Finance
What a future sum is worth today at a given discount rate — the time value of money, with the discount amount shown alongside.
Annual compounding. Results update as you type. All calculations run locally in your browser.
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PV = FV ÷ (1 + r)n, where FV is the future sum, r is the annual discount rate as a decimal, and n is the number of years. The discount is FV − PV: the amount the future sum loses by waiting. This is the mirror image of compound growth — the future value formula run backwards.
$10,000 due in 10 years at a 5% discount rate: PV = 10,000 ÷ 1.0510 = 10,000 ÷ 1.6289 = $6,139.13. The discount is 10,000 − 6,139.13 = $3,860.87. At 5 years instead, the same sum is worth 10,000 ÷ 1.055 = $7,835.26 — waiting twice as long costs more than twice the discount, because compounding accelerates.
This page discounts a single lump sum at a constant annual rate with annual compounding. It does not handle a series of payments (that needs an annuity calculation), a changing rate over time, monthly compounding, taxes, or inflation adjustments — a nominal discount rate and a real (inflation-adjusted) rate give different answers. The rate you pick is doing all the work: a small change in r moves the present value a lot over long horizons, so treat the result as a comparison tool, not a market price.
Because money today can be invested and grown. $6,139.13 invested at 5% for 10 years becomes $10,000, so the two amounts are equivalent at that rate — neither is a bargain, they are the same value at different times.
It depends on the question. For an investment decision, use your expected return or cost of capital. For comparing offers, use the same rate for every option so the comparison is fair. There is no single correct rate.
They are inverses. Future value grows a present sum forward (multiply by (1 + r)n); present value discounts a future sum back (divide by (1 + r)n). Same formula, opposite direction.
Lower. A higher discount rate means future money is penalised more heavily, so its present value falls. At 10% instead of 5%, the same $10,000 in 10 years is worth only $3,855.43.
With monthly compounding the divisor becomes (1 + r/12)12n, which makes the present value slightly smaller than the annual-compounding figure. This page uses annual compounding and says so; for monthly schedules, adjust the rate and periods accordingly.
Only if the future amount is negative (a future payment you must make). A future receipt always discounts to a positive present value. If you are valuing a future liability, enter it as a positive amount and read the result as the amount to set aside today.
Results are estimates only and do not constitute professional advice.