APR from EAR
When compounding is annual, the nominal annual percentage rate equals the effective annual rate.
When to use: Use as a baseline — with annual compounding, no intra-year compounding occurs so the stated APR equals the realized EAR.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| APR | Annual Percentage Rate | Nominal annual rate | % |
| EAR | Effective Annual Rate | True annual return | % |
Real-Life Examples
Example 1: Annual Compounding
A bond yields 5% effective annually. With annual compounding, what nominal APR is implied?
Given
Step-by-Step
With annual compounding, APR equals EAR at 5%.
Example 2: Effective to Nominal
An investment realizes an 8% effective annual return with no intra-year compounding.
Given
Step-by-Step
The implied nominal rate is 8%, identical to the effective rate.
Frequently Asked Questions
Only when compounding is annual. With any intra-year compounding (monthly, daily, continuous), the EAR is higher than the APR because of within-year compounding effects.
Lender disclosures and bond quotes often use APR (nominal). If you have the realized effective yield, this formula gives you the equivalent stated rate at a chosen compounding frequency — useful for comparing quotes across products.
Only if compounding frequency is also disclosed. APR alone is incomplete — a 12% APR compounded monthly costs more than a 12% APR compounded annually. Always pair APR with m, or convert to EAR.