What present value means
Present value is what a future sum, and any equal payments building up to it, is worth right now once the effect of time and a rate is stripped back out. It answers a question that comes up constantly: someone offers money later rather than now, so what is that promise actually worth today? The more periods stand between now and the payoff, the more the rate takes away. Like its mirror, the future value formula, this tool works in generic periods rather than years, since the maths only needs a rate and a period count that match.
Every amount here is entered as a positive figure. Some textbooks enter a future amount as a negative cash outflow so the equation nets to zero; this tool skips that convention and simply reports today's price, with a plain breakdown of what got discounted away.
The formula and its two special cases
The general present value formula, discounting a future lump sum and a run of payments together, is one line:
The first term discounts the future lump sum on its own, like reversing a compound-interest calculation. The second discounts each payment back from whichever period it lands in. Add the two and today's price is the total, with two situations breaking out of that general case.
Annuity due. If each payment is promised at the start of its period rather than the end, it is discounted back one period less, so the whole payment term is multiplied by (1 + r):
Zero rate. When r is exactly 0 there is nothing left to discount, so the formula collapses to plain addition, with timing making no difference:
The calculator switches to this line automatically whenever the rate per period works out to zero.
Discounting is compounding run backwards
Every idea in this formula already exists in the future value formula, just read in the opposite direction. Compounding takes a sum today and asks what it grows into later, multiplying by (1 + r) once per period; discounting takes a sum later and asks what it is worth now, dividing by that same (1 + r) the same number of times. Run the future value formula on a present value and you land on a future one; run the present value formula on that figure and you land back where you started, the same rate and periods simply travelled in reverse.
Why a pound today beats a pound tomorrow
A pound in hand today can be put to work immediately, so waiting for it has a real opportunity cost measured by whatever else it could have earned meanwhile. Prices tend to rise over time, so a pound due later is likely to buy less than a pound spent now. And a promise of future money always carries some chance of not arriving, a company folding, a person unable to pay, a policy changing, so a sure pound now beats an uncertain pound later at an identical face value. The rate you choose reflects some mix of all three.
Turning an annual rate into a per-period rate
The formula only ever wants r as a rate per period, but rates are usually quoted per year. The "derive from annual rate" option divides a stated nominal annual rate by however many periods sit inside a year: 12% annually over 12 periods gives 12% ÷ 12 = 1% per period, and 6% annually paid quarterly gives 6% ÷ 4 = 1.5% per period. That plain division is a different figure from an effective annual rate, which asks what a per-period rate compounds up to over a year; this calculator sticks to the simpler, more common textbook direction.
Why ordinary annuity and annuity due give different answers
Take a payment of 100 a period at 5%, over 10 periods, no lump sum. As an ordinary annuity those ten payments are worth 772.17 today. As an annuity due, each one lands a period sooner, and the total rises to 810.78, exactly 5% more. Rent in advance, insurance premiums and lease payments are commonly annuity due; loan repayments, bond coupons and pension payments are commonly ordinary annuities, paid at the end of the period they cover.
The pension question: what money later is worth now
This is the shape almost every real present value question takes: someone offers a fixed sum, but only after a wait, and the question is what that offer is worth paid out today instead. The results panel runs exactly that on a flat £10,000, promised 10, 20 or 30 periods from now, at whatever rate you have set above. At 5%, £10,000 in 10 periods is worth £6,139 today; in 20 periods only £3,769; pushed to 30 periods it falls to £2,314. Nothing about the sum changed, only how long it takes to arrive, and that alone wipes out well over half its value by the 30-period mark. A pension transfer value, a structured settlement and a lottery's advertised jackpot are all this same question wearing different clothes.
One distinction worth keeping straight: a nominal rate is whatever percentage is stated outright; a real rate has inflation already stripped out of it. This calculator works in nominal terms throughout; an answer in today's purchasing power needs a real rate entered from the start.
Where present value runs the world
Bond pricing is present value with extra steps: a bond's price is the present value of its coupon payments plus its face value at maturity, discounted at the market's required yield. A lottery winner choosing between the advertised jackpot paid as an annuity and a smaller lump sum today is being asked, in effect, to accept the organiser's discount rate or reject it. Legal settlements structured as payments over years get valued the same way when either side wants a single number to negotiate around. Pension transfers out of a defined-benefit scheme are quoted as a present value so they can be compared against other retirement options on equal terms.
Choosing a discount rate is the whole argument
There is no single correct discount rate waiting to be found in a textbook; the honest answer depends on what else the money could plausibly have earned, how risky the promise is, and how sure you need to be. Move the rate a point either side of your own figure and watch the present value shift, sometimes substantially over a long timeline; that sensitivity is the entire argument people have over what a future payment is worth. Anyone quoting a present value without saying which rate they used has told you only half the answer.
Reading the split, the chart and the tables
The headline splits the present value into the face value, everything added with no discounting, and what discounting took away to reach today's number. The chart plots the same two figures across every period from 0 up to n: the dashed line is that undiscounted face value building up, the solid line is what the promise would be worth today if it only ran that many periods, and the widening gap is value lost to discounting. The period table thins itself past 120 periods to a readable set while always keeping the final one. The smaller table shows how present value moves if the rate were a point higher or lower, a sensitivity check rather than a forecast.
Which calculator actually fits your question
This page runs the discounting direction of the time-value-of-money formula: a future sum and a payment stream, brought back to a value today. If the question runs the other way round, the Future Value Calculator shares the same rate-per-period and ordinary/due framing in reverse. For an everyday savings account with years and a monthly contribution rather than generic periods, the Compound Interest Calculator is the more practical fit. With no rate at all, only a flat percentage on a fixed sum over a fixed time, the Simple Interest Calculator handles that plainer arithmetic.
Questions people ask
What is the difference between present value and future value?
Present value asks what a future sum, and any payments building up to it, is worth today once a rate and a wait are stripped back out. Future value asks the reverse: what a sum today grows into after that same rate and wait. They share the same formula; only the direction of the question changes.
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity pays at the end of each period; an annuity due pays at the start. Because an annuity-due payment arrives sooner, it is discounted back one period less, so its present value is always the ordinary annuity's multiplied by (1 + r), never less, for any rate above zero.
How do I get a per-period rate from an annual rate?
Divide the stated annual rate by the number of periods in a year: a nominal 12% a year over 12 monthly periods is 1% a period, and the same 12% over 4 quarterly periods is 3% a period. The "derive from annual rate" option does that division for you.
What happens if the payment (PMT) is zero?
With no payment, the formula reduces to the present value of a single future sum, PV = FV ÷ (1 + r)n, and the ordinary annuity and annuity due toggle stops making any difference.
What happens if the rate is zero?
The formula switches to plain addition, PV = FV + PMT × n, since there is nothing left to discount. Timing no longer matters either, since there is no rate at work.
Can the discount rate be negative?
Yes, though it is unusual; a negative rate makes a future sum worth more today, which can happen in distressed or negative-yield conditions. A rate of exactly −100% or lower is not workable, since the sum would vanish entirely each period, so this calculator floors the maths at −99.99% and shows a note when that happens.
Why does the choice of discount rate matter so much?
Present value is highly sensitive to the rate used, especially over a long timeline, because the rate compounds once per period discounted. There is no universally correct rate; it should reflect what the money could otherwise have earned, how risky the promise is, and how much uncertainty is acceptable.
This calculator illustrates the standard present value formula for study and planning purposes. It is not financial advice. Real bonds, settlements and pensions may discount unevenly, charge fees, or apply a day-count or sign convention different from the one used here.