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EAR Calculator

Convert a nominal APR and compounding frequency into an effective annual rate (EAR).

What this tool does

Convert a nominal APR and compounding frequency into an effective annual rate (EAR). You fill in these fields: Nominal APR and Compounding frequency. It shows effective annual rate and periodic rate.

Inputs

  • Nominal APR (%): A number. Must be greater than -100. The stated annual rate before compounding, as a percentage.
  • Compounding frequency: Choose one: Annually (1), Semiannually (2), Quarterly (4), Monthly (12), Weekly (52), Daily (365). Starts as Monthly (12).

How to use

  1. Enter the nominal APR as a percentage.
  2. Choose an option for "Compounding frequency".
  3. Read the result: effective annual rate and periodic rate. It appears once every required field has a valid value.

Worked examples

Example 1. Inputs:

  • Nominal APR: 12%
  • Compounding frequency: Monthly (12)

Results:

  • Effective annual rate: 12.683% (EAR = (1 + APR / n)^n - 1)
  • Periodic rate: 1.000% (Rate applied at each compounding period)

How this is worked out: Monthly periodic rate = 12 / 12 = 1 percent. EAR = (1.01)^12 - 1. 1.01^2 = 1.0201, 1.01^4 = 1.04060401, 1.01^8 = 1.0828567056, 1.01^12 = 1.0828567056 × 1.04060401 = 1.126825030. EAR = 12.6825030 percent.

Example 2. Inputs:

  • Nominal APR: 5%
  • Compounding frequency: Annually (1)

Results:

  • Effective annual rate: 5.000% (EAR = (1 + APR / n)^n - 1)
  • Periodic rate: 5.000% (Rate applied at each compounding period)

How this is worked out: With one compounding period a year the EAR equals the nominal rate: (1 + 0.05)^1 - 1 = 0.05 = 5 percent. Periodic rate = 5 / 1 = 5 percent.

Example 3. Inputs:

  • Nominal APR: 8%
  • Compounding frequency: Quarterly (4)

Results:

  • Effective annual rate: 8.243% (EAR = (1 + APR / n)^n - 1)
  • Periodic rate: 2.000% (Rate applied at each compounding period)

How this is worked out: Quarterly periodic rate = 8 / 4 = 2 percent = 0.02. EAR = 1.02^4 - 1. 1.02^2 = 1.0404, 1.0404^2 = 1.08243216. EAR = 0.08243216 = 8.243216 percent.

Example 4. Inputs:

  • Nominal APR: 10%
  • Compounding frequency: Daily (365)

Results:

  • Effective annual rate: 10.516% (EAR = (1 + APR / n)^n - 1)
  • Periodic rate: 0.027% (Rate applied at each compounding period)

How this is worked out: Daily periodic rate = 10 / 365 = 0.0273972603 percent. EAR = (1 + 0.1/365)^365 - 1. ln(1 + 0.000273972603) = 0.000273972603 - 0.0000000375305 + 0.0000000000069 = 0.000273935079. Times 365 = 0.0999863039. e^0.0999863039 = 1.10517091808 × e^-0.0000136961 = 1.10517091808 × 0.99998630396 = 1.10515578. EAR = 0.10515578 = 10.515578 percent.

Limitations

  • Assumes the nominal rate stays the same for the whole year.
  • Uses only the nominal rate and the compounding frequency. Fees and taxes are not included.
  • Results are for one year. The tool does not model partial years or irregular compounding.

FAQs

Q: What is the difference between APR and EAR?
A: APR is the stated annual rate without compounding. EAR includes the effect of interest being added to the balance during the year, so it is the true yearly rate.
Q: Does more frequent compounding always raise the EAR?
A: Yes, for any positive rate. The same nominal rate gives a higher EAR when interest is added more often, because each addition earns interest too.
Q: Can I enter a negative rate?
A: Yes, as long as it is above -100 percent. A negative rate gives a negative EAR.
Q: Does this include fees?
A: No. Only the nominal rate and the compounding frequency are used, so fees and other charges are not included.

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