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Equivalent Rate Calculator

Restate an interest rate under a different compounding frequency without changing the real return.

Inputs
Rate conversionRates matched
Equivalent nominal rate12.682503%
Formula
Effective annual rateEAR = (1 + i/m)^m - 1
Re-quoted ratej = q x ((1 + EAR)^(1/q) - 1)
ContinuousEAR = e^i - 1 and i = ln(1 + EAR)
Inputs
Quoted rate12.0000%
Compounded now12 times a year (per month)
Wanted as1 time a year (per year)
Working
Effective annual rate12.682503%
Growth factor per year1.12682503
Re-quoted nominal rate12.682503%
Result
One unit grows to1.12682503
1,000 grows to in a year1,126.8250
ComparisonThe new quote is numerically higher for the same real return
Runs locally in your browser

About the Equivalent Rate Calculator

Two rates are equivalent when a deposit grows to the same amount after a year under both. A quote of 12 percent compounded monthly is not 12 percent of growth: each month adds one percent to a slightly larger base, so a year ends at 12.6825 percent. This tool moves a quote between yearly, half yearly, quarterly, monthly, weekly, daily and continuous compounding by passing through the effective annual rate.

The route is always the same. First the quoted nominal rate becomes an effective annual rate with EAR = (1 + i/m)^m - 1, where m is the number of compounding periods in the current quote. Then that effective rate is re-quoted at the target frequency with j = q x ((1 + EAR)^(1/q) - 1). Continuous compounding uses the exponential pair, so the effective rate is e^i - 1 and the nominal rate is the natural logarithm of one plus the effective rate.

This matters whenever offers are quoted on different terms. A savings account paying 6.2 percent compounded quarterly and a bond paying 6.3 percent paid annually are closer than they look, and the ranking can flip once both are on the same basis. Lenders also switch bases: a card quoting a monthly rate of 1.8 percent is really 23.87 percent a year. Use the FD Calculator to see the same effect as a cash amount on a deposit.

How to use

  1. Enter the quoted rate exactly as the bank or bond prospectus states it.
  2. Set the frequency it is compounded at right now.
  3. Choose the frequency you want it restated in, including continuous if you are pricing derivatives.
  4. Compare the effective annual rate line when you are ranking two offers.

Common questions

What is the difference between nominal and effective?
A nominal rate ignores compounding within the year. The effective rate includes it, so it is the number to compare offers with.
When is continuous compounding used?
Mostly in option pricing and academic finance, where the mathematics is cleaner. Retail products almost never compound continuously.
Does more frequent compounding always pay more?
For the same nominal rate, yes, but the gain shrinks fast. Moving from daily to continuous changes the yearly outcome by a rounding error.
Can I convert a negative rate?
Yes, negative quotes are accepted for the deposit rates seen in some markets, as long as the periodic factor stays above zero.