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Formula & Calculator

Effective Annual Rate (EAR)

Converts a nominal annual interest rate with periodic compounding into the true effective annual rate.

Written by the Vorzep Team

FinanceInterest RatesDaily Life

Effective Annual Rate CalculatorEAR = (1 + r/n)n − 1

EAR = (1 + r/n)n − 1
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EAR = (1 + r/n)n − 1 · r = nominal annual rate · n = compounding periods/year
EAR = (1 + r/n)^n - 1
Effective Annual Rate (EAR)

Variables

SymbolQuantityUnit
EAREffective annual rate
rNominal annual interest rate
nNumber of compounding periods per year

What it means

The Effective Annual Rate (EAR) reflects the actual annual interest rate when compounding occurs more than once per year. It is calculated from the nominal rate r and the number of compounding periods n per year. EAR is higher than the nominal rate if n>1. It is used to compare financial products with different compounding frequencies, such as savings accounts, loans, and credit cards. It ensures that investors can make apples‑to‑apples comparisons. Understanding EAR is crucial for making informed financial decisions and for understanding the true cost of borrowing or return on saving.

Worked example

Effective Annual Rate – Two Detailed Examples

Real‑World
Scenario: A credit card company advertises an APR (annual percentage rate) of 18% with monthly compounding. A consumer wants to understand the true cost of borrowing, as the effective rate is higher than the stated rate. They compute the EAR to compare this card with other cards that compound daily or quarterly, helping them choose the cheapest option.
ParameterValue
Nominal Rate18%
Compounding (n/year)12
1EAR = (1 + 0.18/12)^12 − 1 = (1.015)^12 − 1 = 1.1956 − 1 = 19.56%
Result 19.56% ✓ Effective annual rate
Scenario: A saver is comparing two savings accounts: one offers 5% APR compounded daily (365 times a year), and another offers 5% APR compounded monthly. The saver wants to know the true annual return on each to choose the best account. By calculating the EAR for the daily compounding account, they see the advantage of more frequent compounding.
ParameterValue
Nominal Rate5%
Compounding365
1EAR = (1 + 0.05/365)^365 − 1 = 0.05127 = 5.127%
Result 5.13% ✓ Effective yield
Insight: The EAR reflects the actual annual return after accounting for compounding frequency. It is always higher than the nominal rate when compounding is more frequent than annually.

Common mistakes

  • Stated rate r: The nominal annual interest rate (APR) – in decimal form.
  • Compounding periods n: The number of compounding periods per year.
  • EAR: The effective annual rate – accounts for compounding within the year.
  • EAR is always ≥ APR (for n>1) – equal only if n=1.
  • Continuous compounding: For continuous, EAR = e^r − 1.

Applications

The Effective Annual Rate (EAR) adjusts the nominal annual rate for compounding within the year, giving the true annual cost of borrowing or return on investment. EAR is crucial for comparing financial products with different compounding periods. Banks and consumers use it to evaluate credit cards, loans, and savings accounts. By converting all rates to EAR, one can make an apples‑to‑apples comparison. This formula is also used in corporate finance to evaluate financing options. Understanding EAR helps avoid underestimating the cost of debt and ensures that investment returns are accurately measured. It is a fundamental concept in personal and corporate finance, ensuring transparency and fair comparisons.

  • Comparison of credit card APRs with different compounding
  • Selection of savings accounts and certificates of deposit
  • Corporate borrowing – choosing among loan offers
  • Investment performance reporting and benchmarking
  • Regulatory compliance – truth in lending disclosures