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Actuarial Vocabulary

Pension & Actuarial Glossary

Authoritative definitions and formulas for the core mathematical concepts used in defined benefit pension valuations.

Net Present Value (NPV)

NPV = Σ [ C_t / (1 + r)^t ]

The current total value of a future stream of pension payments, discounted by a specific expected rate of return.

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Discount Rate

PV = FV / (1 + r)^n

The interest rate used in actuarial discounting to calculate the present value of future pension cash flows.

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Commuted Value

Commuted Value = Actuarial PV of Accrued Benefit

The lump-sum dollar equivalent that a pension plan sponsor is legally required to pay to settle an individual’s pension obligation.

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Actuarial Present Value

APV = Σ [ C_t × p(t) / (1 + r)^t ]

A present value calculation that factors in both compound interest discounting and conditional survival probabilities.

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Annuity Factor

a_n|r = [ 1 - (1 + r)^(-n) ] / r

The present value of a $1 per year annuity over a specified retirement horizon or lifetime.

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Mortality Table (Life Table)

q_x = d_x / l_x

A statistical table showing the probability of a person of a given age dying before their next birthday.

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Breakeven Age

Cumulative Payouts(Age_B) ≥ Lump Sum Compounded(Age_B)

The exact age at which the cumulative monthly pension payments equal or surpass the value of taking a lump sum buyout.

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Cost-of-Living Adjustment (COLA)

P_t = P_0 × (1 + g)^t

An annual periodic percentage increase applied to pension payments to protect purchasing power against inflation.

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