Effective Annual Rate (EAR) Calculator
Convert a nominal interest rate to the Effective Annual Rate (EAR) for any compounding frequency, and compare EAR across all compounding periods.
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How to use this calculator
r = nominal annual rate, n = number of compounding periods per year. For continuous compounding: EAR = e^r − 1.
- 1
Enter the nominal annual interest rate as stated on the financial product.
- 2
Select the compounding frequency — how often interest is applied to the balance.
- 3
The EAR shows the true annual return after accounting for compounding.
- 4
Use the comparison table to see how EAR changes across different compounding frequencies.
Frequently asked questions
What is the difference between APR and EAR (APY)?
APR (Annual Percentage Rate) is the nominal rate — it does not account for compounding within the year. EAR (also called APY — Annual Percentage Yield) reflects the actual annual return after compounding. Banks advertise loan rates as APR (lower-sounding) and savings rates as APY (higher-sounding). They can be quite different for the same nominal rate with frequent compounding.
Why does more frequent compounding give a higher EAR?
Each compounding event earns interest on previously earned interest. The more frequently this happens, the more total interest accumulates over the year. The difference between annual and daily compounding at 12% nominal: EAR goes from 12.00% to 12.75% — a meaningful difference on large balances over long periods.
What is continuous compounding?
Continuous compounding is the mathematical limit as compounding frequency approaches infinity. The formula simplifies to EAR = e^r − 1. At 12% nominal, continuous compounding gives EAR = 12.7497%. It's used in derivative pricing and some bond calculations rather than practical bank products.
When does the difference between nominal and EAR matter most?
When you're comparing products with different compounding frequencies. A 5.00% APR compounding daily is equivalent to a 5.13% APY. A 5.13% APR compounding annually is the same 5.13% APY. Always compare financial products using EAR/APY for an apples-to-apples comparison.
EAR vs nominal rate: the compounding effect explained
How compounding frequency affects your returns
At 10% nominal rate: annually = 10.00% EAR; semi-annually = 10.25%; quarterly = 10.38%; monthly = 10.47%; daily = 10.516%; continuously = 10.517%. The gap narrows as compounding increases — most of the benefit comes from going annual to monthly. Beyond monthly compounding, the incremental gain is small for most practical purposes.
EAR for borrowers vs savers
For savers, higher EAR means more money earned. For borrowers, higher EAR means more interest paid. A credit card quoted at 24% APR with daily compounding has an EAR of 27.11% — significantly more than the stated rate. Always use EAR to compare the true cost of borrowing or the true yield of saving.
EAR in international finance
Different countries have different conventions for quoting rates. The US uses APR for loans and APY for savings. The EU mandates APR disclosure under the Consumer Credit Directive. The UK uses APR for consumer credit. Australia uses comparison rates that include fees. Despite different names, the underlying math of converting nominal to effective rates is universal.
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