For a 10-year certain and life annuity-due on (65) with annual payments 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 payments on a non-discounted basis made under the annuity will exceed the expected present value of the annuity at issue.

• 0.826
• 0.836
• 0.846
• 0.856
• 0.866

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

Answer: C

[math]\ddot{a}_{65: \overline{10}}=\ddot{a}_{10 \mid}+{ }_{10} E_{65} \times \ddot{a}_{75}=8.10782+0.55305 \times 10.3178=13.8141[/math]

Assuming payments of 1 (any other payment amount would just cancel, giving the same number of years), 14 payments are needed for the sum of payments to exceed 13.8141. That requires surviving to the start of year 14, thus surviving 13 years.

[math]{ }_{13} p_{65}=\frac{l_{78}}{l_{65}}=\frac{80,006.2}{94,579.7}=0.846[/math]