SOA Exam ALTAM Fall 2024, Question 3

You are the actuary for a small defined benefit pension plan. You are given the following information.

(i) The plan is a career average earnings plan with an accrual rate of 2%.

(ii) The retirement benefit for each plan member is a whole life annuity payable monthly in advance from age 65.

(iii) On the death of a plan member after retirement a 75% reversionary benefit is payable to their surviving spouse for the remainder of the spouse's lifetime.

(iv) The current membership information, as of December 31, 2023, is given in the following table.

Employee	Exact Age	Years of Service	Accrued Benefits	2023 Salary
Active Members
A	25	2	1,100	30,000
B	45	10	7,400	40,000
C	45	15	10,500	40,000
D	55	25	20,000	50,000
E	55	30	25,000	50,000
Retired Member
F	70		25,000

The valuation assumptions are as follows:

(i) There are no exits before age 65.

(ii) Each member, including the retired member, is assumed to have a spouse of the same age as the member.

(iii) Post-retirement mortality for members and their spouses follows the Standard Ultimate Mortality Model.

(iv) Members and their spouses are assumed to have independent future lifetimes.

(v) All salaries increased by 2% on January 1, 2024.

(vi) Monthly annuity values are determined using Woolhouse's 2-term approximation.

(vii) The Traditional Unit Credit funding method is used for valuing the accrued benifits (as printed) and for determining the Normal Contribution.

(viii) $i = 0.05$

Part a (1 point)

Show that $\ddot{a}^{(12)}_{65|65} = 1.9$ to the nearest 0.1. You should calculate the value to the nearest 0.0001.

Part b (3 points)

Show that the Actuarial Liability, as of January 1, 2024, is 827,000 to the nearest 1000. You should calculate the value to the nearest 1.

Part c (2 points)

Calculate the Normal Contribution for 2024 as a percentage of the total active members' salaries in 2024.

Part d (3 points)

Following your valuation, the Plan Sponsor decides to improve benefits for active members as follows. The annual retirement benefit will be equal to

2% of 2023 salary per year of service, for service prior to January 1, 2024 plus
2% of all earnings after January 1, 2024.

(i) Calculate the increase in the Actuarial Liability, as of the valuation date January 1, 2024.

(ii) State with reasons whether the Normal Contribution would increase, decrease, or stay the same.

Part e (1 point)

Assume that the marginal post-retirement mortality of members and their spouses is unchanged, but that there is a common shock risk while both are alive. State with reasons whether the Actuarial Liability for the pension plan would increase, decrease or stay the same.

Answer this question and see the worked solution