Effective Annual Rate Calculator

Q: What is the difference between EAR and APR?

APR is the nominal annual rate before accounting for compounding. EAR (also called APY) includes the effect of compounding within the year, so it is always equal to or higher than the APR for the same nominal rate.

Q: Is APY the same as EAR?

Yes, APY (Annual Percentage Yield) and EAR (Effective Annual Rate) refer to the same concept: the actual annual return after accounting for compounding.

Q: What units does this calculator use?

The nominal rate and the resulting effective annual rate are both expressed as a percent per year.

3 min read 3 steps 7 terms 3 examples 6 FAQs EAR = (1 + i/n)^n − 1

A nominal interest rate on its own does not tell you the full story — it ignores how often interest compounds.

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Walk-through

How to Use This Calculator

3 steps

Enter the nominal annual rate

Type the nominal (stated) annual interest rate as a percent — for example, the APR printed on a loan disclosure or the stated rate on a savings account. This is the rate before any compounding is applied.

Choose a compounding frequency

Select how often interest compounds: Annual, Semiannual, Quarterly, Monthly, Daily, or Continuous. The Effective Annual Rate Calculator updates the result instantly as you change this.

Compare frequencies and continuous compounding

Switch to the Frequency Comparison tab to see the EAR at every compounding frequency side by side, or the Continuous tab to see the theoretical maximum EAR using e^i − 1.

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Reference

Formula & Methodology

2 formulas

Effective annual rate (discrete compounding)

EAR = (1 + i/n)^n − 1

i is the nominal annual rate as a decimal (e.g. 0.06 for 6%) and n is the number of compounding periods per year (1 for annual, 12 for monthly, 365 for daily, etc.). The result is the effective annual rate as a decimal — multiply by 100 for a percent.

Effective annual rate (continuous compounding)

EAR = eⁱ − 1

As the number of compounding periods n approaches infinity, the discrete formula converges to this continuous-compounding limit, where e is Euler's number (≈ 2.71828).

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Trust, Methodology & Sources

Written by Calculover Editorial Team · Updated 2026-07-19 · 2 sources

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Author: {{^authorProfileUrl}}Calculover Editorial Team{{/authorProfileUrl}} - Finance content review

Owner: Calculover Editorial Team - Finance content review

Last reviewed: 2026-07-19

Last verified: 2026-07-19

Methodology

EAR is computed with the standard compound-interest formula (1 + i/n)^n − 1 for discrete compounding periods, and e^i − 1 for the continuous-compounding limit, where i is the nominal annual rate and n is the number of compounding periods per year.

Assumption: The nominal rate entered is assumed to be an annual rate with no account fees, promotional periods, or tax adjustments applied.

Assumption: Compounding is assumed to occur at even intervals throughout the year (e.g. exactly 12 equal monthly periods).

Limitations & guidance

This calculator does not account for account fees, minimum-balance requirements, promotional teaser rates, or tax treatment, all of which can change the real return you experience.

For loans, some lenders disclose an APR that already includes fees (an 'effective APR') — converting that figure again with this tool would double-count the fee adjustment.

Professional guidance: This calculator is for educational purposes only and does not constitute financial, tax, or investment advice. Consult a licensed financial advisor before making borrowing or investment decisions.

Primary sources

Truth in Savings Act / Regulation DD (12 CFR Part 1030)

Truth in Lending Act / Regulation Z (12 CFR Part 1026)

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Glossary

Key Terms Explained

7 terms

Effective annual rate (EAR) The actual annual rate of return earned or paid after accounting for the effect of compounding within the year. Also called APY.

APY Annual Percentage Yield — the term banks use for the effective annual rate on deposit accounts. Mathematically identical to EAR.

Nominal rate The stated annual interest rate before accounting for compounding, also called the annual percentage rate (APR) in a lending context.

Compounding frequency How often interest is calculated and added to the principal within a year — for example annually, monthly, or daily. A higher compounding frequency produces a higher EAR for the same nominal rate.

Continuous compounding The theoretical limit of compounding frequency as the number of periods per year approaches infinity. It uses the formula EAR = e^i − 1.

APR Annual Percentage Rate — the nominal interest rate that does not account for compounding within the year. Lenders are required to disclose APR under Regulation Z.

Interest The cost of borrowing money or the return earned on a deposit, calculated as a function of the principal, the rate, and the compounding schedule.

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Scenarios

Real-World Examples

3 worked examples

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Savings account

6% nominal rate, monthly compounding

Nominal rate 6% Compounding Monthly (n = 12)

EAR = (1 + 0.06/12)^12 − 1 = 6.17%. Because interest compounds 12 times a year, the effective annual rate (6.17%) is slightly higher than the nominal 6% rate.

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Credit card

6% nominal rate, daily compounding

Nominal rate 6% Compounding Daily (n = 365)

EAR = (1 + 0.06/365)^365 − 1 = 6.18%. Daily compounding produces a slightly higher EAR than monthly compounding for the same nominal rate, because interest is calculated on prior interest more often.

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Theoretical maximum

6% nominal rate, continuous compounding

Nominal rate 6% Compounding Continuous (n → ∞)

EAR = e^0.06 − 1 = 6.18%. Continuous compounding is the mathematical ceiling — no compounding frequency can push the EAR any higher than this for a 6% nominal rate.

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Deep Dive

Understanding the Effective Annual Rate Calculator

3 chapters · 3 min read

A nominal interest rate on its own does not tell you the full story — it ignores how often interest compounds. The Effective Annual Rate Calculator converts any nominal rate into the true annual rate of return (EAR, also called APY), accounting for compounding frequency, so you can compare loans, savings accounts, and investments on equal footing.

How the Effective Annual Rate Calculator works

The calculator applies the compound-interest formula EAR = (1 + i/n)^n − 1, where i is the nominal annual rate as a decimal and n is the number of compounding periods per year. For continuous compounding, the formula converges to EAR = e^i − 1, using Euler's number as the compounding frequency approaches infinity. Because interest earned during each period itself begins earning interest, a higher compounding frequency always produces a higher (or equal) effective rate for the same nominal rate.

Inputs and what they mean

The calculator takes two inputs: the nominal annual rate, entered as a percent, and the compounding frequency, chosen from Annual, Semiannual, Quarterly, Monthly, Daily, or Continuous. The nominal rate is the number typically advertised on loan or savings disclosures. The compounding frequency has an outsized effect at higher nominal rates — the gap between annual and continuous compounding widens as the nominal rate increases.

Limits and edge cases

This calculator computes the mathematical effective annual rate only; it does not account for account fees, promotional teaser rates, or tax treatment, all of which can change the real return you experience. For loan comparisons, always check whether a lender's disclosed APR already reflects fees (an 'effective APR') before converting it again. Consult a licensed financial advisor before making borrowing or investment decisions based on this calculator alone.

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Questions

Frequently Asked Questions

6 questions

What is the formula for effective annual rate?+

EAR = (1 + i/n)^n − 1, where i is the nominal annual rate as a decimal and n is the number of compounding periods per year. For continuous compounding, the formula becomes EAR = e^i − 1.

What is the difference between EAR and APR?+

APR (Annual Percentage Rate) is the nominal rate before accounting for compounding within the year. EAR (Effective Annual Rate) includes the effect of compounding, so it is always equal to or higher than the APR for the same nominal rate — the more frequent the compounding, the bigger the gap.

Does a more frequent compounding period increase the EAR?+

Yes. For a fixed nominal rate, more frequent compounding (daily vs. monthly vs. annual) produces a higher effective annual rate, because interest is calculated on previously earned interest more often.

How is continuous compounding calculated?+

Continuous compounding is the limit of compounding frequency as it approaches infinity. It uses the formula EAR = e^i − 1, where e is Euler's number (approximately 2.71828). No compounding schedule can produce an EAR higher than the continuous-compounding result for the same nominal rate.

Is APY the same as EAR?+

Yes. APY (Annual Percentage Yield) is the term used on savings and deposit accounts, while EAR (Effective Annual Rate) is the general finance term — both refer to the same effective-rate calculation.

What units does this calculator use?+

Both the nominal rate you enter and the effective annual rate the calculator returns are expressed as a percent per year.

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Effective Annual Rate Calculator

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