Effective annual rate (EAR) calculator

Enter a stated annual rate and how often it compounds. It gives the effective annual rate, and the equivalent stated rate at every other compounding frequency.

How it works

EAR = (1 + stated rate ÷ m)^m − 1

Continuous compounding: EAR = e^{stated rate} − 1

Here m is the number of compounding periods a year. More frequent compounding raises the EAR toward the continuous limit, which is its ceiling for a given stated rate.

A worked example

A stated rate of 12% compounded monthly earns 1% a month. After a year that is 1.01¹² − 1 = 12.6825%, more than the stated 12% because interest is earned on interest. Compounded continuously the same stated rate gives e^0.12 − 1 = 12.7497%.

Common mistakes on the exam

• Compare rates only on the same basis. A 6% stated rate compounded monthly is not the same as 6% compounded annually.
• To go from an EAR back to a stated rate, take the m-th root first: m × [(1 + EAR)^1/m − 1].
• Continuous compounding uses e^r, and the continuous rate is the natural log of (1 + EAR).

The exam allows only certain calculator models, and the rules change: check CFA Institute's current calculator policy before you rely on any keystroke here.

Where this is taught

• Restate a yield at a different compounding frequency CFA Level I · Fixed Income
• Work out a holding period return and explain what it means CFA Level I · Quantitative Methods
• Contrast a stated annual rate with the effective annual rate CFA Level I · Quantitative Methods
• Explain continuous compounding and the lognormal distribution CFA Level I · Quantitative Methods

Read the guide

• Effective annual rate and compounding: comparing rates properly

Practise what you read

• Today's practice question One question, with every wrong option explained.
• Free Level I diagnostic test Twelve questions that show which topics to start with.
• Free finance calculators Check your arithmetic on the exam's core formulas.

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