6.1678%
0.1678%
$1,061.68
$61.68
0.500000%
6.1678%
0.1678%
$1,061.68
$61.68
0.500000%
The Effective Annual Rate (EAR) Calculator converts a nominal (stated) interest rate into the actual annual rate you earn or pay after accounting for the effect of compounding. This is the true measure of interest that allows you to compare financial products on an equal basis, regardless of how frequently they compound.
Financial institutions often advertise nominal rates (also called stated or quoted rates), but these rates don't tell the whole story. A savings account advertising '6% interest compounded monthly' actually earns more than 6% per year because the monthly interest earns interest of its own. The EAR captures this compounding effect: EAR = (1 + r/n)n - 1, where r is the nominal annual rate and n is the number of compounding periods per year.
The difference between nominal and effective rates increases with both the interest rate and the compounding frequency. At 6% nominal: annual compounding gives an EAR of exactly 6.0000%, monthly compounding gives 6.1678%, daily compounding gives 6.1831%, and continuous compounding gives 6.1837%. At 24% nominal (common for credit cards): monthly compounding gives an EAR of 26.8242% — nearly 3 percentage points higher than the advertised rate.
The EAR is mandated by regulation in many countries under the name APY (Annual Percentage Yield) for deposit products. Banks must disclose the APY alongside the nominal rate so consumers can make informed comparisons. When evaluating savings accounts, CDs, money market funds, or any interest-bearing investment, always compare EARs (or APYs), not nominal rates.
On the borrowing side, the EAR reveals the true cost of debt. Credit cards compounding daily at a 24% nominal rate actually cost 27.11% effectively. Understanding this distinction helps borrowers appreciate the full cost of high-frequency compounding and make more informed decisions about debt management and repayment strategies.
The EAR formula is: EAR = (1 + r/n)n - 1
The formula calculates the single annual rate that would produce the same result as the nominal rate compounded n times per year. For continuous compounding, the formula becomes EAR = er - 1.
The Effective Annual Rate is the true annual rate of return or cost after compounding. The Difference from Nominal Rate shows how much extra interest compounding generates — this gap widens with higher rates and more frequent compounding. Growth of $1,000 provides a concrete example of what you would actually receive after one year.
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Results
5% nominal compounded monthly = 5.1162% EAR — $1,000 grows to $1,051.16
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Results
24% nominal compounded daily = 27.11% EAR — significantly higher than the stated rate
The EAR is the actual annual rate of return earned or paid after accounting for the effect of compounding within the year. It converts a nominal rate with intra-year compounding to an equivalent single annual rate.
The nominal (stated) rate ignores compounding effects. EAR accounts for the fact that interest earned during the year itself earns interest. EAR always equals or exceeds the nominal rate (they are equal only with annual compounding).
Yes, for deposits and savings products, EAR and APY (Annual Percentage Yield) are the same calculation. Banks in the US are required by the Truth in Savings Act to disclose APY to facilitate comparison shopping.
APR (Annual Percentage Rate) is used for loans and includes fees but may not fully account for compounding. EAR accounts for compounding but not fees. For a fair comparison, convert APR to EAR if compounding frequencies differ.
Continuous compounding gives the highest EAR, but daily compounding (365 times per year) is very close. The formula for continuous compounding is EAR = e^r - 1. The difference between daily and continuous compounding is typically less than 0.01%.
Tradition, competitive positioning, and regulatory requirements all play a role. Savings products typically compound daily or monthly. Bonds usually compound semi-annually. Mortgages in Canada compound semi-annually, while US mortgages compound monthly.
Over multiple years, the EAR compounds on itself. A seemingly small EAR difference matters enormously over time. An EAR of 6.17% vs. 6.00% on a $100,000 investment results in a $2,500+ difference over 10 years.
No. With positive interest rates and compounding more than once per year, EAR is always greater than the nominal rate. They are equal only when compounding is annual (n=1).
Use the formula: nominal rate = n × ((1 + EAR)^(1/n) - 1). For example, an EAR of 6.1678% with monthly compounding gives a nominal rate of 12 × ((1.061678)^(1/12) - 1) = 6.00%.
Because 365 is already a large number. Mathematically, as n approaches infinity, (1+r/n)^n approaches e^r. With n=365, the result is very close to this limit. The difference is typically less than 0.01 percentage points.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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