Discount Rate Calculator
The rate implied by two amounts, and the two conventions for it.
Work out Discount Rate. The rate implied by two amounts, and the two conventions for it. Flags the cases where the formula has no valid answer.
Implied discount rate
8.45%
turns $1,000 into $1,500 over 5 periods
At 8.45% money doubles every 8.5 periods. The rule of 72 estimates that as 8.5, which is close enough for mental arithmetic and drifts at higher rates.
How the Discount Rate Calculator works
Two questions share this name. One is what rate turns a price into a payoff over some number of periods, which is the compound growth rate read backwards. The other is a conversion nobody expects to need until they meet it: a discount rate and an interest rate describe the same money against different bases, and the discount rate is always the smaller.
Also known as: discount rate to interest rate calculator · interest rate to discount rate calculator · find discount rate · implied discount rate calculator · annual discount rate calculator
Two questions with one name
The first is what rate turns one amount into another over some number of periods. That is the compound growth rate, and read backwards it is the discount rate a price implies about a payoff.
The second is a conversion most people meet only when something does not reconcile: an interest rate and a discount rate can describe the identical transaction against different bases.
Interest is charged on the money advanced. A discount is deducted from the money repaid. So d = i ÷ (1 + i), and the discount rate is always the smaller of the pair.
In practice
Turning $1,000 into $1,500 over five periods implies 8.4472% — the fifth root of 1.5, less one.
At that rate money doubles every 8.55 periods. The rule of 72 estimates 8.52, which is close enough for mental arithmetic and drifts upward as rates rise.
For the conversion: a 10% interest rate is a 9.0909% discount rate. Same money, same term, different denominator. Convert back and you get exactly 10% again.
The gap widens quickly. At 25% interest the equivalent discount rate is 20%; at 50% it is 33.3%. Anywhere a rate is quoted on the discount basis, the borrower is paying more than the number suggests.
What this is not
It is not the Federal Reserve discount rate, which is the rate at which banks borrow from the central bank. That is a named policy rate that happens to share the word, and nothing here computes or predicts it.
It is also not a retail discount. Taking 20% off a price and discounting a cash flow at 20% are unrelated operations that English unhelpfully gives one name — this site keeps them in separate clusters for that reason.
And an implied rate is not a forecast. It describes the relationship between two numbers you already have; it says nothing about whether the later one will materialise.
Where the figure deceives
An implied rate over a long horizon flattens everything that happened in between. A price that trebled with a crash in the middle produces the same implied rate as one that rose smoothly, and the two are not the same investment.
The rate is also per period, and the period has to match the cash flows. Feeding annual amounts and monthly periods into the same calculation is a common and large error.
For a business, the honest answer to what discount rate to use is the cost of capital, adjusted for project risk. Any rate chosen because it produces an acceptable answer is a decision dressed as an input.
Acting on it
Match the period to the cash flows before anything else — annual with annual, monthly with monthly.
When someone quotes a rate on an instrument where interest comes off the top, convert it before comparing against an ordinary loan.
For company decisions, derive the rate from WACC rather than picking one. A rate chosen to justify a project is not an input, it is a conclusion.
Not financial advice. This calculator is for planning and illustration, not financial advice. Real products carry fees, taxes, and terms it does not model. Confirm figures with your lender or a qualified adviser before committing.
Frequently asked questions
How do I find the discount rate between two amounts?
Take the ratio of future to present, raise it to one over the number of periods, and subtract one. Doubling in ten years implies 7.18%, which is where the rule of 72 comes from.
What is the difference between a discount rate and an interest rate?
An interest rate is charged on the money advanced; a discount rate is deducted from the money repaid. So d = i / (1 + i): a 10% interest rate is a 9.09% discount rate, describing an identical transaction.
Which is bigger?
The interest rate, always, for the same transaction. That is precisely why quoting the discount rate makes a loan sound cheaper, and why the convention persists on instruments where interest is taken up front.
Is this the same as the Federal Reserve discount rate?
No. That is the rate at which banks borrow from the central bank — a named policy rate that happens to share the word. Nothing here computes or predicts it.
What discount rate should a business use?
Its weighted average cost of capital, adjusted upward for projects riskier than the business as a whole. There is no rate that is correct independent of who is investing.
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