What is the Effective Annual Rate (EAR)?
The Effective Annual Rate (EAR) — also called Annual Percentage Yield (APY) — is the actual annual interest rate earned or paid on an investment or loan, accounting for the effect of compounding. It is the most accurate measure of the true cost or return of a financial product.
Unlike the Nominal Annual Rate (NAR), which simply divides annual interest across periods, the EAR reflects what really happens when interest is added to the principal each period.
EAR Formula
EAR = (1 + r/n)ⁿ - 1
Where:
- r = Nominal annual rate (as a decimal, e.g. 0.12 for 12%)
- n = Number of compounding periods per year
| Frequency | n (periods/year) | |---|---| | Daily | 365 | | Weekly | 52 | | Monthly | 12 | | Quarterly | 4 | | Semi-annual | 2 | | Annual | 1 |
Example: NAR = 12%, monthly compounding (n=12):
EAR = (1 + 0.12/12)¹² - 1 = (1.01)¹² - 1 = 12.68%
This means that even though the bank advertises 12% nominal, you actually pay or earn 12.68% annually.
Nominal Rate vs EAR: Which Matters More?
| Feature | Nominal Rate | EAR | |---|---|---| | What it is | Advertised rate | Real rate | | Compounding | Not included | Included | | Comparability | Difficult across products | Direct and fair | | Use | Bank marketing | True comparison |
Golden rule: When comparing loans, credit cards, or investments, always compare the EAR, not the nominal rate.
Monthly Equivalent Rate
From the EAR, you can find the monthly rate that produces the same annual result:
Monthly rate = (1 + EAR)^(1/12) - 1
This rate is useful for calculating monthly loan or deposit payments.
When to Use This Calculator
Use the EAR calculator when you need to:
- Compare two loans with different nominal rates or compounding frequencies
- Understand the true return on a fixed-term deposit
- Calculate the real cost of a credit card
- Verify whether the rate you're being offered is competitive
- Convert between nominal and effective rates for financial analysis