Present Value Calculator
Investing & ReturnsDiscount future cash flows to today's value.
Present value: $50,835
Present value inputs
Present value is the default. The other modes work backwards from a target value.
Advanced (inflation, fees & tax)
- Present value$50,835
- Lost to discounting$49,165
Rate metrics
How the present value is built
Each line works from the future cash down to today's value, then strips out fees and tax.
- Total future cash flows$100,000
- Time-value discount− $49,165
- Present value$50,835
Present value discount curve
How the present value accumulates over the horizon, and how far it lags the undiscounted cash.
Value lost to discounting
Discounted cash flow by period
Each period's gross cash flow (faint) and its present value (solid) — the gap is the discount.
- Present value (cumulative)
- Future cash (cumulative)
Present vs future value
What the cash flows add up to versus what they are worth today.
- Total future cash$100,000
- Present value$50,835
Present value at different discount rates
- 3.0%$74,409
- 5.0%$61,391
- 7.0%$50,835
- 9.0%$42,241
- 11.0%$35,218
Inflation impact
Time-value discounting and inflation erode value in different ways.
- Total future cash$100,000
- Purchasing power$78,120
- Present value$50,835
Nominal cash vs purchasing power over time
Sensitivity to the discount rate
Present value falls as the discount rate rises — the marker shows your current rate.
| Discount rate | Present value | vs base |
|---|---|---|
| 2.0% | $82,035 | +61.4% |
| 3.0% | $74,409 | +46.4% |
| 4.0% | $67,556 | +32.9% |
| 5.0% | $61,391 | +20.8% |
| 6.0% | $55,839 | +9.8% |
| 7.0% | $50,835 | +0.0% |
| 8.0% | $46,319 | -8.9% |
| 9.0% | $42,241 | -16.9% |
| 10.0% | $38,554 | -24.2% |
| 11.0% | $35,218 | -30.7% |
| 12.0% | $32,197 | -36.7% |
Year-by-year discounted cash flow
Every cash flow, its discount factor and the present value it contributes.
| Period | Year | Cash flow | Discount factor | Present value | Cumulative PV |
|---|---|---|---|---|---|
| 10 | 10 | $100,000 | 0.5083 | $50,835 | $50,835 |
Present value breakdown
| Total future cash flows | $100,000 |
|---|---|
| Lost to discounting | $49,165 |
| Present value | $50,835 |
Future value comparison
| Total future cash | $100,000 |
|---|---|
| Present value | $50,835 |
| Lost to discounting | $49,165 |
| Value retained | 50.8% |
| Rate per period | 7.000% |
| Effective annual rate | 7.00% |
Inflation-adjusted values
| Total future cash | $100,000 |
|---|---|
| Purchasing power today | $78,120 |
| Eroded by inflation | $21,880 |
| Real discount rate | 4.39% |
| Present value | $50,835 |
Discount-rate scenarios
How the present value shifts if your discount-rate assumption is a couple of points lower or higher.
- Lower rate$61,391
- Base case$50,835
- Higher rate$42,241
| Scenario | Discount rate | Present value |
|---|---|---|
| Lower rate | 5.0% | $61,391 |
| Base case | 7.0% | $50,835 |
| Higher rate | 9.0% | $42,241 |
Inputs & outputs
| Inputs | |
|---|---|
| Cash flow type | Single lump sum |
| Future value (amount received later) | $100,000 |
| Discount rate | 7.00% |
| Number of years | 10 yrs |
| Discount frequency | Annual |
| Results | |
| Present value | $50,835 |
| Effective annual rate | 7.00% |
| Lost to discounting | $49,165 |
The present value formula
For a single lump sum, present value discounts each future cash flow back to today:
PV = FV ÷ (1 + i)ⁿwhere:
- PV
- Present value — today's worth of the future cash
- FV
- Future value — the lump sum received later
- C
- Cash flow or payment per period
- i
- Discount rate per period (annual rate ÷ frequency)
- g
- Growth rate of the payment per period
- n
- Number of periods (years × frequency)
Above annual frequency the per-period rate is the annual rate divided by the number of periods (i = r ÷ m), and n counts periods, not years.
Present value is already in today's money, so it is never deflated twice. Purchasing power instead deflates the future cash by inflation alone.
An annual fee is applied as a drag on the cash flows — arithmetically the same as discounting them at a slightly higher rate.
Worked example
This example updates live with the inputs above.
Your numbers
Receiving $100,000 in 10 years, discounted at 7.0%, is worth $50,835 today.
Key terms
- Present value (PV)
- The worth today of money you will receive or pay in the future, given a discount rate.
- Discount rate
- The annual rate used to shrink future cash to today — usually your opportunity cost or required return.
- Time value of money
- The principle that a sum today is worth more than the same sum later, because today's money can be invested.
- Annuity
- A series of equal payments at regular intervals — at period end (ordinary) or period start (due).
- Perpetuity
- An annuity with no end date; its present value is finite as long as the discount rate exceeds any growth.
- Purchasing power
- What a future amount will actually buy in today's prices, once inflation is stripped out.
- Net present value (NPV)
- Present value of the cash flows minus the price paid today; a positive NPV signals a worthwhile deal.
- Effective annual rate
- The true yearly rate once the discount frequency is compounded — comparable across frequencies.
Assumptions & methodology
What the calculator assumes, so you can read the numbers with the right caveats.
- The annual discount rate is converted to a per-period rate by dividing by the discount frequency — the APR convention used by spreadsheet PV functions.
- Cash flows are assumed to arrive exactly on schedule: annuity payments at the end of each period, or at the start for an annuity due.
- Present value is reported in today's money. Inflation is shown separately as purchasing power and the real (Fisher) rate, and is never deducted from the present value itself.
- An annual fee is modelled as a constant drag on the cash flows and tax as a flat rate on the amounts received; real-world fees and tax can be more complex.
- Perpetuities are valued with their closed-form formula; the schedule and charts show only a finite display horizon.
- Results are estimates for planning and comparison, not financial advice — and are only as reliable as the cash-flow forecast and discount rate you provide.
Know what this estimate is based on
- Jurisdiction
- General mathematical model
- Scope and limitations
- Scenario model, not a forecast. Returns, volatility, inflation, fees, and taxes are assumptions and actual investment outcomes can be lower or negative.
- Source links checked
- Jul 30, 2026
Built and regression-tested by Smart Tools Lab. It has not been individually reviewed by a licensed financial, tax, or legal professional.
How to use
- 01
Choose the cash-flow type — a single lump sum, an ordinary or due annuity, a level or growing perpetuity, or a custom series of period-by-period amounts.
- 02
Enter the amounts (a future value or a payment), the annual discount rate and the time horizon, then pick how often discounting compounds: annually, semi-annually, quarterly or monthly.
- 03
Open Advanced to layer in inflation (for the purchasing-power and real-rate views), an annual fee, a flat tax and an optional cost paid today to unlock the net present value (NPV) check.
- 04
Read the present value and the breakdown, then use the solve modes to work backwards — find the rate, term, payment or future value that hits a present-value target — and compare discount-rate scenarios.
Formula
Present value is the future amount divided by one plus the discount rate, compounded once for each year: PV = Future / (1 + r)^years, where r is the discount rate written as a decimal. The value lost to discounting is the future amount minus this present value, and the discount factor is present value divided by future value, which equals 1 / (1 + r)^years. For the year-by-year curve, the same factor 1 / (1 + r)^y is applied at each year y, and the cost of one more year of delay is the present value minus Future / (1 + r)^(years + 1).
Example
Suppose you are promised $100,000 ten years from now and you decide a 6 percent discount rate reflects what you could otherwise earn. First convert the rate to a decimal: r = 0.06. Raise (1 + r) to the number of years: 1.06^10 ≈ 1.7908. Divide the future amount by that figure: $100,000 ÷ 1.7908 ≈ $55,839. So the present value is about $55,839 — that is the sum you could invest today at 6 percent to end up with $100,000 in ten years. The value lost to discounting is $100,000 − $55,839 = $44,161, and the discount factor is $55,839 ÷ $100,000 ≈ 0.558, meaning 55.8 percent of the future amount survives the trip back to today. If the payment slipped to eleven years instead of ten, its present value would fall to about $52,679, so that single extra year of waiting would shave roughly $3,161 off today's value.
Definitions
- Future value
- The fixed amount of money you expect to receive on a specific future date, entered in your currency and used as the anchor the calculation discounts back to today.
- Discount rate
- The annual percentage return you could otherwise earn — or the yearly penalty charged for waiting — which determines how quickly the future amount loses value as it is brought back to the present.
- Years from now
- The whole number of years you must wait before the future payment arrives, applied as the exponent that compounds the discount once for each year.
- Present value
- The headline result: the worth today of the future amount, equal to the sum you could invest now at the discount rate to grow into that future amount exactly.
- Value lost to discounting
- The portion of the future amount that does not survive the trip back to today, calculated as the future value minus the present value.
- Discount factor
- The present value divided by the future value, a decimal between 0 and 1 showing what one unit of future money is worth today under the chosen rate and horizon.
Good to know
Why a dollar later is worth less than a dollar now
Present value rests on one of the most reliable ideas in finance: a sum of money is worth more the sooner you can get your hands on it. The reason is opportunity. A dollar today can be put to work — earning interest, paying down debt, or buying something that would otherwise cost more later — while a dollar promised for next decade sits idle until it arrives. To compare amounts that land at different moments, you cannot simply line up their face values; you have to translate every future amount into its equivalent worth today. That translation is discounting, and the number it produces is the present value. Take the calculator's default: a promise of $100,000 in ten years. At a 7% discount rate that promise is worth only $50,835 right now, because $50,835 invested at 7% would itself grow into $100,000 over the same decade. The other $49,165 is the price of waiting — value that exists only on paper because you cannot touch the money yet. Once you internalise this, a surprising number of financial questions become the same question wearing different clothes: what a pension is worth, whether a lawsuit settlement is fair, how much a bond should cost, whether a business is cheap. Each is answered by discounting future cash back to a single, comparable number you can hold up against a price tag today.
The discounting formula, one period at a time
At its core the calculation is short: divide each future amount by one plus the rate, raised to the number of periods you must wait. For a single lump sum that is PV = FV ÷ (1 + i)ⁿ, where i is the rate per period and n is the number of periods. The exponent does the heavy lifting — because it compounds, each extra year of waiting discounts the money a little more steeply than the last, which is why a long horizon can cut a large future sum down to a modest present figure. When a payment arrives every period rather than once, the calculator discounts each instalment separately and adds the pieces together; a custom series does exactly that, applying its own divisor to every entry. The standard annuity and perpetuity formulas are just tidy shortcuts for those sums, and this tool checks its closed-form answers against the period-by-period total so the two always agree. The year-by-year table lets you watch the mechanism work: each row shows the discount factor — the shrinking fraction 1 ÷ (1 + i)ⁿ — and the present value it produces, with the running total climbing toward the headline figure. Seeing the factors fall from near one in the early years to a fraction in the later ones makes the abstract formula concrete.
Choosing a discount rate — the decision that drives everything
No single input changes the answer as much as the discount rate, and none is as easy to choose carelessly. The rate represents the return you forgo by tying money up in these particular cash flows instead of the best comparable alternative — your opportunity cost — and it should rise with the risk and uncertainty of the cash flows themselves. Discounting a government bond's near-certain coupons calls for a low rate close to safe market yields; valuing a risky start-up's hoped-for profits demands a much higher one to reflect the chance they never materialise. A swing of just a few percentage points reshapes the result dramatically: the same $100,000 due in ten years is worth about $61,391 at 5%, $50,835 at 7%, and only $38,554 at 10%. That sensitivity is a feature, not a flaw — it is the market telling you that risk has a price. Because the right rate is rarely obvious, treat it as a range rather than a single guess. The sensitivity chart sweeps the rate across a band and plots how the present value responds, and the discount-rate scenarios put a low, base and high assumption side by side, so you can see how robust a decision is before you commit to one number.
Lump sums, annuities and custom cash-flow series
Future money arrives in different shapes, and the calculator models each one directly. A lump sum is a single payment at one future date — an inheritance, a maturing bond, a balloon payment. An ordinary annuity is a run of equal payments at the end of each period, the pattern behind most loans, leases and pensions; an annuity due shifts each payment to the start of the period, which raises its present value because every instalment is discounted for one period less. When you expect payments to climb over time — a salary, a rent roll, a dividend that grows — the growing annuity applies a steady growth rate to each successive payment before discounting it. And when the cash flows follow no neat pattern at all, the variable series lets you type the amounts in one by one and discounts each on its own date, which is precisely how analysts value an irregular project or a lumpy stream of receipts. Picking the shape that matches reality matters: treating an annuity due as an ordinary annuity, or ignoring growth in a rising stream, understates or overstates today's value by a meaningful margin. The cash-flow type selector exists so you never have to force a real situation into the wrong mould.
Perpetuities: valuing income that never stops
Some streams have no end date. A consol bond, a well-funded endowment's spending, the rent on land you never plan to sell, or a stable dividend can all be treated as cash flows that continue indefinitely. It seems paradoxical that an infinite stream could have a finite value, but discounting resolves it: each future payment is worth so much less than the one before that the whole series converges to a number. For a level perpetuity that number is beautifully simple — the payment divided by the rate — so $5,000 a year discounted at 5% is worth exactly $100,000 today. A growing perpetuity, the basis of the Gordon dividend model used to value shares, divides the payment by the rate minus the growth rate instead, which captures a stream that rises forever at a steady pace. The crucial condition is that the discount rate must stay above the growth rate; if growth catches up to or overtakes the rate, the sum no longer converges and the value is, mathematically, infinite. The calculator flags that case rather than printing a meaningless number, and because a perpetuity has no natural end, its schedule and charts simply show the first stretch of years so you can see how quickly the early payments dominate the total.
Inflation, purchasing power and the real rate
Inflation is where present-value intuition most often goes wrong, so the calculator is deliberate about it. The key fact is that the present value is already stated in today's money — it is the value at this instant — so subtracting inflation from it a second time would count the same erosion twice. What inflation genuinely changes is purchasing power: how much the future cash will actually buy when it arrives. The tool shows that as a separate figure. At 2.5% inflation, the $100,000 due in ten years will buy only what about $78,120 buys today, even though discounting for opportunity cost is a different matter entirely. It also reports the real discount rate, found through the Fisher relation — roughly the nominal rate minus inflation, or 4.39% when a 7% rate meets 2.5% inflation. There is a neat consistency check hiding here: if you deflate the future cash by inflation and then discount it at the real rate, you arrive back at the same present value the nominal calculation produced. That equivalence is why the present value needs no inflation adjustment of its own, and why the honest way to show inflation's bite is through purchasing power and the real rate rather than a second, smaller present-value figure.
Net present value and the investment decision
Present value answers what a stream of future cash is worth; net present value answers whether it is worth buying. Subtract the price you would pay today from the present value of everything you expect to receive, and the difference is the NPV. The rule it gives is the cleanest in finance: take the deal when NPV is positive, walk away when it is negative, and you are indifferent at zero. A positive NPV means the cash flows are worth more than their cost at your chosen discount rate, so the investment creates value over and above the return you required; a negative NPV means you would be paying more than the future money justifies. Suppose those cash flows are worth $50,835 today and the asset is offered at $45,000 — the NPV of $5,835 says it clears your hurdle with room to spare. Because NPV depends on the discount rate, it inherits all of that rate's sensitivity, which is why serious analysis tests a decision across several rate assumptions rather than trusting a single point estimate. Enter a cost in the calculator's Advanced panel and it computes the NPV and labels the verdict, turning an abstract valuation into a concrete yes-or-no.
Fees, taxes and the value you actually keep
A headline present value assumes you receive every future dollar in full, but real cash flows leak. Investment fees skim a percentage off the top each year, and tax claims a share of what lands in your account, so the value you genuinely keep is smaller than the gross figure. The calculator models both. An annual fee is treated as a drag that compounds against the cash flows over the holding period, which is arithmetically identical to discounting them at a slightly higher rate — a useful way to see that costs and required returns are two sides of the same coin. Tax is applied as a flat charge on the cash flows you receive. The step-by-step breakdown then reads from the top down: it starts with the total future cash, removes the time-value discount to reach the gross present value, and then strips out fees and tax to arrive at the present value you actually pocket. Seeing those deductions laid out is sobering, because a fee that sounds trivial as an annual percentage can quietly erode a large slice of a long-dated value once it compounds across the whole horizon. Treat the after-cost present value, not the gross one, as the number that matters when you compare real alternatives.
Solving backwards: rate, term, payment and future value
Often you do not want the present value at all — you know what something is worth today and need to back out one of the inputs that produced it. The calculator's solve modes turn the formula inside out for you. Solve for the discount rate to find the implied return baked into a price, which is exactly how you read the yield embedded in a bond or the rate of return on a structured payout. Solve for the term to learn how long a future sum can sit before its present value falls to a given threshold. Solve for the payment to size the level instalment whose discounted value matches a target — the heart of pricing a loan or a fixed pension. Solve for the future value to discover what amount, received later, would justify a price you are paying now. Each mode runs the same discounting machinery in reverse, using a target present value you supply, and then rebuilds the full result so the charts and tables reflect the solved figure rather than your starting guess. Because some targets cannot be reached with sensible inputs — a payment that would have to be negative, a rate beyond any plausible market — the calculator checks feasibility and tells you when a goal is out of reach instead of returning a misleading answer.
Common mistakes and how to avoid them
A handful of errors account for most present-value mishaps, and each is easy to sidestep once named. The first is mismatching the rate and the period: if payments are monthly, the rate and the number of periods must be monthly too, which the calculator handles automatically by converting your annual rate and reporting the effective annual rate so comparisons stay honest. The second is double-counting inflation by discounting at a nominal rate and then shaving the result for inflation as well — the present value is already in today's money, so lean on the purchasing-power figure instead. The third is using one discount rate for cash flows of wildly different risk; a safe coupon and a speculative profit do not deserve the same rate, and blending them flatters the riskier stream. The fourth is forgetting the timing convention — whether payments fall at the start or end of each period — which quietly shifts the answer. The fifth is trusting a single rate when the decision is sensitive to it; the scenarios and sensitivity views exist precisely so you can pressure-test a number before acting on it. Finally, remember that a present value is only as good as the cash-flow forecast feeding it: discounting cannot rescue optimistic projections, it can only translate them. Get the inputs honest and the present value becomes one of the most powerful comparisons in personal and business finance.
Frequently asked questions
What is present value?
Present value is what money you will receive (or pay) in the future is worth today, once you discount it for the time you must wait. Because a sum in hand can be invested and grow, a payment that arrives later is worth less than the same payment now. Discounting $100,000 due in ten years at a 7% rate, for example, gives a present value of about $50,835 — roughly half its face amount.
How does the discount rate change the present value?
The discount rate is the engine of the calculation: a higher rate shrinks future cash more aggressively, so the present value falls, while a lower rate leaves more of it intact. The rate usually reflects your opportunity cost — the return you could earn on a comparable investment — or the risk of the cash flows. The sensitivity chart shows exactly how the present value slides as the rate moves up or down.
What is the difference between present value and future value?
They are two ends of the same calculation. Future value grows a sum forward in time at a given rate; present value discounts a future sum backward to today. If $50,835 grows at 7% for ten years it becomes $100,000, and discounting that $100,000 back at 7% returns $50,835. This calculator runs the backward direction, and the future-value solve mode lets you run it forward.
How is an annuity different from a perpetuity?
An annuity is a fixed number of equal payments — a 20-year pension, a car loan, a bond's coupons — and its present value adds up a finite, discounted stream. A perpetuity pays the same amount forever, like a consol bond or an endowment's spending; its present value is simply the payment divided by the rate. A perpetuity only has a finite value when the discount rate stays above any growth in the payment.
Does inflation reduce the present value?
No — and this is a common trap. The present value is already expressed in today's dollars, so deflating it again for inflation would double-count. Instead the calculator shows purchasing power separately: at 2.5% inflation, the $100,000 due in ten years will buy what about $78,120 buys today. It also reports the real (Fisher) discount rate, which strips inflation out of the nominal rate.
What does net present value (NPV) tell me?
Enter a price or cost you would pay today and the calculator subtracts it from the present value of the cash flows to give the net present value. A positive NPV means the future cash flows are worth more than the price, so the deal adds value; a negative NPV means you would overpay. NPV is the standard yardstick for comparing investments and capital projects.
Can the discount rate be negative?
Yes, and the calculator handles it. A negative rate makes future cash worth more than its face value today — which can happen in deflationary conditions or when modelling a guaranteed real return. In that case the present value rises above the future amount, and the result flags it as a premium to face value.
Why does the discounting frequency matter?
Discounting more often than once a year applies a smaller rate over more periods, which slightly changes the result and raises the effective annual rate above the stated nominal rate. The calculator converts your annual rate to a per-period rate (rate ÷ frequency) and reports the effective annual rate so you can compare quotes on equal terms.