SOA Exam ALTAM Fall 2023, Question 6
Study guide: Exam ALTAM
You are the actuary for a defined benefit pension plan that offers a Final Average Salary (FAS) pension. The final average salary is the average of the earnings in the final two years, and the pension is paid as a whole life annuity due, payable monthly from retirement. The accrual rate is 2%.
You are given the following valuation assumptions:
(i) Decrements are assumed to follow the Standard Service Table up to age 61. All lives in force at age 61 retire immediately.
(ii) All retirements not occurring at exact ages 60 or 61 are assumed to occur at age 60.5.
(iii) i = 0.05
(iv) Under the post-retirement mortality assumptions: \ddot{a}_{60}^{(12)} = 14.441 \quad \ddot{a}_{60.5}^{(12)} = 14.315 \quad \ddot{a}_{61}^{(12)} = 14.186
(v) The valuation date is 12/31/2022.
(vi) There were no salary increases in 2021 or 2022.
(vii) Salaries increased by 10% on 1/1/2023.
(viii) The valuation uses the Traditional Unit Credit funding method.
The plan has two members. Their information at the valuation date is given in the following table:
| Employee | Age | Number of years of service | FAS at valuation |
|---|---|---|---|
| A | 35 | 10 | 60,000 |
| B | 60 | 30 | 100,000 |
Part a (4 points)
(i) Show that the Actuarial Liability for Employee A's retirement benefits is 21,000 to the nearest 1,000. You should calculate the value to the nearest 1.
(ii) You are given that Employee B did not retire at exact age 60. Show that the Actuarial Liability for Employee B's retirement benefits is 810,000 to the nearest 1,000. You should calculate the value to the nearest 1.
Part b (4 points)
(i) (1 point) Calculate the Normal Contribution for Employee A's retirement benefits.
(ii) (2.5 points) Calculate the Normal Contribution for Employee B's retirement benefits.
(iii) (0.5 points) The Aggregate Normal Contribution Rate is the total Normal Contribution divided by the total annual salary rate as of 1/1/2023.
Calculate the Aggregate Normal Contribution Rate for the plan.
Part c (2 points)
A new entrant who is age 35 joins the plan on 12/31/2022.
(i) State with reasons whether the plan's total Actuarial Liability for retirement benefits would increase, decrease, or stay the same.
(ii) State with reasons whether the Aggregate Normal Contribution Rate for retirement benefits would increase, decrease, or stay the same.
Answer this question and see the worked solution
Concepts tested
- Traditional Unit Credit Method
- Defined Benefit Plan
- Actuarial Accrued Liability
- Normal Cost
- Service Table