Present value calculator

This calculator works out the present value (PV) of a single future amount (lump sum) or a series of equal end-of-period payments (ordinary annuity). It's a simplified model: fixed rate, optional fixed inflation, equal payments. Got uneven or irregular cash flows? Use the NPV cal

This calculator works out the present value (PV) of a single future amount (lump sum) or a series of equal end-of-period payments (ordinary annuity). It's a simplified model: fixed rate, optional fixed inflation, equal payments. Got uneven or irregular cash flows? Use the NPV calculator instead - don't confuse it with PV.

Input data

Result

Future amount, Annual discount rate (%), Time horizon and Compounding. The result shows up here.

How results are calculated

Present value (PV) for a single future amount: PV = FV ÷ (1 + r/m)^(m·t), where r is the annual discount rate, m is compounding periods per year, and t is time in years.

Series of equal payments (ordinary annuity, end of period): PV = PMT × (1 − (1+r)^(−n)) ÷ r, where n is the number of periods from horizon × compounding. This is still a simplification: fixed rate and equal amounts - it does not model uneven or irregular cash flows (use NPV for those).

Discount effect = FV − PV (lump sum) or total payments − PV (annuity) - one “cost of waiting” card showing the gap versus nominal amounts.

The idea of discounting cash flows dates back to the early 20th century - Irving Fisher formalized the link between interest rates, time, and the value of money in The Theory of Interest (1930), while John Maynard Keynes explored expectations and time preference in investment analysis.

Those ideas underpin every PV and NPV formula used today.

If you turn on the inflation adjustment, the calculator also reports PV at a real rate (the Fisher effect): (1 + nominal rate) = (1 + real rate) × (1 + inflation) - also in annuity mode, assuming constant inflation.

How to use the calculator

  1. By default, enter the future amount (FV) in the header currency - lump sum mode.
  2. Enter the annual discount rate (%), time horizon, and compounding.
  3. Optionally turn on a series of equal end-of-period payments instead of a single FV.
  4. Optionally turn on inflation (constant real rate) - works in both modes.
  5. Read PV and the discount effect; in annuity mode, also total payments. Uneven cash flows belong on the NPV page.

PV of a lump sum or an ordinary annuity

Present value of one future amount or equal end-of-period payments. 10000 in 5 years at 5% with annual compounding is a PV of about 7835.26.

PV
Present value in this calculator. 10000 / 1.05^5 ≈ 7835.26. At 50000, 8%, 10 years, monthly compounding, PV falls to about 22526.
lump sum
One future amount, not a series. 10000 in 5 years at 5% annual is that 7835.26. Uneven cash flows sit outside this formula.
annuity
Optional equal end-of-period payments. Not NPV of many different CFs. 2.5% inflation on 20000 / 6% / 7 years lifts real PV versus nominal.

Usage examples

Example 1

  • Future amount: 10,000
  • Discount rate: 5%
  • Time: 5 years
  • Compounding: annual

PV ≈ 7,835.26
Discount effect ≈ 2,164.74

At a moderate rate and a shorter horizon, the discount is relatively small.

Example 2

  • Future amount: 50,000
  • Discount rate: 8%
  • Time: 10 years
  • Compounding: monthly

PV ≈ 22,526.17
Discount effect ≈ 27,473.83

Monthly compounding at the same annual rate gives a lower PV than annual - discounting happens more often.

Example 3

  • Future amount: 20,000
  • Discount rate: 6%
  • Time: 7 years
  • Compounding: annual
  • Inflation: 2.5%

PV ≈ 13,301.14
Discount effect ≈ 6,698.86
Real PV (~3.41%) ≈ 15,810.88

The real rate (after subtracting inflation) gives a higher PV than the nominal rate, since it "cuts" the future amount less.

Example 4

  • Mode: series of equal payments
  • Payment: 500 per period
  • Rate: 5%
  • Time: 5 years
  • Compounding: annual (5 payments)

PV ≈ 2,164.74
Total payments 2,500.00
Discount effect ≈ 335.26

Five equal annual payments of 500 - ordinary end annuity. Unequal amounts still require NPV.

Example 5

  • Mode: series of equal payments
  • Payment: 200 per period
  • Rate: 6%
  • Time: 10 years
  • Compounding: monthly (120 payments)

PV ≈ 18,014.69
Total payments 24,000.00

Here the period is one month: 10 years × 12 = 120 equal monthly payments - a different case than Example 4 (annual).

Example 6

  • 20,000
  • 4%
  • 8 years

PV ≈ 14,613.80

What is 20,000 in 8 years worth today at 4%? PV ≈ 14,613.80.

Example 7

  • 5,000
  • 7%
  • 3 years

PV ≈ 4,081.49

What is 5,000 in 3 years worth today at 7%? PV ≈ 4,081.49.

Related calculators

Future value calculator

The future value calculator, FV, grows a starting amount and optional contributions at the compounding you pick.

Use calculator →

NPV: net present value

The NPV calculator, net present value, discounts each cash flow back to today and adds them up.

Use calculator →

Purchasing power under inflation

The inflation calculator shows how much of today's amount remains under a flat yearly inflation rate.

Use calculator →

All finance calculators

FAQ

How should I read present value (PV)?

What a single future amount is worth right now, once you discount it at a fixed rate - its equivalent value today.

How is Present value (PV) calculator different from Future value (FV)?

PV here values a single future amount or a series of equal payments. NPV sums any (including uneven) cash flows over time - that is what the NPV calculator does.

When does discounting matter most?

The longer the horizon and the higher the rate, the more a future amount loses versus its value today - that's when discounting really bites.

What assumption does the model make?

One constant annual discount rate for the whole period, with no change over time and no default risk.

What usually throws off a PV number?

Mixing up the nominal rate with the real rate (ignoring inflation), or a sign error - entering a discount rate below −100%.

How does compounding affect the result?

More frequent compounding (e.g. monthly) at the same annual rate produces a lower PV than annual compounding, because discounting happens more often.

What changes when I turn on the inflation adjustment?

The calculator also reports PV at a real (Fisher) rate - including in annuity mode with constant inflation. It shows real purchasing power; still a simplification.

What should I compare the PV result with?

With the future value (FV) calculator, with NPV for multiple cash flows, and with inflation, to see the full picture of the time value of money.

What if “Future amount” is blank?

Nothing calculates. A blank field stops the calculation, not a hidden zero. Type a number or clear the form and start from an example further down the page.

What is the PV of 10,000 in 5 years at 5%?

About 7,835. Discount is about 2,165. 10,000 / (1.05)^5. Uneven project cash flows belong on the NPV page, not this single-amount PV.

Knowledge sources

PV is one future amount or equal payments. You type the rate yourself.

Page updated in 2026.