A profile of the investments owned by an agent’s clients follows:

1. 228 own annuities.
2. 220 own mutual funds.
3. 98 own life insurance and mutual funds.
4. 93 own annuities and mutual funds.
5. 16 own annuities, mutual funds, and life insurance.
6. 45 more clients own only life insurance than own only annuities.
7. 290 own only one type of investment (i.e., annuity, mutual fund, or life insurance).

Calculate the agent’s total number of clients.

• 455
• 495
• 496
• 500
• 516

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

Solution: D

Then 290 = 45 + 45 + x + x, thus x = 100.

Also 228 = 100 + y + 16 + 77, thus y = 35.

Total clients = 145 + 82 + 16 + 35 + 100 + 77 + 45 = 500.

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