For a DB plan, calculate and interpret the actuarial accrued liability and the normal cost for benefits payable on age retirement or early exit using the projected unit credit (PUC) and traditional unit credit (TUC) valuation methods.

You value a member who just earned one more year of service. How much liability hit the books this year, and how much was already there? Your answer depends entirely on whether you freeze salary at today's level or project it to assumed exit.

Before mechanics, anchor what plan you are valuing. A Defined Benefit (DB) plan promises a formula-driven pension, so the sponsor bears investment and longevity risk. A Defined Contribution (DC) plan instead credits each employee's notional account with a fixed percentage of salary (often 5% to 10%), and the participant bears all investment risk. Retirement income under a DC plan equals the accumulated contributions plus actual investment returns, converted to an annuity or drawn down ad-hoc.

KEY: Only DB plans have an AAL and NC under PUC/TUC. DC plans have no actuarial liability beyond the unpaid current-period contribution. The "balance" is the sum of contributions plus investment returns.

Everything that follows assumes DB.

A DB benefit formula typically reads

Common mistakes

• Projecting salary to retirement for an early-exit benefit. Under PUC, salary projects to the assumed DECREMENT age. A withdrawal at 55 uses $S_{55}$, not $S_{65}$. Wrong projection inflates AAL by an extra $(1+s{)}^{R-w}$ factor.
• Mixing past and projected service. AAL uses past service $t$ only. NC uses exactly one year. Plugging total expected service $(R-y)$ gives the PV of TOTAL future benefits, not AAL.
• Forgetting decrement probabilities. AAL must be weighted by ${}_{R-x}{p}_x^{(T)}$, the probability of persisting in service to the decrement age. Omitting it overstates the liability.

Bottom line

• TUC values the accrued benefit at CURRENT salary $S_x$; PUC projects to the decrement-age salary. The two coincide when the salary scale is flat (career-average).
• AAL is the PV of benefits attributed to PAST service (uses $t$); NC is the PV attributed to ONE additional service year.
• For final-pay plans with positive salary scale, PUC AAL > TUC AAL; with a flat scale ${\text{AAL}}^{\text{PUC}}={\text{AAL}}^{\text{TUC}}\cdot (1+s{)}^{R-x}$, and the gap widens with growth and time to exit.
• NC progression: TUC normal cost back-loads steeply with age; PUC normal cost grows more smoothly.

Exam shortcut

For a flat salary-scale assumption, compute TUC first, then multiply AAL and NC by $(1+s{)}^{R-x}$ to get PUC. Cuts work in half on multi-part comparison questions. DECISION: Question says "current salary basis" or "accrued benefit" alone, use TUC. Question says "projected salary" or "salary at retirement", use PUC. Question silent but provides a salary scale, assume PUC (the funded-status default).

The full lesson (about 6,202 words, 41 min read) adds 5 worked examples, all 13 common mistakes, a self-check, free in the app.

Learning objectives

• 5e

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