Effective Annual Rate Calculator

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Walk-through

How to Use This Calculator

3 steps

1

Enter the nominal annual rate

Enter nominal annual interest, before product-specific fees, taxes and cash-flow timing.

2

Choose a compounding frequency

Select a named frequency, or choose Custom and open Advanced to enter a whole number of periods per year. Continuous is a separate mathematical limit.

3

Compare frequencies and continuous compounding

Compare the chart and ranked table below the answer. Select a frequency there to apply it; Copy includes the exact conversion and CSV includes all frequency results.

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Reference

Formula & Methodology

2 formulas

Effective annual rate (discrete compounding)

EAR = (1 + i/n)^n − 1

For discrete compounding, n is a positive integer and 1+i/n must be positive. Negative rates are allowed within that domain. Continuous compounding is the separate exp(i)−1 limit. Stable logarithm/exponential functions retain tiny rates.

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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YMYL

Trust, Methodology & Sources

Written by Calculover Editorial Team · Updated 2026-08-11 · 2 sources

Editorial accountability

Author: Calculover Editorial Team - Finance content review

Owner: Calculover Editorial Team - Finance content review

Last reviewed: 2026-08-11

Last verified: 2026-08-11

Methodology

Uses log1p and expm1 for discrete compounding, with continuous expm1(i) as a named limit. Custom n is an integer from 1 to 1,000,000,000; 1+i/n must be positive and results finite. Representable tiny rates retain their first-order value when the compounding adjustment is below floating-point precision. Fees, taxes and actual payment dates are excluded; this is not a regulated APR/APY disclosure calculation.

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.

A regulated loan APR can include fees and timing rules, while a deposit APY can use product-specific balance and term conventions. Do not assume either disclosure is a nominal rate that can be converted again. This tool calculates fee-exclusive effective annual interest only.

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 one-year interest rate implied by a nominal annual rate and compounding schedule, before product-specific fees, taxes and payment timing.

APY A regulated loan APR can include fees and timing rules, while a deposit APY can use product-specific balance and term conventions.

Nominal rate An annual interest quote before compounding. A regulated loan APR may include fees and timing rules and is not automatically this nominal input.

Compounding frequency The number of interest periods per year. For a fixed nonzero rate in the valid domain, more frequent compounding raises EAR; at zero, every frequency gives zero.

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 A regulated loan APR can include fees and timing rules, while a deposit APY can use product-specific balance and term conventions.

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)

At 6% nominal, monthly compounding gives EAR = 6.167781%, displayed as 6.17%. It exceeds the nominal quote by 16.7781 basis points, before product fees, taxes and payment timing.

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Credit card

6% nominal rate, daily compounding

Nominal rate 6% Compounding Daily (n = 365)

At 6% nominal, daily compounding (365 periods) gives EAR = 6.183131%, displayed as 6.18%. The mathematical conversion does not model a card’s actual daily balances, fees or payment dates.

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Theoretical maximum

6% nominal rate, continuous compounding

Nominal rate 6% Compounding Continuous (n → ∞)

At 6% nominal, the continuous limit gives EAR = 6.183655%, displayed as 6.18%. It is about 0.0524 basis point above daily compounding; the shared rounded headline does not make them equal.

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Reference

Cite This Calculator

APA & MLA

Use either format to cite this calculator in a paper, report, or resource list.

APA

MLA

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Deep Dive

Understanding the Effective Annual Rate Calculator

3 chapters · 3 min read

Enter nominal annual interest, before product-specific fees, taxes and cash-flow timing. EAR converts that interest rate for a chosen compounding schedule; it is not a complete comparison of financial products.

How the Effective Annual Rate Calculator works

With i as the nominal annual decimal rate, discrete compounding gives EAR = (1 + i/n)^n − 1. Continuous compounding uses exp(i) − 1. Values are converted to percent once. The chart retains the nominal reference; the table ranks computed rates and reports basis-point differences from the selected rate. One basis point is 0.01 percentage point. This ordering does not rank financial products.

Inputs and what they mean

Enter one nominal annual rate and select a frequency. Custom accepts an integer n from 1 to 1,000,000,000; continuous is a separate limit. Discrete inputs require 1+i/n > 0 and a finite result. Negative rates are valid within this domain; zero stays zero. A missing selected frequency removes its conversion while the independent comparison remains available.

Limits and edge cases

The tool excludes fees, taxes and actual cash-flow dates. A regulated APR or APY may use other disclosure conventions. Editing does not write inputs into the page URL or save a draft. Share previews the rate and frequency and includes them only on explicit selection; anyone with that link can read them. CSV and Copy use current results, not forecasts.

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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?+

A regulated loan APR can include fees and timing rules, while a deposit APY can use product-specific balance and term conventions. Do not assume either disclosure is a nominal rate that can be converted again. This tool calculates fee-exclusive effective annual interest only.

Does a more frequent compounding period increase the EAR?+

For a fixed nonzero nominal rate within each frequency’s valid domain, more frequent compounding raises the computed EAR. At zero, every frequency gives zero. This mathematical ordering does not establish a better product.

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?+

A regulated loan APR can include fees and timing rules, while a deposit APY can use product-specific balance and term conventions. Do not assume either disclosure is a nominal rate that can be converted again. This tool calculates fee-exclusive effective annual interest only.

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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