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AAdmin
Jan 18'24

Exercise

For an annual whole life annuity-due of 1 with a 5 -year certain period on (55), you are given:

(i) Mortality follows the Standard Ultimate Life Table

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

Calculate the probability that the sum of the undiscounted payments actually made under this annuity will exceed the expected present value, at issue, of the annuity.

  • 0.88
  • 0.90
  • 0.92
  • 0.94
  • 0.96

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

AAdmin
Jan 19'24

Answer: C

The expected present value is:

[[math]] \ddot{a}_{5}+{ }_{5} E_{55} \ddot{a}_{60}=4.54595+0.77382 \times 14.9041=16.07904 [[/math]]


The probability that the sum of the undiscounted payments will exceed the expected present value is the probability that at least 17 payments will be made. This will occur if (55) survives to age 71 . The probability is therefore:

[math]{ }_{16} p_{55}=\frac{l_{71}}{l_{55}}=\frac{90,134.0}{97,846.2}=0.92118[/math]

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