EAR Calculator

Convert a nominal (stated) annual interest rate into the Effective Annual Rate using EAR = (1 + i/n)^n - 1, and see how compounding frequency changes the interest earned on a given principal.

Quick Facts

Formula
EAR = (1 + i/n)^n − 1
i is the nominal annual rate as a decimal and n is the number of compounding periods per year; EAR is always ≥ the nominal rate whenever n > 1.
Continuous compounding
EAR = e^i − 1
The mathematical limit as the number of compounding periods per year grows without bound.

Your Results

Calculated
Effective Annual Rate (EAR)
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True annualized rate including compounding
Nominal rate (APR)
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Stated rate before compounding is applied
Year-1 interest earned
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Principal × EAR
Compounding advantage
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Extra interest vs. simple interest at the nominal rate

Ready

Enter the nominal rate, compounding frequency, and principal, then press Calculate.

How the EAR Calculator works

Lenders and savings accounts often quote a nominal (stated) annual interest rate, but that number does not tell the whole story if interest compounds more than once a year. The Effective Annual Rate (EAR), also called the annual equivalent rate, converts a nominal rate into the actual annualized rate you earn or pay once compounding is factored in. Two accounts with the same nominal rate but different compounding frequencies will have different EARs — and the one that compounds more often always wins.

The formula

For a nominal annual rate i (as a decimal) compounded n times per year, the effective annual rate is:

EAR = (1 + i/n)n − 1

Each compounding period, the rate applied is i/n, and that smaller rate is applied n times over the year — with each period's interest added to the balance before the next period compounds. In the limit as n grows very large, compounding becomes continuous and the formula simplifies to EAR = ei − 1, where e is Euler's number (approximately 2.71828).

Worked example

Take a 6% nominal annual rate on a $10,000 balance, compounded monthly (n = 12). The periodic rate is 0.06 / 12 = 0.005, and EAR = (1.005)12 − 1 ≈ 6.1678%. That is about 0.17 percentage points higher than the 6% nominal rate. Applied to the $10,000 balance, the effective rate produces roughly $616.78 in year-one interest, compared with $600.00 under simple (non-compounding) interest at the same nominal rate — a compounding advantage of about $16.78.

What moves EAR the most

  • The nominal rate: a higher stated rate produces a proportionally larger EAR, and the compounding gap also grows in dollar terms as the rate rises.
  • Compounding frequency: annual compounding leaves EAR equal to the nominal rate (n = 1, so the gap is zero). Moving to semi-annual, quarterly, monthly, weekly, and daily compounding each raises EAR a little more — but the incremental gain shrinks quickly. The jump from monthly to daily compounding is much smaller than the jump from annual to monthly.
  • Continuous compounding: this is the theoretical ceiling for a given nominal rate. In practice it is only a hair above daily compounding for typical consumer interest rates.

Why EAR matters when comparing offers

Because EAR strips out the compounding-frequency trick, it is the correct number to compare across savings accounts, certificates of deposit, or loans that quote different compounding schedules. A 5.9% nominal rate compounded daily can produce a higher EAR than a 6.0% nominal rate compounded annually — comparing the stated (nominal) rates alone would give the wrong answer. This calculator performs pure compound-interest arithmetic; it does not account for fees, taxes, promotional rate periods, or minimum-balance requirements that can also affect the return you actually receive.

Frequently Asked Questions

What is the Effective Annual Rate (EAR)?
The EAR is the actual annual interest rate you earn or pay once compounding within the year is taken into account. It is calculated as EAR = (1 + i/n)^n − 1, where i is the nominal (stated) annual rate as a decimal and n is the number of compounding periods per year. Because interest is added to the balance before the year ends, the EAR is always equal to or greater than the nominal rate.
How is EAR different from the nominal rate (APR)?
The nominal rate (often called APR) is the stated annual rate before compounding is applied. The EAR accounts for the fact that interest earned in one period starts earning interest in the next. For a 6% nominal rate compounded monthly, the EAR is about 6.17%, not 6%, because each month's interest is added to the balance before the next month's interest is calculated.
What is continuous compounding and how does it change the formula?
Continuous compounding is the mathematical limit of compounding as the number of periods per year approaches infinity. In that limit the formula simplifies to EAR = e^i − 1, where e is Euler's number (about 2.71828) and i is the nominal annual rate as a decimal. It produces the highest possible EAR for a given nominal rate, though only slightly higher than daily compounding in most cases.
Does compounding more often always add much more interest?
No, the gains shrink quickly as compounding gets more frequent. Moving from annual to monthly compounding raises the EAR noticeably, but moving from daily to continuous compounding changes it by only a tiny fraction of a percent. Most of the benefit of more frequent compounding is captured well before you reach daily or continuous compounding.

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