Free SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) Pension Plans and Retirement Benefits Practice Questions
Pension mathematics on SOA Exam ALTAM covers defined benefit plan calculations, replacement ratios, actuarial funding methods (entry age normal, projected unit credit), and cost allocation techniques.
Sample Questions
Question 1
Easy
Which of the following statements about the replacement ratio in retirement planning is most accurate?
Solution
D is correct.
Financial planning guidelines commonly target a replacement ratio of approximately 70%–85% because retirees typically face: (1) lower income taxes (reduced income, no payroll taxes); (2) elimination of work-related expenses (commuting, clothing, lunches); and (3) no further need to save for retirement. These factors mean a retiree needs less gross income than during their working years to maintain a similar standard of living.
Financial planning guidelines commonly target a replacement ratio of approximately 70%–85% because retirees typically face: (1) lower income taxes (reduced income, no payroll taxes); (2) elimination of work-related expenses (commuting, clothing, lunches); and (3) no further need to save for retirement. These factors mean a retiree needs less gross income than during their working years to maintain a similar standard of living.
Question 2
Medium
A pension plan actuary is comparing three cost methods for the same participant. Which of the following orderings of the actuarial accrued liability (AAL) at mid-career is correct?
Solution
E is correct.
For a final average pay plan where salaries are expected to grow:
- **Unit Credit (UC):** the accrued benefit uses current salary only (not projected), so the AAL is the present value of a benefit based on today's salary — the lowest of the three.
- **Entry Age Normal (EAN):** costs are spread as a level amount or percentage from entry age to retirement based on the projected final benefit; the AAL at mid-career reflects accumulated level contributions, producing a moderate AAL.
- **Projected Unit Credit (PUC):** the accrued benefit uses projected final salary (the full projected benefit prorated by service to date), so the AAL at mid-career is the present value of a benefit reflecting projected salary growth — the highest of the three.
Therefore: .
For a final average pay plan where salaries are expected to grow:
- **Unit Credit (UC):** the accrued benefit uses current salary only (not projected), so the AAL is the present value of a benefit based on today's salary — the lowest of the three.
- **Entry Age Normal (EAN):** costs are spread as a level amount or percentage from entry age to retirement based on the projected final benefit; the AAL at mid-career reflects accumulated level contributions, producing a moderate AAL.
- **Projected Unit Credit (PUC):** the accrued benefit uses projected final salary (the full projected benefit prorated by service to date), so the AAL at mid-career is the present value of a benefit reflecting projected salary growth — the highest of the three.
Therefore: .
Question 3
Hard
An actuary must find the annual contribution rate (as a fraction of current salary) for a DC plan with a target replacement ratio of 70%. Salary grows at 3% per year, the investment return is 7%, there are 30 years to retirement, and the annuity factor at retirement is 13. Contributions are made at the end of each year. Which expression gives ?
Solution
C is correct.
Let be the current salary. End-of-year contributions are for . The accumulated fund at retirement is: Where . The target fund is . Setting the expressions equal and simplifying:
Let be the current salary. End-of-year contributions are for . The accumulated fund at retirement is: Where . The target fund is . Setting the expressions equal and simplifying: