APR from EAR
Backs out the nominal APR equivalent of an effective annual rate at a given compounding frequency.
When to use: Use to find the stated rate a lender or product would quote at a given compounding frequency to match a target effective annual return.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| APR | Annual Percentage Rate | Nominal annual rate at the given compounding frequency | % |
| EAR | Effective Annual Rate | True annual return accounting for compounding | % |
| m | Periods/Year | Compounding frequency | integer |
Real-Life Examples
Example 1: Credit Card Disclosure
A card costs 19.56% effective annually with monthly compounding. What APR would the lender disclose?
Given
Step-by-Step
The disclosed APR is 18%, which is exactly the inverse of the EAR-from-APR example.
Example 2: Daily-Compounded Savings
A savings account yields 4.92% effective annually with daily (365) compounding. What is the nominal APR?
Given
Step-by-Step
A 4.92% EAR with daily compounding corresponds to a 4.80% nominal APR — recovering the original stated rate.
Frequently Asked Questions
Whenever you have an effective yield and need the equivalent nominal quote. Common cases: backing out a competitor lender's stated rate from disclosed effective costs, structuring a product to hit a target effective return at a chosen compounding cadence, or normalizing rates across products with different conventions.
Only if you choose the right m. Most US consumer credit (cards, auto loans) discloses APR with monthly compounding (m=12); most savings accounts use daily (m=365); some money-market products use simple-interest conventions that don't map directly. Match m to the product's convention.
TILA-required APRs are nominal annual rates assuming the loan's actual compounding cadence. Going from EAR back to TILA APR uses this formula with m matching the loan's billing/compounding period.