Actuarial Notes

SOA Exam ALTAM Sample Question 40

Study guide: Exam ALTAM

On December 31, 2015, an individual, who is age 55, has 25 years of service. The individual's salary in 2015 was 50,000.

The annual accrued benefit as of any date is 1.6% of the three-year final average salary as of that date, multiplied by years of service as of that date. The pension is payable only to retired participants as a monthly single life annuity, with the first payment due at retirement.

The valuation assumptions are as follows:

  • There are no benefits paid upon death.
  • There are no benefits paid upon disability prior to age 60.
  • Exits from employment follow the Standard Service Table, except that all lives surviving in employment to age 61 retire at that time.
  • There are retirements at age 60 that occur at exact age 60 while other decrements at age 60 occur throughout the year after the retirement at exact age 60 and prior to exact age 61. Those that retire or become disabled between exact age 60 and exact age 61 are assumed to retire at exact age 61.
  • After retirement, mortality follows the Standard Ultimate Life Table.
  • Annuities are valued using the 2-term Woolhouse formula.
  • The individual has received a 3% salary increase on January 1 of each year for the last five years.
  • Future salaries are expected to increase by 3% each year on January 1.
  • All contributions are paid on January 1 each year.
  • i = 0.05

Part a (1 point)

A pension plan may be classified as a Defined Contribution plan or a Defined Benefit plan. State which type of plan the individual has and briefly describe the other type of plan.

Part b (3 points)

(i) Show that the actuarial accrued liability for the individual at December 31, 2015 using the Projected Unit Credit (PUC) funding method is 220,000 to the nearest 1000. Calculate the actuarial accrued liability to the nearest 1.

(ii) Calculate the normal cost for 2016 using PUC.

Part c (3 points)

(i) Show that the actuarial accrued liability for the individual at December 31, 2015 using the Traditional Unit Credit (TUC) funding method is 186,000 to the nearest 1000. Calculate the actuarial accrued liability to the nearest 1.

(ii) Calculate the normal cost for 2016 using TUC.

Part d (1 point)

For the individual, the normal cost during 2016 using PUC is less than the normal cost during 2016 using TUC. Explain why this will be true for all employees near retirement.

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