What is the Effective Interest Rate?
The effective interest rate (EIR), also known as the effective annual rate (EAR) or annual equivalent rate (AER), is the actual interest rate earned or paid on a loan or investment once the effect of compounding is taken into account. Unlike the nominal rate, the EIR captures the true cost of borrowing or the true return on investment.
The Effective Interest Rate Formula
For regular (periodic) compounding, the effective interest rate is calculated as:
Where:
- EIR — Effective interest rate (as a decimal)
- r — Nominal (stated) annual interest rate (as a decimal)
- m — Number of compounding periods per year
For continuous compounding, the formula becomes:
where e ≈ 2.71828 is Euler's number.
Nominal vs. Effective Interest Rate
The nominal interest rate (also called the stated, quoted, or annual percentage rate) is the rate advertised by a bank or lender. It does not account for how often interest is compounded within a year.
The effective interest rate tells you what you actually earn or pay, accounting for compounding. The more frequent the compounding, the higher the effective rate relative to the nominal rate.
Example: 12% Nominal Rate
| Compounding | Periods (m) | EIR |
|---|---|---|
| Annual | 1 | 12.0000% |
| Semi-annual | 2 | 12.3600% |
| Quarterly | 4 | 12.5509% |
| Monthly | 12 | 12.6825% |
| Weekly | 52 | 12.7341% |
| Daily | 365 | 12.7475% |
| Continuous | ∞ | 12.7497% |
How to Use This Effective Interest Rate Calculator
- Annual interest rate — Enter the nominal (stated) annual rate in percent.
- Compounding frequency — Select how often interest is compounded: daily, weekly, monthly, quarterly, semi-annual, annual, or continuous.
- Currency — Choose your currency (optional, used for balance calculations).
- Initial balance (optional) — Enter a starting amount to calculate the future value.
- Term (optional) — Enter the number of years to compute the final balance.
Click Calculate to instantly see the effective interest rate, periodic rate, and the future value of your investment or loan balance.
Measurement Systems
This calculator supports both the American (Imperial) system (feet, miles, inches) and the Metric system (meters, kilometers, centimeters) for any related dimensional inputs. All monetary values are shown in your selected currency, with the Russian Ruble (₽) and US Dollar ($) featured prominently alongside 23 other world currencies.
Frequently Asked Questions
What is the effective interest rate of 12% compounded monthly?
EIR = (1 + 0.12/12)12 − 1 = (1.01)12 − 1 ≈ 12.6825%
Why is the EIR always ≥ the nominal rate?
Because compounding means interest earns interest. When compounding occurs more than once a year, the effective rate is always higher than the nominal rate. They are equal only when compounding is annual (m = 1).
What is the difference between APR and EIR?
APR (Annual Percentage Rate) is a nominal rate that may include fees but typically does not reflect compounding within the year. EIR (Effective Interest Rate) always accounts for the compounding frequency and represents the true annual cost or yield.
When does continuous compounding apply?
Continuous compounding is a theoretical limit where interest is compounded infinitely often. It is rarely used in practice but appears in advanced finance, options pricing (Black-Scholes), and theoretical economics.