Present Value of Annuity Calculator

The present value of an annuity is the lump sum today that is financially equivalent to a series of equal future payments. Discount the payments at a rate you could otherwise earn, add them up, and you have the number. Example: $1,500 a month for 25 years at a 6% annual discount rate is worth $232,810 today, even though those 300 payments total $450,000.

That gap between $450,000 promised and $232,810 today is the whole point of the calculation. Money you will not touch for twenty years cannot be spent, invested or borrowed against as freely as money in your hand, so it is worth less. The annuity formula puts a precise price on that difference.

The present value of annuity formula

For an ordinary annuity, where each payment lands at the end of its period, the formula is:

Here PMT is the payment per period, r is the discount rate per period (annual rate divided by periods per year), and n is the total number of payments. For an annuity due, where payments arrive at the start of each period, multiply the result by (1 + r):

And when the payment itself grows by a fixed percentage g each period, as with a cost-of-living-adjusted pension, the growing annuity version applies (valid when r is greater than g):

All three are just shorthand for the same underlying idea: discount every individual payment by dividing it by (1 + r) raised to the number of periods you have to wait, then total them. The closed forms simply save you from summing 300 terms by hand.

Worked example, step by step

Suppose a structured settlement will pay you $1,500 at the end of every month for 25 years, and you judge that you could earn 6% a year on a comparable lump sum. Work through the formula:

1. Periodic rate: r = 6% ÷ 12 = 0.5% = 0.005 per month.
2. Number of payments: n = 25 × 12 = 300.
3. Discount the last dollar: (1 + 0.005)⁻³⁰⁰ = 0.223966. The payment 300 months out is worth about 22 cents on the dollar today.
4. Numerator: 1 − 0.223966 = 0.776034.
5. Annuity factor: 0.776034 ÷ 0.005 = 155.2069.
6. Present value: $1,500 × 155.2069 = $232,810.

The stream pays out $450,000 in nominal dollars, so discounting costs $217,190, or 48.3% of the face amount. Each promised dollar is worth about 51.7 cents today. If the same payments arrived at the start of each month instead, the present value would rise by one period of interest to $233,974, an extra $1,164 for nothing more than better timing.

Second worked example: lump sum versus payments

A prize pays $50,000 a year for 20 years, a nominal $1,000,000, and the sponsor offers $620,000 in cash instead. Which is better depends entirely on the rate you can earn. At 4% the annuity factor for 20 annual periods is 13.5903, so the payments are worth $679,516 and the cash offer is a bad deal. At 5% the factor drops to 12.4622 and the payments are worth $623,111, almost exactly the offer. At 7% the factor is 10.5940, the payments are worth $529,701, and the cash wins by roughly $90,000. The break-even discount rate is the rate at which the two are equal, just above 5% here. Anyone who can reliably beat that rate should take the cash; anyone who cannot should take the payments.

Present value annuity factor table

The factor is the present value of $1 per period. Multiply it by your payment to price any stream instantly. Rates across the top are per period, not per year, so a 6% annual rate paid monthly means using 0.5% and counting months.

Read the table as a ceiling: at 8% per period the factor never gets far past 12 no matter how long the stream runs, because 1 ÷ 0.08 = 12.5 is the perpetuity limit. That is why a 40-year annuity at 8% (11.9246) is barely worth more than a 30-year one (11.2578). The last decade contributes almost nothing.

Present value of $1,000 a month

Because the present value scales exactly with the payment, this table prices any monthly stream. A $2,500 monthly payment for 20 years at 5% is 2.5 × $151,525 = $378,813. Rates in the header are annual; the calculation uses one twelfth of each.

Ordinary, due and growing side by side

Three versions of the same $10,000-a-year, 20-year stream, valued at annual periods. The growing column assumes the payment rises 3% each year.

Two lessons stand out. The due premium is always exactly r times the ordinary value, so it grows as rates rise. And a 3% escalator is worth far more than better timing: at 5% it adds $35,026 to the same nominal-looking stream, more than five times the annuity-due advantage.

How to use this calculator

1. Payment amount: enter the money received in a single period, not the annual total. If a pension quotes $36,000 a year but pays monthly, enter $3,000 and choose Monthly.
2. Payment frequency: pick monthly, quarterly, semi-annual or annual. The calculator converts the annual rate and the term to match.
3. Discount rate: enter your annual opportunity cost. Try a low, middle and high value rather than trusting a single guess.
4. Number of years: how long the payments last. The field beneath shows the resulting payment count.
5. Payment timing: choose ordinary (end of period, the default for loans and pensions) or annuity due (start of period, typical for rent and leases).
6. Growing annuity: open the optional panel and add a growth rate if the payment escalates, for example a 2% or 3% cost-of-living adjustment.

The headline number is the present value. Below it you get the nominal total, the amount lost to discounting, the annuity factor, the periodic rate, a perpetuity comparison and a table showing how much present value each year contributes.

Who this calculator is for

• Retirees weighing a pension against a lump-sum buyout offer from an employer or insurer.
• Lottery and settlement winners deciding between a cash option and scheduled payments.
• Investors pricing income streams such as bond coupons, royalties, rental contracts or seller-financed notes.
• Business owners and analysts valuing a lease, a service contract or an equipment payment plan.
• Students checking time-value-of-money homework against a step-by-step factor.
• Anyone comparing offers where one side pays now and the other pays over time.

Key terms explained

• Annuity: in finance, any series of equal payments made at regular intervals. It does not have to be an insurance product.
• Discount rate: the periodic return used to shrink future money back to today. It is the single most consequential input.
• Ordinary annuity: payments at the end of each period. Loan payments and most pension checks work this way.
• Annuity due: payments at the beginning of each period. Rent, leases and many insurance premiums work this way.
• PV annuity factor (PVIFA): the present value of $1 per period, so PV = payment × factor.
• Perpetuity: a stream that never ends. Its present value is simply PMT ÷ r, which caps how large any annuity value can get.
• Growing annuity: a stream whose payment rises at a constant rate each period.
• Nominal total: the plain sum of all payments with no discounting, always larger than the present value whenever the rate is above zero.

What moves the result the most

Four levers dominate, and it is worth knowing their relative weight before you argue over a decimal place:

• Discount rate. On the $1,500-per-month, 25-year stream, the present value is $316,315 at 3%, $232,810 at 6% and $178,742 at 9%. Tripling the rate nearly halves the value.
• Term length, with sharply diminishing returns. At 6%, twenty years of that payment is worth $209,371, twenty-five years $232,810, thirty years $250,187 and forty years $272,621. The fourth decade adds only about 9%.
• Payment size. Strictly proportional. Double the payment and the present value doubles exactly, which is why factor tables are so useful.
• Timing and growth. Moving payments to the start of the period adds one period of interest. A growth rate compounds and can add far more.

The perpetuity limit is the sanity check behind all of this. At 6% annual with monthly payments, $1,500 forever is worth $1,500 ÷ 0.005 = $300,000. A thirty-year version already captures 83.4% of that ceiling, so no realistic extension of the term will move the number much.

Does frequency matter?

Yes, though less than people expect. Take $18,000 a year for 25 years at 6% and split it three ways. Paid once a year, the present value is $230,100. Paid quarterly as $4,500, it is $232,311. Paid monthly as $1,500, it is $232,810. The same nominal money is worth about $2,700 more when it arrives in small early pieces rather than one late lump. The effect widens as the discount rate rises and narrows toward zero as the rate approaches zero.

Practical tips

• Bracket the rate. Run a low, base and high case. If the decision flips between them, the rate assumption is doing all the work and deserves more thought.
• Match the risk. Discount a federally backed stream at a Treasury-like yield and a corporate promise at something higher. Using your stock-market hope rate on a guaranteed payment overstates the case for the lump sum.
• Find the break-even rate. Instead of asking what a stream is worth, ask what rate makes it equal to the cash offer, then judge whether you can beat that rate.
• Compare after tax. A pension taxed as ordinary income and a lump sum rolled into an IRA are not directly comparable until you adjust both.
• Watch the escalator. A payment with a 2% or 3% annual adjustment is worth dramatically more than a level one; enter it in the growing-annuity panel rather than ignoring it.
• Sanity check with the perpetuity. If your answer approaches PMT ÷ r, the term is long enough that adding years barely matters.

Limitations and assumptions

• Payments are assumed certain and equal (or growing at a constant rate). Real streams can stop early, default, or vary with performance.
• The discount rate is constant for the whole term. Actual reinvestment rates change over time.
• The periodic rate is the annual rate divided by periods per year, the standard convention. An effective conversion, (1 + annual)^1/periods − 1, gives slightly different figures.
• No taxes, fees or surrender charges are applied, and insurance-company mortality or life-expectancy assumptions are not modeled.
• Inflation is only handled through the rate you choose; enter a real rate if you want an answer in today's purchasing power.
• Uneven cash flows are outside the annuity formula entirely and need a discounted-cash-flow tool instead.

How this compares to related calculators

This page values a series of equal payments. Neighboring tools answer different questions: use the Present Value Calculator when you have a single future lump sum to discount, the Annuity Calculator when you want to see an annuity balance grow and pay out over time, the Annuity Payout Calculator when you know the balance and need the payment it supports, the NPV Calculator when the cash flows are uneven and you must subtract an upfront cost, and the Future Value Calculator when you want to compound money forward instead of discounting it back. For a coupon stream specifically, the Bond Price Calculator adds the face-value repayment on top of the annuity, and the Pension Calculator estimates the payment itself from years of service.

Method and sources

Every figure on this page comes from the standard time-value-of-money identities shown above, which are exact algebraic results rather than estimates or survey data, so no external source is required. No market rates, tax rules or product-specific charges are assumed anywhere in the calculation. The discount rate, payment, term, frequency, timing and growth rate are yours to supply, and the arithmetic runs entirely in your browser.