What is Effective Annual Rate (EAR)?
The Effective Annual Rate (EAR), also known as the Annual Equivalent Rate (AER) or Effective Annual Interest Rate, is the actual annual interest rate that accounts for the effect of compounding. Unlike the stated Annual Percentage Rate (APR), EAR reflects what you'll truly pay on a loan or earn on an investment when interest compounds more than once per year.
Understanding EAR is crucial for making informed financial decisions because the same nominal APR can result in very different actual costs or returns depending on how frequently interest compounds.
Where:
- EAR = Effective Annual Rate
- APR = Annual Percentage Rate (stated/nominal rate)
- n = Number of compounding periods per year
For Continuous Compounding
When interest compounds continuously (infinite compounding periods), the formula becomes:
Where e is Euler's number (approximately 2.71828).
APR vs EAR: Understanding the Difference
The Annual Percentage Rate (APR) and Effective Annual Rate (EAR) are related but measure different things:
| Feature | APR | EAR |
|---|---|---|
| Also called | Nominal rate, Stated rate | Effective rate, True rate, AER |
| Accounts for compounding | No | Yes |
| Used for comparison | Different loan products | True cost/return comparison |
| Legally required disclosure | Yes (US loans) | Yes (UK/EU savings) |
| Always equal to EAR when | Compounding is annual (n=1) | |
Key Insight
EAR is always greater than or equal to APR. The more frequently interest compounds, the larger the difference between EAR and APR. This is why credit cards (which compound daily) can cost significantly more than the stated APR suggests.
How Compounding Frequency Affects EAR
Let's see how a 12% APR translates to different EARs based on compounding frequency:
| Compounding | Periods (n) | EAR | Extra vs APR |
|---|---|---|---|
| Annually | 1 | 12.00% | 0.00% |
| Semi-annually | 2 | 12.36% | +0.36% |
| Quarterly | 4 | 12.55% | +0.55% |
| Monthly | 12 | 12.68% | +0.68% |
| Daily | 365 | 12.75% | +0.75% |
| Continuous | Infinite | 12.75% | +0.75% |
Why EAR Matters
For Borrowers
Understanding EAR helps you:
- Compare loans accurately - Two loans with the same APR but different compounding can have different true costs
- Understand credit card costs - Credit cards compound daily, making them more expensive than APR suggests
- Make informed decisions - Choose the loan with the lowest EAR, not just the lowest APR
For Investors
EAR helps you:
- Compare investments - CDs and savings accounts with the same rate but different compounding yield different returns
- Calculate true returns - Know exactly how much your investment will grow
- Choose better products - Select accounts with more frequent compounding for higher returns
How to Calculate EAR Step by Step
Let's calculate EAR for a 12% APR with monthly compounding:
- Identify the variables:
- APR = 12% = 0.12
- n = 12 (monthly compounding)
- Calculate periodic rate: APR/n = 0.12/12 = 0.01 (1% per month)
- Add 1: 1 + 0.01 = 1.01
- Raise to power n: 1.0112 = 1.1268
- Subtract 1: 1.1268 - 1 = 0.1268
- Convert to percentage: 0.1268 × 100 = 12.68% EAR
Converting EAR to APR
To find the APR from a known EAR:
This is useful when you know the effective rate and want to find the equivalent nominal rate for a specific compounding frequency.
Real-World Applications
Credit Cards
Credit cards typically compound daily. A card advertising 18% APR actually has an EAR of about 19.72%. On a $5,000 balance, this difference means paying approximately $86 more per year than the APR would suggest.
Mortgages
Most mortgages compound monthly. A 6% APR mortgage has an EAR of 6.17%. While this seems small, on a $300,000 mortgage, it represents thousands of dollars over the loan's lifetime.
Savings Accounts
High-yield savings accounts often compound daily. A 4% APY (which is actually the EAR) with daily compounding corresponds to an APR of about 3.92%. The bank uses daily compounding to offer a higher effective rate.
Frequently Asked Questions
Is APR or EAR more important?
EAR is more important for understanding the true cost or return because it accounts for compounding. However, APR is what's typically advertised and legally required on loan disclosures in the US. Always calculate or compare EARs when making financial decisions.
Why do banks use APR instead of EAR?
For loans, APR is required by law (Truth in Lending Act in the US) and is simpler to understand. It also makes rates look lower than the effective rate. For savings, banks often advertise APY (which is EAR) because it makes their rates look more attractive.
What's the maximum EAR can be for a given APR?
The maximum EAR occurs with continuous compounding. For any APR, the maximum EAR = eAPR - 1. For a 10% APR, the maximum EAR with continuous compounding is 10.52%.
Does more frequent compounding always benefit the borrower?
No, more frequent compounding increases the effective rate, which benefits lenders (for loans) and depositors (for savings). Borrowers should look for less frequent compounding to minimize costs.
How do I convert monthly rate to EAR?
If you have a monthly rate (r), calculate EAR = (1 + r)12 - 1. For example, a 1% monthly rate gives EAR = (1.01)12 - 1 = 12.68%.