Effective Annual Rate from Nominal Calculator
Convert a nominal (stated) annual interest rate into the effective annual rate given how often it compounds — the true yearly cost or yield.
How it works
EAR = (1 + i/m)^m − 1 · where i = nominal rate, m = periods per year
The nominal (stated) rate ignores compounding within the year, so it understates the real cost of a loan or the real yield of a deposit. The effective annual rate rolls the intra-year compounding into a single yearly figure you can compare across products. The more often interest compounds, the larger the gap between the nominal rate and the EAR.
Worked example
At a 6% nominal rate compounded monthly, EAR = (1 + 0.06/12)^12 − 1 = 1.005^12 − 1 = 0.061678, or 6.1678% — about 0.17 percentage points above the stated 6%.
Sources: Effective interest rate — Wikipedia
Frequently asked questions
What is the difference between nominal rate and EAR?
The nominal rate is the headline annual rate before compounding is counted; the effective annual rate (EAR) folds in how often interest is added within the year, so it reflects the true annual cost or yield. Only when interest compounds once a year are the two equal.
Does more frequent compounding always raise the EAR?
Yes, for a fixed nominal rate, moving from annual to monthly to daily compounding increases the EAR, but with diminishing returns. In the limit of continuous compounding the EAR reaches e^i − 1.
Is EAR the same as APY?
For savings products APY is defined the same way as EAR, so the two numbers match. On the borrowing side APR is usually a nominal rate, which is why comparing an APR to an APY without converting can be misleading.
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Educational financial-math tool, not investment or financial advice.