SOA Exam ALTAM Spring 2026, Question 4

Study guide: Exam ALTAM

A company has a hybrid pension plan combining a Final Average Salary Defined Benefit (DB) plan with a Defined Contribution (DC) top-up.

You are given the following plan information and valuation assumptions for a valuation at 1/1/2026.

(i) The DB accrual rate is 1.6%.

(ii) Pensions are paid monthly in advance.

(iii) Final average salary is defined as the average salary paid in the three years before retirement.

(iv) Employees have the option to contribute to a separate DC account throughout their working lives.

(v) Salaries increase at the end of each year by 2%.

(vi) Retirements before age 65 are assumed to occur midway through the year of age.

(vii) $i = 0.045$

(viii) $\ddot{a}_{64.5}^{(12)} = 13.882$ and $\ddot{a}_{65}^{(12)} = 13.723$ at $i = 0.045$

(ix) The Projected Unit Credit method is used for valuation and funding.

The following is an excerpt from the valuation service table. There are no retirements before age 64.

$x$	$l_x$	$r_x$
23	73,804	0
24	66,696	0
$\vdots$	$\vdots$	$\vdots$
63	$\vdots$	0
64	$\vdots$	865
65 exact	8,203	8,203

A new employee, Jeff, joins the plan on the valuation date at age 23, with a starting salary of 80,000.

Part a (4 points)

(i) (1 point) Show that the projected final average salary (FAS) at age 64.5 is 175,000 to the nearest 1000. You should calculate the value to the nearest 1.

(ii) (1 point) Show that the projected final average salary (FAS) at age 65 is 177,000 to the nearest 1000. You should calculate the value to the nearest 1.

(iii) (2 points) Calculate the normal contribution rate for Jeff's DB plan retirement benefits at the valuation date.

Part b (2 points)

Show that Jeff's projected replacement rate from the DB plan if he retires at age 65 is 0.66 to the nearest 0.01. You should calculate the value to the nearest 0.001.

Part c (2.5 points)

Jeff plans to contribute 1% of his annual salary to the DC fund, and to retire at age 65. You are given the following assumptions:

(i) Jeff's contributions are made at each year end, with the last payment at age 64.

(ii) The DC account earns 8% interest per year.

(iii) At retirement, Jeff plans to annuitize the DC account value. The annuitization assumptions are the same as for the DB valuation.

Calculate Jeff's total projected replacement rate at age 65.

Part d (1.5 points)

Describe one advantage and one disadvantage of this hybrid plan from the employee's perspective, compared with a DB plan with a higher accrual rate and an annual employee contribution of 1% of salary.

Answer this question and see the worked solution

SOA Exam ALTAM Spring 2026, Question 4

Part a (4 points)

Part b (2 points)

Part c (2.5 points)

Part d (1.5 points)

Concepts tested

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