Unit Credit Methods Overview

Unit credit methods attribute pension benefits to individual years of service. Each year of employment earns a specific increment of retirement benefit, and the actuarial liability reflects the accumulated value of all past increments. The two variants, traditional unit credit (TUC) and projected unit credit (PUC), differ in how they measure each year's benefit increment. Understanding the differences between these methods and the entry age normal method is essential for Exam LTAM.

Traditional Unit Credit (TUC)

Under the TUC method, the benefit attributed to each year of service is based on current salary at the time of the valuation. If the benefit formula is k% times years of service times final average salary, the TUC accrued benefit at age x uses the current salary (or current final average salary) rather than the projected future salary. The actuarial liability is AL = B_accrued * v^(r-x) * (r-x)_p_x^(tau) * a-ddot_r, where B_accrued = k% * n * current_FAS, n is past years of service, v^(r-x) discounts from retirement, (r-x)_p_x^(tau) is the multiple decrement survival probability to retirement, and a-ddot_r is the life annuity value at retirement age.

The TUC normal cost for the current year equals the present value of one additional year of benefit accrual at current salary. As the employee ages and receives salary increases, the normal cost grows in two ways: the salary itself is higher (so each year's increment is larger) and the discounting period to retirement is shorter (so the present value factor is larger). This creates an accelerating pattern of normal costs over the employee's career.

Projected Unit Credit (PUC)

The PUC method uses projected final salary rather than current salary to measure the accrued benefit. The PUC actuarial liability at age x is AL = k% * n * projected_FAS * v^(r-x) * (r-x)_p_x^(tau) * a-ddot_r. Because projected final salary exceeds current salary, the PUC liability is always larger than the TUC liability for the same employee at the same valuation date.

The PUC normal cost equals the present value of one year of benefit accrual at projected final salary: NC = k% * projected_FAS * v^(r-x) * (r-x)_p_x^(tau) * a-ddot_r. Notice that the salary used in the normal cost calculation does not change from year to year (since the projected final salary is the same regardless of when the accrual occurs). The normal cost under PUC still increases each year because the discounting period shortens and the survival probability changes, but the increase is more gradual than under TUC.

For example, consider an employee age 45 who entered at age 30, will retire at age 65, with a benefit formula of 2% per year of service times final average salary. Current salary is 70,000 and projected FAS is 120,000. Under TUC, the accrued benefit is 0.02 * 15 * 70,000 = 21,000 per year. Under PUC, the accrued benefit is 0.02 * 15 * 120,000 = 36,000 per year. The PUC liability is significantly larger.

Entry Age Normal (EAN) Method

The entry age normal method takes a fundamentally different approach. Rather than attributing specific benefit increments to specific years, EAN determines a level contribution rate that, if applied from the employee's entry age e to retirement age r, would exactly fund the total projected benefit. The normal cost rate P satisfies P * a-ddot_{e:r-e}^(tau) = PVFB_e, where PVFB_e is the present value of future benefits computed at entry age and a-ddot_{e:r-e}^(tau) is a salary-weighted annuity from entry to retirement in the multiple decrement environment.

The EAN actuarial liability at age x can be computed in two equivalent ways. The prospective formula is AL = PVFB_x minus PVFNC_x (present value of future benefits minus present value of future normal costs). The retrospective formula accumulates past normal costs with interest and survivorship. Both approaches yield the same result and Exam LTAM may ask for either computation.

Comparing the Three Methods

The three methods produce different normal cost patterns and different actuarial liabilities at any given valuation date. TUC produces the lowest early-career normal cost but the highest late-career normal cost, creating a steeply increasing contribution pattern. PUC produces a more moderate increase. EAN produces a level normal cost (as a percentage of salary), giving the most stable year-to-year contribution.

The total cost over the employee's career is the same under all three methods (in present value terms at entry age), because all three methods fund the same projected benefit. The differences lie entirely in the timing of contributions. EAN front-loads contributions relative to TUC and PUC, which means the EAN actuarial liability is typically larger than the PUC liability in the early and middle career years, and smaller near retirement.

Gain and Loss Analysis

Actuarial gains and losses arise when actual experience differs from the assumptions used in the valuation. If actual salary increases exceed the assumed salary scale, the projected benefit increases and an actuarial loss occurs. If fewer employees terminate than assumed, the survival probability to retirement increases, also creating a loss. Gains arise from favorable experience (lower than expected salary growth, higher than expected turnover, or investment returns exceeding the assumed rate).

The gain or loss for a given year can be computed as the difference between the expected and actual actuarial liability. The expected AL is the prior year's AL plus normal cost plus interest, minus expected benefit payments. The actual AL is computed directly from updated census data and assumptions. The difference reveals the net impact of experience deviations.

Common Pitfalls

Students often confuse TUC and PUC by using the wrong salary figure. Remember: TUC uses current salary, PUC uses projected final salary. In exam problems, check carefully which method is specified and which salary figure is provided. Another common error is computing the EAN normal cost rate using the wrong annuity denominator. The denominator must be a salary-weighted, survival-adjusted annuity from entry to retirement, not a simple annuity-due.

Also watch for problems that give you the actuarial liability under one method and ask you to compute it under another. You cannot simply convert between methods using a ratio; you must set up each method's calculation from the underlying benefit formula, salary projections, and survival probabilities.

Study Tips

Exam LTAM frequently asks you to compute normal costs and actuarial liabilities under all three methods for the same employee, then compare the results. Practice setting up the full calculation for each method from a common set of inputs (benefit formula, salary scale, entry age, current age, retirement age, interest rate, and multiple decrement table). Organize your work in a table showing the benefit accrual, present value factors, and final results for each method side by side. This makes it easy to verify that TUC gives the smallest AL (when projected salary exceeds current salary), PUC gives a larger AL, and EAN gives the largest AL in early career years.

Pension Funding Methods: Entry Age Normal and Unit Credit