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Effective Annual Rate From Nominal Calculator

Work out effective annual rate from nominal instantly with clear inputs, formula shown and shareable results.

About Effective Annual Rate From Nominal Calculator

A nominal rate ignores the fact that interest credited part-way through the year itself earns interest. The effective annual rate (EAR) restates the nominal rate as the single yearly rate that produces the same growth, so quotes with different compounding frequencies become comparable.

Formula

Effective annual rate

EAR = (1 + i/m)^m - 1

i
Nominal annual rate
m
Compounding periods per year

Worked example

With the default values below, Effective Annual Rate From Nominal Calculator returns Effective Annual Rate of 12.6825%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Nominal Annual Rateaccepts 0–100 %
12 %
Compounding Periods Per Yearaccepts 1–365
12

Results

Effective Annual Rate
12.6825%
Rate Per Compounding Period
1.000000%
Rate If Compounded Continuously
12.7497%
EAR Above Nominal
0.6825%

Step by step

  1. 1Values used
  2. 2Effective annual rate
  3. 3Effective Annual Rate= 12.6825
  4. 4Rate Per Compounding Period= 1.000000
  5. 5Rate If Compounded Continuously= 12.7497
  6. 6EAR Above Nominal= 0.6825

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax or fees or charges into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why is EAR higher than the nominal rate?

Because interest paid early in the year compounds for the remaining months. The more frequent the compounding, the wider the gap.

What happens as compounding gets more frequent?

EAR rises but converges to the continuous limit e^i - 1, so monthly to daily makes far less difference than annual to monthly.

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