Discount Rate Calculator
Work with the rate that connects money today to money later. In rate mode, enter present value and future value in dollars plus the number of periods to solve the implied discount rate; in present-value mode, enter a rate per period as a percent to discount a future amount back to today.
Example: with What to solve for Discount rate (from PV and FV) · Future value ($) 10000 · Present value ($) — rate mode 7500 · Discount rate (%/period) — PV mode 8 · Number of periods (years) 5 → Result: 5.92% per period.
- Discount factor (PV ÷ FV)0.7500
- Total discount (FV − PV)$2,500.00
- A future dollar is worth75.0 cents on the dollar today, 5 periods out
Computed by the calculator below using its default values. Change any input to see your own numbers.
r = (FV ÷ PV)^(1/n) − 1 with one compounding per period; going the other way, PV = FV ÷ (1 + r)^n. State the period (year, quarter, month) and keep r matched to it.
What a discount rate is
A discount rate is compound interest run in reverse: instead of asking what $7,500 grows into, it asks what rate makes $10,000 five years from now equivalent to $7,500 today. Solving (10,000 ÷ 7,500)^(1/5) − 1 gives 5.92% per year — accept a lower return elsewhere and the future money is the better deal; earn a higher one and the money today wins.
In valuation work the logic reverses: you choose the rate first — a hurdle rate, a cost of capital, an opportunity cost — and use it to shrink future cash flows to present value. Both directions are the same identity, PV × (1 + r)^n = FV, and this calculator solves it either way.
Choosing a rate when you need one
There is no universal number. Companies discount projects at their weighted average cost of capital; investors often use the return of the next-best alternative; conservative planning for safe cash flows can use Treasury yields. The higher the risk of the future cash, the higher the rate — and because the factor compounds, small changes swing long-dated values hard: at 20 years out, moving from 3% to 8% cuts a future dollar's present value from about 55 cents to 21 cents.
How it’s calculated
Rate mode solves r = (FV ÷ PV)^(1/n) − 1, the per-period compound rate that grows PV to FV in n periods (one compounding per period). PV mode computes PV = FV ÷ (1 + r)^n. Discount factor = PV ÷ FV = 1 ÷ (1 + r)^n; total discount = FV − PV. Periods can be years, quarters, or months as long as the rate is per that same period.
Single lump sum, constant rate, and discrete per-period compounding — streams of payments need NPV or PVIFA, and results are pre-tax estimates.
Discount factors at common rates
| Periods out | At 3% | At 8% |
|---|---|---|
| 5 | 0.8626 | 0.6806 |
| 10 | 0.7441 | 0.4632 |
| 20 | 0.5537 | 0.2145 |
Computed with factor = 1 ÷ (1 + r)^n; multiply a future amount by the factor for its present value.
Common mistakes
- Confusing the rate with the factor — 8% per year for 5 years is a factor of 0.6806, not 0.92.
- Using an annual rate with monthly periods; divide the nominal annual rate by 12 or solve with n in years.
- Averaging instead of compounding: doubling in 10 years is 7.18% per year, not 10%, because growth compounds.
- Assuming this is the Federal Reserve's discount rate — that is the rate banks pay to borrow from the Fed, a different concept that shares the name.
Frequently asked questions
What is the discount rate formula?
Solving for the rate: r = (FV ÷ PV)^(1/n) − 1. Discounting instead: PV = FV ÷ (1 + r)^n. With $7,500 today and $10,000 in 5 years, r = (10,000 ÷ 7,500)^(1/5) − 1 = 5.92% per year.
What discount rate should I use?
Match it to the risk and your alternatives: a firm's WACC for corporate projects, an expected portfolio return for personal trade-offs, or a Treasury yield for near-certain cash flows. Test a range — long horizons are very sensitive to the choice.
Is this the same as the Fed's discount rate?
No — the Federal Reserve's discount rate is what banks pay to borrow at the Fed's discount window. In finance and valuation, a discount rate is the rate used to translate future cash into present value, which is what this calculator solves.
How does the discount rate relate to NPV and IRR?
NPV discounts every future cash flow at your chosen rate and sums them; IRR is the special rate that makes that sum exactly zero. This tool is the single-cash-flow version of the same machinery.
Can the solved rate be negative?
Yes — if the future value is smaller than the present value, the implied rate is negative, meaning the money shrinks. That shows up with fees, deflation-adjusted figures, or simply a bad deal.