Understanding your EAR result
The table below shows how the same 5.9% nominal rate produces increasingly higher EAR values as compounding frequency increases, which applies identically whether the rate is on a loan or a deposit.
| Compounding frequency | Periods per year | EAR on a 5.9% nominal rate |
|---|---|---|
| Annually | 1 | 5.900% (equals the nominal rate) |
| Semiannually | 2 | Slightly above 5.9% |
| Quarterly | 4 | Slightly higher still |
| Monthly | 12 | 6.0622% — the calculator's default example |
| Daily | 365 | The highest EAR for a given nominal rate, only marginally above the monthly figure |
- EAR is always greater than or equal to the nominal rate, and the two are equal only when compounding occurs exactly once per year.
- EAR is a useful single figure for comparing two financial products with different nominal rates and different compounding frequencies, since it standardizes both into one comparable true annual rate.
- On loans, lenders are separately required by the Truth in Lending Act to disclose APR (annual percentage rate), which is a related but distinct figure that in some cases also incorporates certain fees — APR and EAR are not always numerically identical, and both can be useful depending on what is being compared.
What is the effective annual rate (EAR)?
The effective annual rate (EAR), also called the effective interest rate, is the actual annual rate of interest earned or paid once the effect of compounding within the year is included. Unlike a nominal rate, which is simply the stated annual rate without adjustment, EAR reflects that interest compounding more than once a year causes already-accrued interest to itself earn (or cost) additional interest before the year is over.
EAR applies symmetrically to both borrowing and saving: on a loan, a higher compounding frequency at the same nominal rate increases the true annual cost of borrowing; on a deposit, it increases the true annual yield earned. This calculator computes the same underlying mathematical conversion used in both directions.
EAR is closely related to annual percentage yield (APY), which US banking regulations require to be disclosed on deposit accounts; the underlying formula is the same, though EAR is the more general finance term used across both lending and savings contexts, including corporate finance and investment analysis.
How to use this effective annual rate calculator
- Enter the nominal (stated) annual interest rate.
- Select the compounding frequency — daily, monthly, quarterly, semiannually, or annually.
- Read the resulting effective annual rate (EAR), the nominal rate shown for reference, and the difference between the two in percentage points.
The formula behind EAR
EAR uses the standard compound interest conversion formula: it raises the quantity (1 plus the periodic rate) to the power of the number of compounding periods per year, then subtracts 1. The periodic rate is the nominal annual rate divided by the number of compounding periods.
On the calculator's default example — a 5.9% nominal rate compounded monthly (12 periods per year) — the EAR is 6.0622%, a difference of 0.1622 percentage points above the nominal rate, resulting from interest compounding twelve times within the year rather than once.
Common mistakes
- Assuming EAR only applies to savings accounts — the same compounding-adjustment concept applies equally to the true annual cost of borrowing on a loan or credit line.
- Confusing EAR with APR on a loan — APR can incorporate certain fees in addition to the interest rate, while EAR (as calculated here) reflects only the compounding effect on the stated interest rate itself.
- Ignoring compounding frequency entirely when comparing two rates — a lower nominal rate with more frequent compounding can produce a higher true annual rate than a higher nominal rate compounded less often.
- Assuming the EAR-versus-nominal-rate gap is large — for most everyday interest rates, the difference is typically well under half a percentage point, even between daily and annual compounding.
- Using EAR interchangeably with APY without checking which figure a specific financial product actually discloses — regulatory disclosure requirements differ between deposit accounts and loan products.
Questions fréquentes
What is the effective annual rate (EAR)?
The effective annual rate is the true annual interest rate once compounding within the year is accounted for, applicable to both loans and deposit accounts. It is always equal to or greater than the nominal (stated) rate, with the gap growing as compounding frequency increases.
What is the EAR of a 5.9% rate compounded monthly?
A 5.9% nominal annual rate compounded monthly (12 times per year) produces an effective annual rate of 6.0622%, a difference of 0.1622 percentage points above the nominal rate, because interest compounds on previously accrued interest twelve times within the year.
Is EAR the same as APY?
EAR and APY (annual percentage yield) use the same underlying compound-interest formula and produce the same result for the same nominal rate and compounding frequency. APY is the specific term used for deposit account disclosures required under US banking regulations, while EAR is the more general finance term also applied to loans and other financial calculations.
Is EAR the same as APR on a loan?
Not necessarily. EAR, as calculated here, reflects only the effect of compounding frequency on the stated interest rate. APR (annual percentage rate), which lenders are required to disclose under the Truth in Lending Act, can also incorporate certain loan fees into the rate, so APR and EAR are related but not always numerically identical figures.
Why does a higher compounding frequency increase the effective rate?
More frequent compounding means interest is calculated and added to the balance more often within the year, so previously earned (or charged) interest itself starts earning (or costing) additional interest sooner. This compounding-on-compounding effect is what causes the effective annual rate to exceed the nominal rate whenever compounding occurs more than once per year.
Références
- Federal Reserve Board. Regulation DD — Truth in Savings Act implementing regulation (APY/EAR disclosure basis). federalreserve.gov.
- Federal Reserve Board. Regulation Z — Truth in Lending Act implementing regulation (APR disclosure on loans). federalreserve.gov.
- Brealey RA, Myers SC, Allen F. Principles of Corporate Finance (13th ed.). McGraw-Hill, 2020. Chapter 2: How to Calculate Present Values (effective vs. nominal rates).