SOA Exam ALTAM Fall 2025, Question 6

Study guide: Exam ALTAM

Lin is a member of a final average salary pension plan. On December 31, 2024, Lin is exactly 50 years old, with 20 years of pensionable service. Lin's salary in 2024 was 100,000.

You are given the following information for a plan funding valuation on January 1, 2025:

The accrual rate is 1.5% per year of service.
Final average salary is defined as the average salary in the two years before retirement.
The benefit on retirement is a pension payable monthly in advance for life. There are no spousal benefits.
Annual salaries are assumed to increase by 3% each year on January 1. Salaries are paid in level installments at the end of each month within each calendar year of employment.
Pension payments are assumed to increase monthly at an annual effective rate of 2%.
The pension plan uses the projected unit credit method to determine pension reserves and funding.
You are given the following valuation assumptions:
- All lives remain in service until retirement (that is, there are no deaths or withdrawals before retirement).
- $i = 0.06$
- At an interest rate of $i^* = \dfrac{1.06}{1.02} - 1$ , $\ddot{a}_{60|i^*}^{(12)} = 16.2437$ and $\ddot{a}_{65|i^*}^{(12)} = 14.5260$

Lin is considering two retirement options.

Option A: Retire at age 60 with an actuarial reduction of 0.3% per month up to age 65.
Option B: Retire at age 65 with no actuarial reduction.

Part a (2 points)

(i) Calculate the amount of the first month's pension payment under Option A.

(ii) Calculate the amount of the first month's pension payment under Option B.

Part b (1 point)

Describe briefly the circumstances that would justify the valuation assumption that there are no pre-retirement exits.

Part c (3 points)

(i) Calculate the actuarial liability assuming Lin will choose Option A.

(ii) Calculate the actuarial liability assuming Lin will choose Option B.

(iii) State with reasons whether the actuarial reduction factor appears to be appropriate.

Part d (2 points)

You are also given:

Lin pays contributions of 8% of her salary at the end of each month. The balance of the cost of her benefits is paid by her employer.
Employer contributions are deposited into the pension plan each month, at the same time as the employee contributions.

(i) Calculate the EPV at the valuation date of Lin's pension contributions in 2025.

(ii) Calculate the employer's net normal contribution rate for Lin's retirement benefits in 2025, after taking Lin's contributions into consideration, assuming Lin will choose Option B.

Part e (2 points)

(i) The plan actuary currently assumes that all plan members choose Option B. Critique this assumption.

(ii) The plan actuary currently assumes that the mortality after age 65 of retirees who chose option A is the same as the mortality of those who chose option B. Critique this assumption.

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