SOA Exam ALTAM Spring 2023, Question 5
Study guide: Exam ALTAM
A company has a defined contribution (DC) pension plan with the following features:
(i) The company matches the employee's contributions to their DC fund, up to 4% of the employee's salary. The employee may contribute more than this, but these additional contributions are not matched.
(ii) The employee's salary is paid at the end of each month; employee and employer contributions to the fund are made at this time.
(iii) The investment returns on the fund are i^{(12)} = 0.06.
You are given the following information regarding an employee.
(i) The employee entered the plan at age 25.
(ii) Their starting salary was 60,000 per year.
(iii) The employee is currently age 45.
(iv) The employee has received annual pay increases of 3% at the start of each subsequent year of employment.
(v) The employee has contributed 7% of their salary to their DC fund since entering the plan.
Part a (3 points)
Show that the accumulated amount in the DC fund (including the employee and employer contributions which have just been paid) is 322,000, to the nearest 1000. You should calculate the value to the nearest 50.
Part b (2 points)
The employee is reviewing their retirement preparation, based on the following assumptions.
(i) They will continue to receive annual salary increases of 3%.
(ii) They will retire at age 65.
(iii) They will receive a benefit of 18,000 at the start of each year from their government's retirement program, starting at age 65.
(iv) At age 65 they will use the accumulated amount in their DC fund to purchase a whole life annuity due, payable annually.
(v) The individual is targeting a replacement ratio of 65%, including both the government and annuity benefits.
Show that the yearly annuity payment required to meet the target replacement ratio is 105,500 to the nearest 100. You should calculate the value to the nearest 1.
Part c (3 points)
You are given that future investment returns will be i^{(12)} = 0.06, and that \ddot{a}_{65} = 13.600.
Calculate the level contribution rate needed by the employee over the next 20 years to accumulate sufficient funds to purchase this annuity,
Part d (1 point)
Suppose that the employee wishes to use the fund to purchase a life-and-10-year-guaranteed annuity due instead of a whole life annuity due. State with reasons whether their replacement ratio will increase, decrease, or stay the same.
Answer this question and see the worked solution