Effective Annual Percentage Rate Calculator – Cost Calculator

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Effective Annual Rate (EAR) Calculator

Nominal Annual Interest Rate (%)

Compounding Frequency Annually (1 time/year) Semi-Annually (2 times/year) Quarterly (4 times/year) Monthly (12 times/year) Weekly (52 times/year) Daily (365 times/year)

Effective Annual Rate (EAR):

0.00%

What is the Effective Annual Rate (EAR)?

The Effective Annual Rate (EAR), also known as the Effective Annual Percentage Rate (EAPR) or the Annual Equivalent Rate (AER), is the actual interest rate earned or paid on an investment, loan, or financial product over a one-year period. Unlike the nominal interest rate, the EAR takes the effect of compounding interest into account.

When interest is compounded more frequently than once a year (for example, monthly or daily), the total interest accrued is higher than the stated nominal rate. The EAR provides a standardized way to compare different financial products that have different compounding schedules.

The EAR Formula

To calculate the effective annual rate manually, the following mathematical formula is used:

EAR = (1 + i / n)ⁿ – 1

Where:

i = The nominal annual interest rate (as a decimal)
n = The number of compounding periods per year

Difference Between Nominal Rate and EAR

The nominal rate is the "advertised" or "stated" rate. However, it does not reflect the total cost or yield if interest is added back to the principal more than once a year. The EAR is always equal to or higher than the nominal rate. The more frequent the compounding (e.g., daily vs. annually), the higher the EAR will be relative to the nominal rate.

Practical Example

Suppose you have a savings account with a 6% nominal interest rate compounded monthly.

Nominal Rate (i) = 0.06
Compounding Periods (n) = 12
Calculation: (1 + 0.06 / 12)¹² – 1
Result: (1 + 0.005)¹² – 1 = 1.061677 – 1 = 0.061677 or 6.17%

In this scenario, while the bank advertises 6%, you are actually earning 6.17% due to the monthly compounding of your interest.

Why It Matters for Borrowers and Savers

For savers, a higher EAR is better because it means your money grows faster. For borrowers, a higher EAR means you are paying more for the debt than the nominal rate suggests. Always check the EAR or APR when comparing credit cards, personal loans, or high-yield savings accounts to ensure you are comparing "apples to apples."