Audited 27 Jul 2026·Last updated 28 Oct 2026·6 citations·Tier 1·0 uses

Present Value Calculator

Discount a future lump sum, a stream of level payments, or both to today's value at your rate and compounding frequency, with end or start-of-period timing.

Present Value Calculator

The single lump sum you expect to receive or need at the end of the horizon. Set to 0 if you only have a recurring payment, no lump sum.
$
An annuity payment received every compounding period. Set to 0 for a pure lump-sum problem.
$
Your required rate of return or opportunity cost. The calculator divides by the compounding frequency to get the per-period discount rate.
%
Time between today and the date the lump sum and/or payments arrive. With payments, years times payments per year must be a whole number.
yrs
Compounding Frequency
Payment Timing
Present Value
$17,758.83
The combined value today, in dollars, of the future lump sum and all the periodic payments, discounted at your rate.
PV of the Lump Sum
$7,413.72
PV of the Annuity
$10,345.11
Total Future Cash Flows (Undiscounted)
$22,000.00
Effective Annual Rate (EAR)
6.17%

Background.

Suppose a settlement offers $140,000 now or $1,000 a month for the next 20 years. The monthly option adds up to $240,000, which looks like the obvious winner until you ask what each payment is worth on the day you decide. At a 5 percent annual rate, compounded monthly, the 240 payments are worth $151,525.31 today, more than the lump sum. At 7 percent they are worth $128,982.51, less than the lump sum. The two offers are worth the same at about 5.96 percent. Which one is better depends on what you could do with the money in the meantime, and present value is the arithmetic that makes that comparison.

The idea is compounding run backwards. Money invested at rate i for one period grows by a factor of (1 + i); money that will arrive one period from now is worth that amount divided by (1 + i) today. A payment n periods away is divided n times. A level stream of payments is just many such payments, and its present value is the sum of each one discounted for its own wait.

Here you can value a single future amount, a series of equal payments, or both together, as with a bond's coupons plus its face value or a pension with a final lump sum. The annual rate is split evenly across the compounding periods, which are also the payment periods: choose monthly and the payment is monthly. You also choose whether each payment arrives at the end of its period, as loan repayments and bond coupons do, or at the start, as rent and lease payments usually do.

The results show the combined present value, its two parts, the undiscounted total for comparison, and the effective annual rate your nominal rate amounts to once compounding is included.

What is present value calculator?

Present value is what a future amount, or a series of future amounts, is worth today at a given rate of return: the sum you would need to invest now at that rate to reproduce the same cash flows. For a single sum it is FV ÷ (1 + i)ⁿ, the inverse of compound growth. For a series of equal payments it is the sum of every payment discounted for its own distance from today, a geometric series with a closed form. The rate used is the return you give up by waiting, so a higher rate makes future money worth less, and the effect grows with distance. Present value sits under most of finance: a bond's price is the present value of its coupons and face value at the market yield, lease accounting measures a lessee's lease liability as the present value of the remaining lease payments, and net present value is present value minus what you pay up front.

How to use this calculator.

  1. Enter the future lump sum, the single amount arriving at the end of the horizon, or 0 if there is none.
  2. Enter the periodic payment, the equal amount arriving every period, or 0 if you are valuing only a lump sum.
  3. Enter the annual discount rate: the return you could earn elsewhere on money of similar risk. If your rate is quoted as an APY or other effective annual yield, convert it to a nominal rate first, as explained in the questions below.
  4. Enter the number of years and choose the compounding frequency. The frequency is also how often payments arrive, so monthly payments need monthly compounding. With payments, years times payments per year must come to a whole number: 2.55 years of monthly payments would be 30.6 payments, so the calculator refuses it, while 2.5 years gives 30. A lump sum on its own may use any number of years.
  5. Choose end of period for payments made in arrears, such as loan instalments and bond coupons, or beginning of period for payments made in advance, such as rent, leases and many insurance premiums.
  6. Compare the present value with the undiscounted total to see how much the wait costs, and use the two parts to see where the value comes from.

The formula.

PV = FV⁄(1+i)ⁿ + PMT×[1−(1+i)⁻ⁿ]⁄i
PV · value todayFV · single amount due at the end of the horizonPMT · equal payment received each periodi · rate per period: annual rate ÷ periods per yearn · number of periods: years × periods per year

Let r be the annual rate as a decimal and m the number of periods per year. The rate per period is i = r ÷ m and the number of periods is n = years × m. Then

PV = FV ÷ (1 + i)ⁿ + PMT × [1 − (1 + i)⁻ⁿ] ÷ i

The first term discounts the lump sum. The second is the closed form of PMT ÷ (1 + i) + PMT ÷ (1 + i)² + … + PMT ÷ (1 + i)ⁿ, the sum of every payment discounted for its own wait; the bracket divided by i is called the annuity factor. For payments at the start of each period, every payment is one period closer to today, so the annuity term is multiplied by (1 + i). The lump sum is not affected by the timing choice. At a 0 percent rate there is nothing to discount: the annuity term becomes PMT × n, and the present value equals the undiscounted total.

The effective annual rate is EAR = (1 + i)ᵐ − 1, the yearly rate that one annual compounding would need to match the result. It is always at least the nominal rate, and the gap widens with frequency: 6 percent nominal is 6.09 percent effective with semi-annual compounding, about 6.1678 percent monthly and 6.1831 percent daily.

Distant money responds most to the rate. In the worked example below, moving the rate from 4 to 8 percent cuts the present value of the five-year lump sum by about 18 percent, from $8,190.03 to $6,712.10, but the monthly payments, many of which arrive much sooner, by only about 9 percent, from $10,859.81 to $9,863.69. The formula assumes one fixed rate across the whole horizon and payments of the same size; growing payments, irregular dates and changing rates need a cash-flow-by-cash-flow method instead.

A worked example.

Example

Five years from now you are due $10,000, and you will also receive $200 at the end of each month until then. Your alternative is an account paying 6 percent a year, compounded monthly. The monthly rate is 6 ÷ 12 = 0.5 percent and there are 5 × 12 = 60 periods. Compounded over 60 months, 1.005⁶⁰ = 1.34885, so the lump sum is worth 10,000 ÷ 1.34885 = $7,413.72 today. For the payments, (1.005)⁻⁶⁰ = 0.74137, so the annuity factor is (1 − 0.74137) ÷ 0.005 = 51.7256. Multiplying by $200 gives $10,345.11. Together, the two are worth 7,413.72 + 10,345.11 = $17,758.83 today. The undiscounted total is 10,000 + 60 × 200 = $22,000, so waiting costs $4,241.17 of value at this rate. The effective annual rate is 6.1678 percent, a little above the nominal 6 because interest compounds monthly. If you were offered a sum today in exchange for the whole package, $17,758.83 is the amount at which you would be indifferent, given that 6 percent alternative.

annual Rate Percent6
payment Timingend
payment200
future Value10,000
compounding Per Year12
years5

Frequently asked questions.

Should I take a lump sum or the monthly payments?
Compare the lump sum with the present value of the payments at the return you could realistically earn. For $1,000 a month over 20 years against $140,000 today, the payments are worth $151,525.31 at 5 percent and $128,982.51 at 7 percent, crossing at about 5.96 percent. Taxes, inflation, the payer's reliability and how much you value guaranteed income all belong in the decision as well.
How much difference does paying at the start of each period make?
Each payment arrives one period sooner, so the annuity is worth exactly (1 + i) times as much. In the worked example the $200 monthly payments rise from $10,345.11 to $10,396.84, a factor of 1.005, and the combined value from $17,758.83 to $17,810.56. Rent and leases are usually paid in advance; loan repayments and bond coupons are paid in arrears.
Why does daily compounding give a lower present value than annual?
More frequent compounding means a higher effective rate, and a higher rate shrinks future money more. At 6 percent nominal, $10,000 due in five years is worth $7,472.58 with annual compounding, $7,413.72 with monthly and $7,408.36 with daily. The effective annual rates behind those figures are 6, about 6.1678 and about 6.1831 percent. Compounding more often than daily barely matters: even continuous compounding at 6 percent only reaches about 6.1837 percent effective.
My rate is quoted as an APY. What do I enter?
An APY is already an effective annual rate, while the rate field expects a nominal rate that is divided by the compounding frequency. Convert first: for monthly compounding, the nominal rate is 12 × [(1 + APY)^(1/12) − 1]. A 6 percent APY becomes about 5.8411 percent nominal, and entering that gives an effective annual rate of 6 percent in the results.
How do I use this to price a bond?
Enter the face value as the lump sum, the coupon per period as the payment, the market yield as the rate, and the coupon frequency, usually semi-annual for US bonds. A $1,000 bond paying $20 every six months for five years, at a 6 percent yield, is worth $914.70. It trades below par because its 4 percent coupon is lower than the yield buyers can get elsewhere.
How small does money far in the future become?
Smaller than intuition suggests. At 8 percent compounded annually, $1,000 due in 10 years is worth $463.19 today, and $1,000 due in 40 years only $46.03, under five cents on the dollar. That is why long-dated promises, such as pensions decades away, are so sensitive to the rate chosen to value them. A quick check: at 8 percent, money loses about half its present value for every nine years of waiting, because 1.08 to the ninth power is almost exactly 2.
What discount rate should I use?
The return on the best alternative of similar risk. For payments that are as safe as a government bond, a Treasury yield of similar maturity is a sensible benchmark. Riskier payments, such as a private business promising future income, deserve a higher rate. Match the rate to the payments: fixed-dollar payments lose purchasing power to inflation and call for an ordinary nominal rate, while inflation-linked payments call for a real rate. If you will owe tax on what you earn elsewhere, use an after-tax rate on both sides of the comparison, and test a range of rates rather than relying on one.
What if the payments start in a few years, or grow each year?
For payments that start later, use two steps. First value the payments as of one period before the first one arrives, with the lump sum at 0. Then enter that result as a lump sum, with no payment, and discount it over the delay. Payments that rise each year, such as the graduated annual instalments used by large US lottery jackpots, cannot be represented by one level payment and need to be discounted one by one.
What happens at a 0% discount rate?
Nothing is discounted, so the present value equals the undiscounted total: in the example, $10,000 plus 60 payments of $200 gives $22,000, and payment timing makes no difference. A zero rate fits only when money now and money later really are equivalent to you, which is rare once inflation or any available return is considered.
How is present value different from net present value?
Present value is the worth today of what you will receive. Net present value subtracts what you pay to get it, and it usually handles irregular cash flows year by year. Buying the worked example's package for $16,000 would have an NPV of $1,758.83 at 6 percent; for uneven project cash flows, the NPV calculator takes a list of amounts instead of one level payment.

References& sources.

  1. [1]Brealey, R.A., Myers, S.C., and Allen, F. — Principles of Corporate Finance, 13th edition. Chapter 2 introduces present value and the opportunity cost of capital as the foundation of the whole textbook.
  2. [2]Bodie, Z., Kane, A., and Marcus, A.J. — Investments, 12th edition. §5 covers the time value of money and present-value discounting as applied to portfolio and bond valuation.
  3. [3]CFA Institute — CFA Program Curriculum, Quantitative Methods topic area: the time value of money, present value of a single sum, and present value of an annuity.
  4. [4]U.S. Securities and Exchange Commission, Investor.gov — Compound Interest Calculator and accompanying investor-education materials on the time value of money.
  5. [5]Mishkin, F.S. — The Economics of Money, Banking, and Financial Markets, 13th edition. Chapter 4 derives the present-value formulas for a lump sum and for an annuity.
  6. [6]Consumer Financial Protection Bureau — Regulation Z (Truth in Lending) and Regulation DD (Truth in Savings), which require APR/APY disclosure so nominal rates on different compounding bases can be compared.

How this page was produced

Published by
Quanta Calculator
Overseen by
Daniel, Quanta Calculator Researcher
Primary sources
6 cited below
Method
PV = FV⁄(1+i)ⁿ + PMT×[1−(1+i)⁻ⁿ]⁄i
Published
Last verified

Built with AI assistance and verified by automated tests against the cited sources — every worked example on this page is computed by the same code that runs the calculator. How we build and check calculators.

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