Actuarial Notes

SOA Exam ALTAM Sample Question 48

Study guide: Exam ALTAM

B is the sole member of a final average salary pension plan which is being valued on January 1, 2022. At the valuation date B is 63 years old and has 12 years of service. B's salary at the valuation date is 72,100. B's salary in 2021 was 70,000.

The pension plan benefits are as follows:

  • The annual benefit is 1.6% of final average salary times years of service.
  • Final average salary is the salary earned during the 12 months preceding retirement.
  • Benefits are reduced by 0.4% for each month retirement precedes age 65.

The valuation at January 1, 2022 uses the projected unit cost (as printed) (PUC) method with the following assumptions:

  • (i) Salaries increase by 3% each January 1.
  • (ii) Retirements before 65 occur in the middle of the year of age.
  • (iii) Decrements before retirement follow the Standard Service Table.
  • (iv) i = 0.05
  • (v) Under post-retirement mortality \ddot{a}_{63.5}^{(12)} = 13.5139.

Part a (3 points)

  • (i) Show that if B retires on July 1, 2022, the expected present value of B's retirement benefits at that time would be 178,200 to the nearest 50. You should calculate the value to the nearest 1.
  • (ii) Show that the expected cost of mid-year retirement decrements in 2022 is 16,500 to the nearest 50. You should calculate the value to the nearest 1.

Part b (2 points)

You are also given that the projected accrued liability for B's retirement benefits on January 1, 2023, assuming that B is employed then, is 191,309.

  • (i) Show that the actuarial liability of B's retirement benefits at January 1, 2022 is 167,150 to the nearest 10. You should calculate the value to the nearest 1.
  • (ii) Calculate the normal cost for B's retirement benefits as of January 1, 2022.

Part c (2 points)

The pension trustees are considering changing to the traditional unit credit (TUC) funding method.

  • (i) State with reasons whether the actuarial liability as of January 1, 2022, under the TUC funding method will be bigger or smaller than the actuarial liability as of January 1, 2022 under the PUC funding method.
  • (ii) State with reasons whether the normal cost for 2022 under the TUC funding method will be bigger or smaller than the normal cost for 2022 under the PUC funding method.

Part d (2 points)

You are given the following additional information

  • The plan is 100% funded at January 1 2022, under the PUC funding method.
  • B retires on January 1, 2023.
  • The earned interest rate during 2022 was 5.1%.
  • The valuation as of January 1, 2023 uses the PUC funding method, based on the same assumptions as the previous year.
  • The normal cost for 2022 was paid in full on January 1, 2022.
  • \ddot{a}_{64}^{(12)} = 13.3735.

Calculate the gain or loss to the pension plan during 2022.

(This is Question 5 from the Spring 2022 Written Answer exam.)

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