Discount Rate Calculator
Back out the implied annual discount rate from present value, future value, periods and compounding frequency.
Input Data
Results
At a glance:The discount rate is the annual rate used to convert a future cash flow into today's value, reflecting the time value of money and risk. Discrete: annualized DR = [(FV/PV)^(1/(m*t)) - 1] x m; continuous: DR = ln(FV/PV) / t. A higher discount rate makes a future amount worth less today. WARNING: It can be negative when FV < PV (value shrinks); results are estimates excluding fees and taxes.
Formula
Discrete: per-period rate = (FV/PV)^(1/(m·t)) − 1; annual = per-period × m.
Continuous: DR = ln(FV/PV) / t.
How to Use
- Enter today's present value and the future value at maturity.
- Enter the number of years and the compounding frequency (continuous optional).
- View the annualized and per-period discount rates.
FAQ
What is a discount rate?
It is the annual rate used to discount a future cash flow to its present value, reflecting the time value of money and risk. The higher it is, the less a future amount is worth today.
Annual vs per-period discount rate?
The per-period rate applies to one compounding interval (e.g. a month); the annualized rate multiplies it by the number of periods per year so it can be compared with other annual rates.
Can the discount rate be negative?
Yes. When the future value is below the present value (the money shrinks over time), the implied rate is negative — a sign of loss or negative real return after inflation. The formulas still compute it.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.