The discount rate is the rate at which future money is converted into today's money. Enter any three of present value, future value, term, and rate below, and the calculator returns the missing one.
It also splits the answer three ways. The nominal annual rate is the one usually quoted. The periodic rate is what actually gets applied at each compounding step. The effective annual rate is what you truly earn or pay once compounding is accounted for, and it is the only one of the three that is comparable across different compounding frequencies.
What a discount rate actually is
Money available today is worth more than the same amount later, for three separate reasons: it can be put to work, prices rise, and the future payment might not arrive. The discount rate is the single percentage that bundles all three.
Applied forwards, it turns present value into future value. Applied backwards, it turns future value into present value. That second direction is the one that gets used in valuation, capital budgeting, and any decision involving cash arriving at different times.
One note on terminology, because the same phrase means two different things. In corporate finance, the discount rate is the rate used to bring future cash flows to present value. In monetary policy, the discount rate is the rate a central bank charges commercial banks for short-term borrowing. This calculator, and everything below, is about the first.
The discount rate formula
Starting from the relationship between the two values:
Future value = Present value × (1 + Rate ÷ m)^(m × Years)
Where m is the number of compounding periods per year. Rearranged to solve for the rate:
Periodic rate = (Future value ÷ Present value)^(1 ÷ (m × Years)) − 1
Nominal annual rate = Periodic rate × m
Effective annual rate = (1 + Periodic rate)^m − 1
And the two rearrangements that get used most often in practice:
Present value = Future value ÷ (1 + Rate ÷ m)^(m × Years)
Years = ln(Future value ÷ Present value) ÷ (m × ln(1 + Rate ÷ m))
Nominal, periodic, and effective
These three get treated as interchangeable and they are not.
Take $1,000 growing to $2,000 over ten years with monthly compounding. The periodic rate is 0.579% a month. Multiply by twelve and the nominal annual rate is 6.952%. But compound that monthly rate through a full year and the effective annual rate is 7.177%.
The gap between 6.952% and 7.177% is the compounding itself, and it widens with frequency. Two products quoted at the same nominal rate are not equivalent if one compounds monthly and the other yearly.
There is a neat consequence worth noticing. The effective annual rate here is simply the ratio of the two values raised to the power of one over the term: 2^(1/10) − 1 = 7.177%. It does not depend on the compounding frequency at all, because the start and end values already contain whatever compounding happened in between. This is why effective annual rate is the honest basis for comparison and nominal rate is not.
Three worked examples
Finding the implied rate. An investment doubles from $1,000 to $2,000 over ten years, compounded monthly.
Periodic rate = 2^(1 ÷ 120) − 1 = 0.579%
Nominal annual rate = 0.579% × 12 = 6.952%
Effective annual rate = 7.177%
Discounting a future amount. A contract will pay $500,000 in five years. At a 9% discount rate compounded yearly, what is it worth now?
Present value = $500,000 ÷ 1.09⁵ = $324,966
That is the most you should pay today for the right to receive $500,000 in five years, if 9% is genuinely your cost of capital. Pay more and the deal destroys value even though the headline number is larger than what you paid.
Finding the term. How long does $1,000 take to become $2,000 at 7% compounded yearly?
Years = ln(2) ÷ ln(1.07) = 10.24 years
How to choose a discount rate
The formula is arithmetic. Choosing the rate is judgment, and it is where valuations are won and lost.
Weighted average cost of capital. The standard choice for discounting a company's free cash flow, because that cash is owed to lenders and shareholders together.
Cost of equity. The right rate when the cash flows in question belong to shareholders alone.
Your own hurdle rate. For internal project appraisal, many companies set a rate above their cost of capital to reflect that management time is scarce and forecasts are optimistic.
A risk-free rate plus a risk premium. For one-off decisions, a government bond yield of matching duration plus an explicit premium for how uncertain the cash flow is.
The market rate for comparable risk. For anything with a traded equivalent, the rate at which similar cash flows actually change hands.
The consistent principle is that the rate should match the riskiness of the specific cash flow being discounted, not the average riskiness of the business doing the discounting. Discounting a safe contracted payment and a speculative new product at the same rate misprices both.
How much the rate matters
The sensitivity is severe, and it compounds with time. Discounting $500,000 received in five years:
Discount rate | Present value |
|---|---|
5% | $391,763 |
7% | $356,493 |
9% | $324,966 |
11% | $296,725 |
13% | $271,379 |
A four point range that any two reasonable analysts might disagree over, say 7% against 11%, moves the answer by nearly $60,000, which is 18% of the middle value. Across the full span in the table it is $120,000. Over twenty years the same spread would move it by considerably more.
Two practical consequences. Always present a range rather than a point. And be suspicious of any valuation whose conclusion depends on a discount rate assumption you could argue either side of.
Where discount rates mislead
A single rate is applied to unlike cash flows. Contracted revenue and speculative upside do not carry the same risk and should not carry the same rate.
Real and nominal get mixed. If your cash flows are in today's money, the discount rate should exclude inflation. If they are in future money, it should include it. Mixing the two is one of the most common and least noticed modelling errors.
Nominal rates get compared across different compounding. Convert to effective annual before comparing anything.
Precision implies confidence. A rate quoted to two decimal places has the appearance of measurement and the substance of an estimate.
Risk gets counted twice. Applying a high discount rate to cash flows that have already been probability-weighted penalises the same uncertainty in two places.
Discount rate, interest rate, and rate of return
Term | What it describes | Direction |
|---|---|---|
Discount rate | The rate used to bring future money to today | Backwards |
Interest rate | The rate at which money grows or borrowing costs | Forwards |
Rate of return | What an investment actually delivered | Backwards looking |
Hurdle rate | The minimum return required to approve something | A decision rule |
Mathematically the first three are the same operation viewed from different ends. The distinction is one of purpose: a discount rate is chosen before the fact to value something, while a rate of return is measured after the fact to judge it.
Further reading from Revenue Memo
FAQs
How do I calculate the discount rate?
Divide the future value by the present value, raise the result to the power of one divided by the number of compounding periods, and subtract one. That gives the periodic rate. Multiply by the number of periods per year for the nominal annual rate. Going from $1,000 to $2,000 over ten years with monthly compounding gives 6.952% a year.
What is the difference between the nominal and effective discount rate?
The nominal rate is the periodic rate multiplied by the number of periods in a year, which ignores the fact that each period compounds on the last. The effective rate accounts for that compounding. A 6.952% nominal rate compounded monthly is an effective 7.177%.
Can the discount rate be negative?
Yes. If the future value is lower than the present value, the implied rate is negative. It means the money is expected to be worth less later than it is now, which happens with depreciating assets and with real rates during periods of high inflation.
What discount rate should I use?
Match the rate to the risk of the specific cash flow. Weighted average cost of capital is the standard for company cash flows, cost of equity for shareholder cash flows, and a risk-free rate plus a premium for one-off decisions. Whichever you choose, run the calculation at a range of rates rather than a single one.
What is the difference between a discount rate and an interest rate?
They describe the same relationship from opposite directions. An interest rate grows money forwards in time. A discount rate shrinks future money back to today. The arithmetic is identical, and the difference is which end you are standing at.
How do I calculate present value from a future value?
Divide the future value by one plus the rate, raised to the power of the number of periods. $500,000 received in five years, discounted at 9% a year, is worth $324,966 today.
Should the discount rate include inflation?
Only if your cash flows do. Nominal cash flows, which include expected price rises, must be discounted at a nominal rate. Real cash flows, expressed in today's money, must be discounted at a real rate that excludes inflation. Mixing the two overstates or understates the answer by the whole inflation assumption.