Irish Calculators
Saving & investing

Interest Rate Converter: Nominal, AER and APY

Convert rates between stated compounding conventions and calculate their periodic equivalents. A fee-inclusive APR or APRC does not by itself reveal a loan's contractual interest rate.

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How the calculation works

Nominal, effective and continuously compounded rates can describe the same annual growth using different conventions. This converter makes those conventions explicit before deriving the rate for a selected output period and illustrating interest on a constant balance.

Effective annual = (1+nominal/m)^m−1; periodic effective = (1+annual effective)^(1/p)−1; continuous annual growth = exp(rate)−1.

  1. Find annual effective growth

    A nominal rate is divided by its compounding count and compounded for a year. A continuous rate is converted with an exponential; an effective rate needs no conversion.

  2. Convert to the requested period

    Take the annual factor to the reciprocal of the output periods per year, then subtract one. This preserves the same annual compound growth.

  3. Apply an illustrative balance

    Multiply the constant entered balance by the output-period rate. This illustration is one period's interest, without repayments, fees or a changing balance.

Worked example: Check Annual effective rate

Sample inputs demonstrate the method. They are not a forecast or product offer.

The first example converts 12% nominal compounded monthly. A 1% monthly factor repeated twelve times produces an annual effective rate of approximately 12.682503%, exceeding the nominal 12% because interest compounds.

Known rate (%)
12
Known rate convention
Nominal annual, compounded m times
Compounding periods per year (m)
12
Output periods per year
12
Balance for one-period interest illustration
1000
Currency for all amounts
Euro (EUR)

Expected result

Annual effective rate
12.682503%
Worked example: Check Effective rate per output period

Sample inputs demonstrate the method. They are not a forecast or product offer.

Known rate (%)
21
Known rate convention
Annual effective (AER/APY)
Compounding periods per year (m)
2
Output periods per year
2
Balance for one-period interest illustration
1000
Currency for all amounts
Euro (EUR)

Expected result

Effective rate per output period
10%

Understanding your result

Matching effective annual rates represent matching mathematical accumulation, not necessarily equivalent products. Fees, tax, access restrictions and rate changes are absent from this conversion.

A regulated APR or APRC may include borrowing costs. Treating that figure as a nominal contractual rate can produce an incorrect monthly interest amount.

Questions you might have

What does the result include?

Convert nominal, annual effective and continuously compounded rates while keeping payment frequency explicit.

Which limits should I check?

Conversions describe mathematical compounding, not a regulated APR/APRC calculation.

Choosing the right inputs

Known rate convention
Identify how the known rate is quoted. A nominal rate needs a compounding frequency; an effective annual rate already includes one year's compounding.
Compounding periods per year (m)
For a nominal input, use the contractual number of compounds per year. This is separate from the frequency requested for the output.
Output periods per year
Choose how many output periods make one year. The corresponding periodic rate is derived from the annual growth factor.

Common mistakes to avoid

  • Do not divide an effective annual percentage by twelve and label the answer an exact monthly equivalent.
  • The currency selector does not translate the illustrative balance between currencies.

Assumptions to check

  • Conversions describe mathematical compounding, not a regulated APR/APRC calculation.
  • All calculations run on your device. Figures are scenarios based on your inputs, not investment recommendations.

Sources and method

Read our calculation and testing approach.