One-year rate that incorporates within-year compounding so rates quoted with different periodic conventions can be compared consistently.
The effective annual rate (EAR) is the one-year rate of growth or cost produced after all within-year compounding is included. It converts a periodic or nominal annual rate into a common annual basis, making rates with different compounding frequencies easier to compare. EAR usually reflects interest mechanics only; it does not automatically include fees, taxes, credit risk, or cash-flow differences.
EAR is also called the effective annual interest rate or annual effective rate in some finance texts. A regulated APR, APY, AER, or accounting effective interest rate can use related ideas but follows its own definition and should not be treated as an automatic synonym.
If \(r_{nom}\) is a nominal annual rate compounded \(m\) equal times per year:
where:
For a 12% nominal rate compounded monthly:
A GBP 10,000 balance with no transactions would grow to approximately GBP 11,268.25 over one year under those simplified assumptions.
If \(i_p\) is the rate for each of \(m\) equal periods:
This form is useful when the statement or contract gives the periodic interest rate directly.
If periodic rates vary during the year, one constant rate cannot represent the path. With period-specific rates \(i_1, i_2, \ldots, i_m\), the realized one-year factor is:
That calculation still needs adjustments when cash enters or leaves during the year because a return on a changing investment balance is not determined by rate multiplication alone.
Two one-year products have the same risk, currency, access, fees, and tax treatment for this simplified comparison.
| Product | Quoted rate | Compounding |
|---|---|---|
| A | 12.10% | Annually |
| B | 11.80% nominal | Monthly |
Product A compounds once, so:
For Product B:
Although Product B displays the lower nominal rate, its EAR is about 0.3596 percentage points higher.
On GBP 25,000 held for the full year with no cash flows:
The modeled difference is about GBP 89.89. If Product B charges a GBP 120 unavoidable fee not reflected in the EAR, Product A can still produce the better net result. EAR standardizes compounding; it does not replace a full cash-flow comparison.
For a 12% nominal annual rate and equal periods:
| Compounding frequency | Periodic rate | Approximate EAR |
|---|---|---|
| Annual | 12.0000% | 12.0000% |
| Semiannual | 6.0000% | 12.3600% |
| Quarterly | 3.0000% | 12.5509% |
| Monthly | 1.0000% | 12.6825% |
| Daily, 365 | 0.03288% | 12.7475% |
These values assume the nominal quote is convertible at the stated frequency and that the balance remains invested. Crediting frequency, withdrawals, rounding, and contract terms can alter actual earnings.
| Measure | Main purpose | Does it reflect compounding? | Fees included automatically? |
|---|---|---|---|
| EAR | Mathematical one-year equivalent | Yes | No |
| APR | Annualized borrowing-cost disclosure | Depends on product rules and quotation | Specified finance charges, not necessarily every fee |
| APY | U.S. deposit-yield disclosure | Yes | Based on prescribed deposit rules rather than a generic fee-inclusive return |
| AER | Annualized savings comparison in markets using that label | Yes | Follow the applicable disclosure convention |
The mathematical EAR formula can match a disclosed yield in a simple fixed-rate case. That does not make every EAR a compliant APY or AER disclosure.
Use a fuller model when a product has:
For investment performance, money-weighted and time-weighted returns answer different questions. EAR should not be attached to a multi-cash-flow return without identifying the method.
This page provides general financial education, not legal, lending, deposit, tax, accounting, investment, or personalized financial advice. Product disclosures and jurisdiction-specific calculation rules control actual rates and costs.