What does the present value of an annuity tell me?

It tells you what a series of future periodic payments is worth in today's dollars, given a chosen discount rate. The PV is always smaller than the sum of the payments because a dollar received next year is worth less than a dollar today — that gap is the time-value of money.

What discount rate should I use?

For low-risk pension buyouts, use the long-term Treasury rate (currently ~4-4.5% on 10-30 year maturities). For corporate annuity offers, use your blended portfolio expected return (5-7%). For structured settlements involving counterparty risk, add a credit spread of 1-3% on top. Higher discount rates produce smaller present values.

Why is a lump sum sometimes better than an annuity?

If you can earn a higher return on the lump sum than the implicit discount rate in the annuity offer, take the lump. Conversely, take the annuity when you value the guaranteed income, want longevity protection (life-contingent payouts), or know you'd spend a lump sum imprudently.

How is annuity PV used for lottery payouts?

State lotteries advertise the 30-year annuitized amount but offer a smaller lump-sum 'cash option' (typically 50-60% of advertised total). The cash option equals the PV of the 30 payments using the lottery commission's discount rate (usually long-term Treasury yields). Powerball and Mega Millions disclose the exact methodology in their official rules.

What's the difference between ordinary annuity and annuity due PV?

Annuity due payments arrive at the BEGINNING of each period instead of the end, so each payment is discounted by one fewer period. PV of an annuity due = PV of ordinary annuity × (1+r). For monthly annuities the gap is small (~0.5%); for annual annuities it can be 5-8%.

Does PV apply to perpetuities too?

Yes — a perpetuity is just an annuity with infinite duration. PV = PMT / r. A $1,000/year perpetuity at 5% is worth $20,000. Useful for valuing preferred stock and assumed-perpetual cash flows like dividend-paying utilities.

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Annuity Present Value Calculator

What is a series of future payments worth in today's dollars?

Payment Amount ($)

Discount Rate (%/yr)

Number of Years

Payment Frequency

Type

Formulas:
PV (Ordinary) = PMT × [1 − (1+r)^(−n)] / r
PV (Due) = PMT × [1 − (1+r)^(−n)] / r × (1+r)

Whenever you're offered a stream of future payments — a pension, a structured settlement, a lottery annuity, a lease — somebody has implicitly priced that stream. The present-value-of-an-annuity formula lets you check whether the price is fair, expensive, or a steal. It's the single most useful calculation in personal finance for "lump sum vs payments" decisions.

Why present value matters

A dollar received next year is worth less than a dollar today: you lose a year of investment growth, you incur inflation, and you bear credit risk that the future payment might not arrive. Present value rolls all three into a single discount rate and produces one number that summarizes the stream in today's purchasing power. If the lump sum offered exceeds the PV, take the cash. If not, take the annuity.

The discounting formula in one line

PV_ordinary = PMT × [ 1 − (1+r)⁻ⁿ ] / r
PV_due = PV_ordinary × (1+r)

Worked example: $1,000/month for 10 years at 6%

r = 0.06/12 = 0.005, n = 120 months
(1 + 0.005)⁻¹²⁰ ≈ 0.5496
PV ordinary = 1,000 × (1 − 0.5496) / 0.005 = $90,073
Sum of future payments: $120,000
Discount (time-value gap): $29,927 (25% of nominal)

Anyone offering you less than $90,073 for this stream is winning the trade; anyone offering more than $90,073 is paying you the time premium.

Choosing the right discount rate

Scenario	Discount rate
Highly-rated pension (PBGC-backed)	4-5% (long Treasury + small spread)
Lottery annuity (state-backed)	Use state's published rate (~4-5%)
Commercial fixed annuity	Match issuer credit rating's yield curve
Structured settlement (corporate)	Treasury + 100-300 bps credit spread
Personal opportunity cost	Your portfolio expected return (5-7%)

Five real-world scenarios where PV decides

Pension lump-sum buyout offers — compare PV of monthly pension to the cash offer; choose the higher.
Lottery annuity vs cash option — Powerball cash option is ~52% of advertised jackpot, equal to PV at the commission's discount rate.
Structured settlement sale — Factoring companies offer a discounted lump sum; courts must approve at "fair discount rates" under state statutes.
Lease vs buy — PV of lease payments versus purchase price + opportunity cost of capital.
Alimony / child support buyout — Some divorces structure a lump-sum buyout of future support obligations.

FAQ

Should I include inflation in the discount rate?

If the payments are fixed in nominal terms (most pensions, fixed annuities), use a nominal discount rate. If payments are inflation-indexed (Social Security, TIPS-backed), use a real discount rate.

What if the discount rate is zero?

PV = PMT × n. The formula collapses to simple addition — no time-value discount.

Are taxes considered in PV?

Not in the basic formula. For decisions that have different tax consequences (pre-tax lump sum vs annuity payments), compute after-tax PV using your marginal rate.

How is PV used for bond pricing?

A coupon bond is PV of an annuity (coupons) plus PV of a single sum (face value at maturity). The same formula applies.

What's a "growing annuity"?

An annuity where payments grow at a constant rate g. PV = PMT/(r−g) × [1 − ((1+g)/(1+r))ⁿ]. Useful for inflation-indexed pensions.

Does PV account for credit risk?

Only if you raise the discount rate to include a credit spread. PV at the risk-free rate assumes payments are certain to arrive.

Related calculators

Sources

Educational only; not investment advice. Reviewed by David Roehrig, ChFC®, on March 2, 2026.