Nominal and Effective Rate Calculator
Convert between annual nominal rates and effective annual rates based on compounding frequency.
Understanding Nominal vs. Effective Rates
The Nominal Annual Rate is the interest rate stated on a financial product, such as a credit card or savings account, before taking into account the effects of compounding within the year. It is often referred to as the Annual Percentage Rate (APR).
The Effective Annual Rate (EAR) represents the true rate of interest earned or paid over a year. It accounts for the power of compounding, where interest earned in one period starts earning interest itself in the next period. The more frequently interest compounds, the higher the effective rate becomes relative to the nominal rate.
The Mathematical Formula
To calculate the Effective Annual Rate from a Nominal Rate, use the following formula:
EAR = (1 + (r / n))^n – 1
- r = Nominal Annual Interest Rate (as a decimal)
- n = Number of compounding periods per year
Example Calculation
Suppose you have a nominal rate of 12% compounded monthly (n = 12):
- Convert the percentage to a decimal: 12% = 0.12
- Divide by periods: 0.12 / 12 = 0.01 (Periodic Rate)
- Add 1: 1 + 0.01 = 1.01
- Raise to the power of periods: (1.01)^12 ≈ 1.1268
- Subtract 1: 1.1268 – 1 = 0.1268
- Result: 12.68% is the Effective Annual Rate.
Why It Matters
When comparing financial products, always look at the effective rate. A loan with a 10% nominal rate compounded daily will actually cost you more than a loan with a 10% nominal rate compounded annually. This tool helps you see the impact of that frequency immediately.