Example 1 — 5 years, annual compounding
- 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.
Present value (PV)
Find out what a future lump sum or a series of equal payments is worth today — got uneven cash flows instead? Use the NPV 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 calculator instead — don't confuse it with PV.
Result
Enter data and click Calculate.
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
- By default, enter the future amount (FV) in the header currency — lump sum mode.
- Enter the annual discount rate (%), time horizon, and compounding.
- Optionally turn on a series of equal end-of-period payments instead of a single FV.
- Optionally turn on inflation (constant real rate) — works in both modes.
- Read PV and the discount effect; in annuity mode, also total payments.
- Uneven cash flows → go to NPV.
Usage examples
Example 2 — 10 years, monthly compounding
- 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 — with inflation adjustment
- 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 — annuity, annual compounding
- 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 — annuity, monthly compounding
- 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).
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 PV different from NPV?
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.
How is a series of equal payments different from NPV?
An annuity assumes a fixed amount at the end of each compounding period. NPV allows different amounts and any schedule — use NPV when payments are not equal or terms change.