APR Calculator

A 12% nominal rate compounded monthly has a periodic rate of 1% and an effective annual rate of 12.6825030132%.

How it works

• Read the nominal annual rate and the compounding frequency.
• Divided the nominal rate by the number of compounding periods for the periodic rate.
• Compounded the periodic rate over a year to obtain the effective annual rate (or used the continuous limit e^r − 1).

effective = (1 + 12/100/12)^12 − 1 = 0.126825030132

• A regulated APR can include lender fees and points that this conversion does not know about.
• This is an illustration for information only, not financial advice.

Methodology

1. Divide the nominal annual rate by the number of compounding periods per year to get the periodic rate.
2. Compound the periodic rate over one year: effective = (1 + nominal/(100·n))^n − 1.
3. For continuous compounding, use the limit effective = e^(nominal/100) − 1.
4. Round the result to 12 significant digits.

Usage

1. Enter the nominal annual rate as a percentage.
2. Choose the compounding frequency.
3. Read the periodic rate and the effective annual rate with the formula used.

Examples

These are examples, not current values: they use fixed inputs, while the interactive tool computes live results in your browser.

12% compounded monthly

{
  "nominalRatePercent": 12,
  "compounding": "monthly"
}

5% compounded annually

{
  "nominalRatePercent": 5,
  "compounding": "annually"
}

10% compounded continuously

{
  "nominalRatePercent": 10,
  "compounding": "continuous"
}

Limitations

APR versus effective annual rate

In everyday usage 'APR' sometimes means the nominal rate and sometimes the regulated annual percentage rate. This page uses 'APR' as a nominal annual rate and reports its effective annual equivalent. That conversion ignores one-off fees and points, so it is not the regulated APR a lender must disclose.