SOA Exam ALTAM Sample Question 38
Study guide: Exam ALTAM
A company sponsors a defined benefit pension plan. Key attributes of the pension plan are:
- Benefits are payable as a single life annuity, paid at the beginning of each month.
- The annual benefit payable at age 65 is calculated as 2% of the final 3-year average salary up to 100,000 multiplied by years of service, plus 3% of the final 3-year average salary over 100,000 multiplied by years of service. The monthly benefit is the annual benefit divided by 12.
- You are given:
(i) i = 5\%
(ii) A^{(12)}_{65} = 0.470
An individual joined the company on January 1, 2009 at exact age 40. The individual is planning to retire on January 1, 2034 at age 65. The salary for 2014 is 80,000 and the individual receives annual raises of 4% each January 1.
Part a (2 points)
Assuming the individual works until age 65, show that the monthly accrued benefit at age 65 is 8050, to the nearest 10. You should calculate the benefit to the nearest 1.
Part b (1 point)
Calculate the replacement ratio at age 65.
Part c (2 points)
Calculate the expected present value of the benefit at age 65.
Part d (4 points)
In addition to accruing a benefit in the defined benefit plan, the individual will contribute a constant percentage of their annual salary to a defined contribution plan.
You are also given:
(iii) Contributions are made at the start of each year, beginning on January 1, 2014.
(iv) Contributions earn an investment return of 7% per year.
(v) The contribution balance is converted to a monthly life annuity using assumptions (i) and (ii) above.
Calculate the percentage of each year's salary that the individual needs to contribute so that their total replacement ratio is 80% at age 65.
(This is Question 2 from the Fall 2014 Written Answer exam.)
Answer this question and see the worked solution