Effective Annual Rate (EAR)
When compounding is annual, the effective annual rate equals the stated APR.
When to use: Use as a baseline — with annual compounding, nominal and effective rates are the same.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| EAR | Effective Annual Rate | True annual return | % |
| k | APR | Stated annual percentage rate | % |
Real-Life Examples
Example 1: Annual Compounding
A savings account states 5% APR with annual compounding. What is the EAR?
Given
Step-by-Step
With annual compounding, EAR equals APR at 5%.
Example 2: Annual Bond Yield
A bond yields 8% with annual compounding.
Given
Step-by-Step
The effective rate is 8%, same as stated.
Frequently Asked Questions
The effective annual rate is the actual annual return after accounting for compounding. When compounding is annual, EAR equals the stated APR because interest is compounded only once per year — there is no intra-year compounding effect.
With annual compounding, interest is added once at year-end, so there is no additional compounding within the year to create an effective rate higher than the stated rate. The stated rate and effective rate are identical.
This formula serves as a baseline reference. Use it to confirm that with annual compounding, no adjustment is needed. For other compounding frequencies, use the m-times or continuous EAR formulas to find the true annual rate.