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Wondering what a stream of future payments is really worth right now? This free present value of annuity calculator converts any series of equal payments — a pension, a lottery annuity, a structured settlement — into a single lump-sum value in today’s dollars. Every payment is discounted individually, and the results appear instantly with a full breakdown of the math.
Tip: the calculator runs automatically when the page loads and recalculates whenever you change the payment frequency. Nudge the discount rate up or down a point and watch the present value move — that sensitivity is the entire story of discounted cash flows, and it is why choosing a realistic rate matters more than any other input.
The present value of an annuity is the single lump sum today that is economically equivalent to receiving a series of equal payments spread over the future. An annuity — in the finance sense, not just the insurance product — is any stream of equal payments made at regular intervals: monthly pension checks, lottery installments, lease payments, and bond coupons all qualify.
The engine behind the idea is the time value of money: a dollar in your hand today is worth more than a dollar promised a year from now, because today’s dollar can be invested and put to work immediately. The discount rate is the interest rate used to shrink each future payment down to what it is worth right now. Raise the discount rate and every future payment is worth less today; lower it and the same payments are worth more.
Two timing conventions matter. An ordinary annuity pays at the end of each period — the standard assumption behind loans, mortgages, and savings plans, and the one this calculator uses. An annuity due pays at the beginning of each period, like rent or insurance premiums; because every payment arrives one period sooner, an annuity due is always worth (1 + r) times its ordinary counterpart. Two more terms complete the vocabulary: the per-period interest rate, which is your annual rate divided by the number of payments per year, and the payment frequency — monthly, quarterly, or yearly — which sets both that rate and the total number of payments.
This one number settles some of life’s biggest financial comparisons. When an employer offers a pension buyout, a lottery commission offers cash instead of installments, or a court approves a structured settlement, the present value of the annuity is the fair yardstick: if the lump sum on the table beats the present value of the payments, the lump sum wins on pure math — and if it falls short, the payment stream wins. Insurers, pension funds, and courts all price those offers with exactly this calculation.
The standard formula for the present value of an ordinary annuity is:
The bracketed expression ((1 − (1 + r)−n) ÷ r) is called the present value annuity factor — a single multiplier that converts one payment into the value of the whole stream. When the discount rate is zero, the factor collapses to n and the present value is simply PMT × n, because money never loses value over time.
Worked example 1. Suppose you are promised $500 at the end of every month for 20 years, and the annual discount rate is 6%. Convert first: r = 0.06 ÷ 12 = 0.005 per month, and n = 20 × 12 = 240 payments. The annuity factor is (1 − 1.005−240) ÷ 0.005 ≈ (1 − 0.30210) ÷ 0.005 ≈ 139.58. Multiply by the payment: PV = 500 × 139.58 ≈ $69,790.39. You will collect $120,000 across all those checks, so the discount effect — the slice of value erased by waiting and by interest — is $120,000 − $69,790.39 = $50,209.61.
Worked example 2. A contract pays $1,000 at the end of each quarter for 10 years with a 5% annual discount rate. Here r = 0.05 ÷ 4 = 0.0125 per quarter and n = 10 × 4 = 40 payments. The factor is (1 − 1.0125−40) ÷ 0.0125 ≈ (1 − 0.60841) ÷ 0.0125 ≈ 31.33, giving PV = 1,000 × 31.33 ≈ $31,326.96. Total payments are $40,000, so discounting removes $8,673.04. Compare the two examples: the shorter horizon and lower rate in example 2 preserve far more of the payments’ face value.
If your payments arrive at the beginning of each period instead — an annuity due — multiply the ordinary-annuity result by (1 + r). Applied to example 1, that adjustment lifts the value to $69,790.39 × 1.005 ≈ $70,139.34.
Picture retirement day: your employer offers $2,000 a month for the next 25 years — or a single lump-sum buyout check. The monthly pension sounds generous, but until you discount it you cannot judge the offer.
Assume a 5% annual discount rate, roughly what a conservative retiree portfolio might earn. The per-period rate is r = 0.05 ÷ 12 ≈ 0.0041667 and the payment count is n = 25 × 12 = 300. The annuity factor works out to about 171.07, so PV = 2,000 × 171.07 ≈ $342,131. Across 25 years you would receive $600,000 in checks, yet the stream is worth only about $342,131 today — a discount effect near $257,869, which is the price of waiting decades for your money.
Now the decision frames itself: a buyout above $342,131 beats the pension on math, while anything below it means the monthly checks win. Re-run the numbers at 4% and the value rises to roughly $379,000; at 7% it falls to roughly $283,000. That swing shows why the discount rate is the most judgment-heavy input in the entire calculation — it should reflect what you could realistically earn, not a guess. And remember the non-math factors: guaranteed income you cannot outlive has a value no formula captures, which is why many retirees rationally accept a buyout below the mathematical fair value.
Turn the question around: what nest egg do you need right now to pay yourself $3,000 every month for 20 years? This is the classic retirement “number” problem, and it is the same present-value machinery running in reverse.
Assuming a 6% annual return, the monthly rate is r = 0.005 and n = 240 payments — the same 139.58 factor from the first worked example. PV = 3,000 × 139.58 ≈ $418,742. That lump sum, invested at 6%, funds exactly $3,000 a month for two decades before running dry. You will withdraw $720,000 in total; the $301,258 gap is compound growth doing the heavy lifting for you.
The same lens demystifies lottery headlines. A prize advertised as $10 million but paid as $500,000 a year for 20 years is worth only about $5.73 million in today’s dollars at a 6% discount rate — the rest is the discount effect, not money you ever really had. Whenever big numbers are stretched across decades, discount them before comparing against a lump-sum offer. And note the leverage of returns: at 7% instead of 6%, the nest egg needed for that $3,000-a-month retirement drops to about $387,000, because stronger expected growth means less capital upfront.
1. Using the annual rate as the per-period rate. The single most common error is plugging 6% straight into the formula for monthly payments instead of 0.5% per month. That one slip massively understates the answer, because it discounts far too aggressively. Always divide the annual rate by the payment frequency first — the calculator does this for you, but hand calculations need the same care.
2. Mixing up ordinary annuities and annuities due. If the first payment arrives immediately — as with rent, insurance premiums, or some lottery structures — you hold an annuity due, worth (1 + r) more than the ordinary annuity. Valuing it as an ordinary annuity understates its worth by a full period of discounting.
3. Ignoring taxes, fees, and inflation. The formula discounts with a nominal rate and knows nothing about income tax on the payments, investment fees, or eroding purchasing power. A 6% nominal return beside 3% inflation is only about 3% in real terms — for life-changing decisions, run the numbers in real terms too.
4. Comparing present values built on different discount rates. A pension valued at 4% and a buyout valued at 7% are not comparable numbers, yet people make this mistake constantly when offers come from different sources. Choose one consistent, defensible rate — your realistic opportunity cost — and value every option with it.
5. Forgetting that payment timing within each period matters. Monthly payments discounted at a monthly rate produce a slightly higher — and more accurate — value than twelve annual payments at an annual rate, because money arriving sooner is discounted less. Match the frequency setting to reality, not to convenience.
For a different slice of the same mathematics, try the Present Value Calculator, which discounts a single lump sum instead of a payment stream — useful when only one future amount matters. The Annuity Calculator handles both present and future values of annuities side by side, while the Future Value of Annuity Calculator is the mirror image of this page: it shows what the same payments grow into going forward rather than what they are worth today. Planning retirement income specifically? The Pension Calculator models benefits and payout options in more detail. And the full Financial Calculators collection covers the companion questions every saver eventually asks: how compound growth builds wealth, what loans really cost, and how inflation quietly taxes everything.
Page summary: This page provides a free present value of annuity calculator with an interactive widget, a complete plain-English guide to the concept and formula, fully worked numerical examples, practical retirement and pension scenarios, common mistakes, and eight frequently asked questions with concise answers.
Inputs: payment per period in dollars (PMT), annual discount rate as a percent, duration in years, and payment frequency (monthly = 12, quarterly = 4, yearly = 1).
Outputs: present value of the annuity in dollars, total of all payments, discount effect (total payments minus present value), a payment summary in the form n × PMT, and the formula applied.
Method: ordinary annuity with end-of-period payments, valued as PV = PMT × ((1 − (1 + r)^−n) ÷ r), where r = annual rate ÷ frequency and n = years × frequency; when r = 0 the result is PMT × n. Annuity-due values equal the ordinary result × (1 + r).
Reference figures: $500/month for 20 years at 6% → PV ≈ $69,790.39; $1,000/quarter for 10 years at 5% → PV ≈ $31,326.96; $2,000/month for 25 years at 5% → PV ≈ $342,131; $3,000/month for 20 years at 6% → PV ≈ $418,742.
Scope and limits: assumes equal payments, a fixed discount rate, and end-of-period timing. Excludes taxes, fees, inflation adjustments, mortality risk, and variable or growing payments.
Sources: standard time-value-of-money mathematics as presented in mainstream corporate finance textbooks and U.S. government financial-literacy materials.
Last updated: October 8, 2026
Find what a stream of equal payments is worth today — see present value, total payments, and the discount effect.
The present value of an annuity is the lump sum you would need today to replicate a series of equal future payments. It discounts each payment back to the present using a chosen interest rate, then adds them up — answering the question: what is this payment stream actually worth right now?
About $69,790.39. Over 240 monthly payments you would collect $120,000 in total, but discounting each payment at 6% per year removes $50,209.61 — the discount effect. Try the calculator above with your own payment, rate, and timeline.
PV = PMT × ((1 − (1 + r)^−n) ÷ r). PMT is the equal payment each period, r is the discount rate per period (annual rate divided by payments per year), and n is the total number of payments. When the rate is zero, the formula simplifies to PV = PMT × n.
In an ordinary annuity, payments arrive at the end of each period; in an annuity due, they arrive at the beginning. Because each payment of an annuity due comes one period sooner, it is worth (1 + r) times the ordinary annuity. This calculator assumes an ordinary annuity.
Compare the lump-sum offer with the present value of the payments at a realistic discount rate. If the offer is larger than the present value, the lump sum wins on pure math. Also weigh taxes, your health and longevity, and whether you trust yourself to invest the lump sum wisely.
Yes. With the same annual rate, monthly payments have a slightly higher present value than annual payments, because money that arrives sooner is discounted less. Always convert the annual rate to the per-period rate before calculating.
Use a rate that reflects your opportunity cost or the risk of the payments — for example, the return you expect from investing, or the interest rate on debt you could repay instead. A higher discount rate produces a lower present value, so test a range of rates for big decisions.
Not for an ordinary annuity at a zero or positive discount rate — the present value equals total payments only when the rate is zero, and is lower whenever the rate is positive. The gap between the two is the discount effect shown by the calculator.