Present Value Calculator
Calculate the present value of future cash flows.
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About
Present Value Calculator
Present value is what a sum of money promised in the future is worth today. The two calculators on this page cover both shapes the question takes: a single amount arriving on one future date, and a run of equal payments arriving period after period. Enter the rate and the number of periods, and each returns the value in today's dollars along with the interest that separates the two figures.
What present value means
Money available now is worth more than the same amount later, because you can put it to work in the meantime. Present value turns that idea into a number. It asks how much you would need today, invested at a given rate, to end up with a specific amount on a specific date.
Take the default: $1,000 arriving in ten periods with a 6% rate. The present value is $558.39. Put $558.39 aside today at 6%, leave it for ten periods, and you land on $1,000. The remaining $441.61 is interest the money earns on the way. So $1,000 ten periods out and $558.39 today are the same thing priced at two different moments, and a promise of $1,000 in ten years should not cost you more than $558.39 if 6% is the return you could otherwise earn.
The formula is short:
PV = FV ÷ (1 + r)n
where r is the rate per period and n is the number of periods. Raising the denominator to a power is why distance matters so much. At 6%, money arriving in 10 periods is discounted to 56% of its face amount; at 30 periods it falls to 17%.
The discount rate is the whole argument
Everything hinges on the rate, and it is the input people fight over. A discount rate is an interest rate pointed backwards: instead of growing a sum forward, it shrinks a future sum back to today.
Choosing it means answering what the money could earn elsewhere at similar risk. A guaranteed government payment is discounted at close to the Treasury yield. A risky business project is discounted at something much higher, often the company's weighted average cost of capital, because the return has to compensate for the chance the cash never turns up.
The choice swings the answer hard. That $1,000 in ten periods is worth $558.39 at 6%, $613.91 at 5%, and $385.54 at 10%. Anyone valuing an asset with a discount rate has made an assumption about risk, whether or not they say so, which is why sensible valuations test a range of rates rather than defending one.
Present value of a stream of payments
The second calculator prices an annuity, meaning a fixed payment repeating each period. Rather than discounting one amount, it discounts every payment separately and adds them up. The standard shorthand is:
PV = PMT × [1 − (1 + r)−n] ÷ r
With the defaults, $100 a period for ten periods at 6% has a present value of $736.01. You will receive $1,000 in total, but the later payments are worth progressively less, so the whole stream is worth $736.01 today. Left to accumulate instead, those same deposits grow to a future value of $1,318.08, of which $1,000 is your own money and $318.08 is interest.
The timing switch matters more than it looks. An ordinary annuity pays at the end of each period, which is how loan payments and most bond coupons work. An annuity due pays at the beginning, which is how rent and leases work. Each payment in an annuity due sits one period longer, so its present value is higher by a factor of exactly (1 + r), here about 6%.
Payments that never stop
A stream with no end date is called a perpetuity, and it collapses to something much simpler:
PV = PMT ÷ r
At 6%, a payment of $100 a period forever is worth $1,666.67 today. That a never-ending stream has a finite value surprises people, but it follows directly from discounting: the payment arriving in period 100 is worth 29 cents at that rate, and the ones after it round to nothing. Perpetuities are not a curiosity either. Preferred shares, endowment spending rules, and the terminal value at the end of a discounted cash flow model all use the formula, usually with a growth rate g subtracted from the denominator.
Present value against net present value
PV and NPV get used interchangeably and should not be. Present value discounts money coming in. Net present value nets the discounted inflows against the discounted outflows, including the cost of getting started, which is what the word net is doing.
Spend $700 today on equipment that pays $100 a period for ten periods at a 6% cost of capital, and the present value of the inflows is $736.01 while the NPV is $36.01. The rule is straightforward: a positive NPV means the project earns more than the discount rate you demanded, and a negative NPV means it does not. NPV is the version that shows up in real capital budgeting, depreciation analysis, and lease-versus-buy decisions, while plain PV is the building block underneath it. The IRR Calculator answers the same question from the other side, solving for the rate that would drive NPV to zero.
Where present value gets used
- Lottery and settlement payouts: the lump sum offered instead of annual instalments is the present value of those instalments, which is why the cash option is always far below the advertised jackpot.
- Bond pricing: a bond's fair price is the present value of its coupons plus the present value of its face amount. Discount rates rise, prices fall, and that mechanical relationship is the entire reason bonds lose value when rates go up.
- Pensions: the choice between a monthly pension and a lump-sum buyout is a present value comparison, and the rate the plan uses determines how generous the buyout looks.
- Business valuation: discounted cash flow analysis values a company as the present value of the cash it is expected to produce.
- Leases and legal damages: accounting rules require lease obligations on the balance sheet at present value, and courts discount future lost earnings to a present sum.
Present value in the time value of money
PV is one of the five variables that make up the time value of money, alongside future value (FV), the rate (I/Y), the number of periods (N), and the payment (PMT). Fix any four and the fifth follows. Mortgages, car loans, and credit cards are all applications of that relationship: a loan balance is nothing more than the present value of the payments you have promised to make.
To run the calculation in the other direction, use the Future Value Calculator. To solve for any of the five variables, including the rate or the number of periods, the Finance Calculator covers the whole set.
Reading the results properly
Two habits prevent most mistakes. First, keep the rate and the period on the same footing: a monthly payment needs a monthly rate, so an annual 6% becomes 0.5% a month and ten years becomes 120 periods, not 10. Mixing them is the single most common error with these formulas.
Second, remember that present value is only as good as its two assumptions, the rate and the certainty of the cash arriving. The arithmetic is exact and the inputs are estimates. Discounting a payment that may never be made produces a precise number that describes something that might not happen, which is a reason to state your discount rate openly rather than bury it.
Common questions
Frequently asked questions
What a future sum is worth today, given a rate you could otherwise earn. At 6%, $1,000 arriving in ten periods has a present value of $558.39, because $558.39 invested at 6% for ten periods grows to exactly $1,000.
PV = FV / (1 + r)^n, where r is the rate per period and n is the number of periods. For a stream of equal payments, PV = PMT x [1 - (1 + r)^-n] / r, which discounts each payment and adds them together.
The return you could earn elsewhere at comparable risk. A guaranteed government payment is discounted near the Treasury yield; a risky project uses something much higher, often the cost of capital. It matters enormously: $1,000 in ten periods is worth $613.91 at 5% but $385.54 at 10%.
PV discounts money coming in. NPV nets the discounted inflows against the outflows, including the upfront cost. Spend $700 on something paying $100 a period for ten periods at 6%: the PV of the inflows is $736.01, and the NPV is $36.01. A positive NPV means the project beats your required rate.
An ordinary annuity pays at the end of each period, as loan payments and most bond coupons do. An annuity due pays at the beginning, as rent does. Each payment in an annuity due earns one extra period, so its present value is higher by a factor of exactly (1 + r).
Because the advertised jackpot is the total of payments spread over decades, and the lump sum is their present value. Money arriving in year 25 is worth a fraction of the same amount today, so discounting the whole schedule produces a figure well below the headline number.
Convert the rate and the periods to the same frequency. An annual 6% becomes 0.5% per month, and ten years becomes 120 periods. Using an annual rate with a monthly count, or the reverse, is the most common mistake in these calculations.
A bond price is the present value of its coupons plus its face amount. Raising the discount rate lowers every one of those discounted figures, so the price falls. Longer bonds fall further because their cash flows sit further out and are discounted harder.