A man turns 40 today and wishes to provide supplemental retirement income of 3000 at the beginning of each month starting on his 65th birthday. Starting today, he makes monthly contributions of X to a fund for 25 years. The fund earns an annual nominal interest rate of 8% compounded monthly. On his 65 th birthday, each 1000 of the fund will provide 9.65 of income at the beginning of each month starting immediately and continuing as long as he survives.

Calculate X.

• 324.70
• 326.90
• 328.10
• 355.50
• 450.70

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: A

To receive 3000 per month at age 65 the fund must accumulate to 3,000(1,000/9.65) = 310,880.83. The equation of value is

[[math]] 310,880.83 = X\ddot{s}_{\overline{300}|0.08/12} = 957.36657X \implies 324.72. [[/math]]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.