05 X=250,000[/math]

[math]\Rightarrow X=17,794[/math]

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

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