Effective Interest Rate (EIR) Calculator
Convert a nominal interest rate to the effective annual interest rate (EAR) by accounting for the number of compounding periods per year.
How to use this tool
- Enter nominal interest rate and compounding periods per year in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your effective annual rate (ear) and the full breakdown beneath it.
⚠ This tool provides general estimates for education only and is not financial, tax or legal advice. Figures may not reflect your situation — verify with a qualified professional.
Formula
EIR = (1 + r/n)n − 1
Where r is the nominal annual interest rate (as a decimal), and n is the number of compounding periods per year.
How it works
The effective interest rate (also called effective annual rate or EAR) converts a nominal rate with intra-year compounding into an equivalent annual rate. For example, a 12% nominal rate compounded monthly is not the same as 12% compounded annually — the monthly compounding generates interest on interest within the year, yielding a higher effective rate. This calculator lets you compare rates across different compounding frequencies on an apples-to-apples basis.
Worked example
12% Nominal Rate Compounded Monthly
- Inputs: Nominal rate = 12% = 0.12, Compounding periods = 12 (monthly)
- Periodic rate = 0.12 / 12 = 0.01 (1% per month)
- Growth factor = (1 + 0.01)^12 = (1.01)^12 = 1.126825
- EIR = 1.126825 − 1 = 0.126825 = 12.6825%
Effective Annual Rate = 12.6825%, which is higher than the nominal 12% due to monthly compounding.
Common mistakes to avoid
- Entering the nominal rate as a whole number (e.g., 5) rather than a decimal (0.05) — the formula EIR = (1 + r/n)^n - 1 requires r as a decimal.
- Assuming EIR equals APR — APR is the nominal rate, EIR is the effective rate after compounding; they differ whenever n > 1.
- Using a 360-day year (banker's convention) for n when the product compounds on a 365-day basis, causing a slight understatement of the true EIR.
Key terms
- What is the effective interest rate?
- The effective interest rate (EIR) is the actual annual return on a loan or investment, accounting for intra-year compounding. It is always equal to or greater than the nominal rate.
- What is the difference between nominal and effective rate?
- The nominal rate is the stated annual rate without considering compounding frequency. The effective rate accounts for compounding within the year, making it the true cost or yield.
- What does APY mean?
- Annual Percentage Yield (APY) is another name for the effective annual rate, commonly used in banking to express savings account returns after accounting for compounding.
- When does EIR equal the nominal rate?
- When compounding occurs once per year (n=1), EIR equals the nominal rate. More frequent compounding always increases the effective rate above the nominal rate.
Frequently asked questions
- What compounding period should I use for a credit card?
- Most credit cards compound daily, so use n = 365. This is why a 20% APR credit card has an EIR of about 22.1%.
- Is a higher compounding frequency always worse for borrowers?
- Yes, for the same nominal rate, more frequent compounding increases the EIR and therefore the total interest paid by the borrower.
- How does continuous compounding relate to EIR?
- As n approaches infinity, EIR approaches e^r - 1 (where e is Euler's number). Continuous compounding represents the theoretical upper bound on the EIR for a given nominal rate.