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Effective Annual Rate (EAR) Calculator

Annual equivalent rate of interest when compounding occurs multiple times a year.

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Effective Annual Rate

Formula first

Overview

The Effective Annual Rate (EAR) represents the actual interest rate earned or paid on a financial product after accounting for the effects of compounding over a given period. It serves as a standardized metric to compare the true economic cost or yield of instruments with different compounding frequencies.

Symbols

Variables

EAR = Effective Annual Rate, r = Nominal Rate, n = Periods per Year

Effective Annual Rate
Nominal Rate
Periods per Year

Apply it well

When To Use

When to use: Use this formula when comparing financial products that have different compounding schedules, such as a monthly-compounded savings account versus a quarterly-compounded bond. It is required whenever you need to determine the true annual return on an investment or the real cost of a loan beyond the quoted nominal rate.

Why it matters: EAR exposes the hidden costs of frequent compounding; as the number of compounding periods increases, the interest paid or earned also increases. This allows for an 'apples-to-apples' comparison of diverse financial options, ensuring that consumers and investors understand their actual yield or debt obligations.

Avoid these traps

Common Mistakes

  • Forgetting to use decimals for rates.
  • Subtracting 1 inside the parenthesis.

One free problem

Practice Problem

A high-yield savings account offers a nominal annual interest rate of 4% compounded monthly. Calculate the Effective Annual Rate for this account.

Nominal Rate0.04
Periods per Year12

Solve for:

Hint: Divide the nominal rate by the number of months in a year and add 1 before raising to the 12th power.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Effective interest rate
  2. Brealey, Myers, and Allen, Principles of Corporate Finance
  3. Brigham and Houston, Fundamentals of Financial Management
  4. Wikipedia: Effective annual rate
  5. Brealey, Richard A., Myers, Stewart C., and Allen, Franklin. Principles of Corporate Finance. McGraw-Hill Education.
  6. Kellison, Stephen G. The Mathematics of Finance. McGraw-Hill.
  7. Wikipedia: Effective interest rate (https://en.wikipedia.org/wiki/Effective_interest_rate)
  8. AQA A-Level Business Specification (or equivalent A-Level Finance/Economics textbook)