Effective Annual Rate (EAR)
Converts a nominal annual rate with periodic compounding to an effective annual rate.
When to use: Use to compare rates with different compounding frequencies on an equal basis.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| EAR | Effective Annual Rate | True annual return accounting for compounding | % |
| k | Nominal Rate | Stated annual rate (APR) | % |
| m | Periods/Year | Compounding frequency | integer |
Real-Life Examples
Example 1: Credit Card Rate
A credit card charges 18% APR compounded monthly. What is the true annual cost?
Given
Step-by-Step
The true annual cost is 19.56%, significantly higher than the stated 18%.
Example 2: Savings Account Comparison
Bank A offers 4.8% compounded daily (365). What is the EAR?
Given
Step-by-Step
Daily compounding boosts the effective rate from 4.80% to 4.92%.
Frequently Asked Questions
Convert each rate to its effective annual rate (EAR) using this formula. The EAR accounts for compounding differences, letting you directly compare a 5% rate compounded monthly with a 5.1% rate compounded quarterly, for example.
Because interest earned during the year starts earning its own interest within the same year. This intra-year compounding effect generates additional returns beyond the stated rate, making the effective rate higher.
The impact depends on the rate level. At 5% APR: annual gives 5% EAR, monthly gives 5.12%, daily gives 5.13%. At 18% APR (like credit cards): annual gives 18%, monthly gives 19.56%, daily gives 19.72%. Higher rates amplify the compounding effect.
The truth-in-lending APR is the nominal annual rate lenders must disclose, but it understates the true cost when compounding is more frequent than annual. The EAR shows the real annual cost. Credit cards quoting 18% APR actually cost about 19.56% per year.