Actuarial Notes

SOA Exam ALTAM Sample Question 43

Study guide: Exam ALTAM

Person X is a member of a defined benefit pension plan which offers an annual pension of 2% of the final one year's salary for each year of service. The benefit is a whole life annuity-due paid monthly. At the valuation date, 1/1/2020, X is 40 years old with 20 years' service. X's salary during the 12 months prior to the valuation was 110,000.

You are given:

  • (i) All members in service at age 65 retire immediately.
  • (ii) There are no other retirements or withdrawals (other than death).
  • (iii) Mortality follows the Standard Ultimate Life Table.
  • (iv) i = 0.05
  • (v) Salary increases occur annually on 1 January each year.
  • (vi) Salaries are assumed to increase by 3% each year up to and including age 54, and by 2.5% each year from age 55.
  • (vii) Woolhouse's 2-term formula is used for monthly annuity functions.
  • (viii) The benefits are funded using the Projected Unit Credit method.

Part a (3 points)

  • (i) Show that the Actuarial Liability for X's retirement benefits is 323,000 to the nearest 1,000. You should calculate the value to the nearest 1.
  • (ii) Calculate the Normal Contribution rate for X's retirement benefits.

Part b (4 points)

The plan proposes the following enhancement:

  • A reversionary annuity benefit to the member's partner at 50% of the member's pension benefit, or
  • For members who do not have a partner at their retirement dates, the pension would be increased by 5%.

Assume:

  • (i) 90% of members have partners at their retirement dates.

  • (ii) Partners are the same age as the member, for members with partners.

  • (iii) The mortality of members and their partners follows the Standard Ultimate Life Table.

  • (iv) Members and their partners have independent future lifetimes.

  • (i) Calculate the revised Actuarial Liability for X's enhanced retirement benefits (including the partner benefit).

  • (ii) Calculate the revised Normal Contribution rate for X's enhanced retirement benefits.

Part c (1 point)

The plan actuary is concerned that couples may have future lifetimes which are positively correlated. State with reasons whether the expected present value of the reversionary partner benefits would increase, decrease, or stay the same, in this case.

(This is Question 6 from the Spring 2020 Written Answer exam.)

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