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EAR Calculator (Effective Annual Rate)

Convert a nominal annual interest rate and compounding choice into EAR, periodic rate, compounding periods, and one-year future value.

Published

Effective annual rate
Effective annual rate (EAR)
12.68%
Periodic rate
1%
Compounding periods per year
12
One-year future value
$1,126.83

A stated 12% rate compounded 12 times per year has an EAR of 12.68%.

The stated annual rate before compounding adjustment.
%
Optional amount used to show the one-year future value.
$

Results update as you type.

EAR Calculator (Effective Annual Rate)

Effective annual rate is the cleanest way to ask what a stated rate really becomes after compounding. A 12% nominal annual rate compounded monthly is not the same as 12% compounded annually, because monthly interest is credited or charged before the year is over. This calculator converts the nominal annual interest rate into EAR, shows the periodic rate for the selected compounding frequency, reports the number of compounding periods per year, and applies the EAR to a one-year future value.

Use it when rate quotes look similar but compounding differs. It can help compare savings offers, bond assumptions, loan terms, crediting rates, or classroom finance problems. For a deposit-specific view with multi-year final value, use the APY calculator. For borrowing offers with fees, use the APR calculator. For a payment-by-payment loan schedule, use the amortization calculator.

How the EAR calculation works

The form has three inputs: nominal annual interest rate, compounding frequency, and initial balance. The frequency can be annual, semiannual, quarterly, monthly, weekly, daily, or continuous. For periodic compounding, the calculation divides the nominal annual rate by the number of periods and compounds that periodic rate for one year. For daily compounding, the number of periods is 365.242, the calculator’s average-year convention. For continuous compounding, it uses the exponential formula instead of a periodic rate.

The future value is always one year only. The calculator multiplies the initial balance by one plus EAR. That makes the output a focused rate-conversion tool rather than a long-term savings planner. If you want recurring deposits or multi-year projections, the compound interest page is the better sibling.

Because the page isolates one variable, it is also helpful for checking spreadsheets. If your own model converts a nominal rate into a different annual result, compare the compounding periods and rounding before changing the economic assumption.

Formula

For periodic compounding, EAR is:

EAR=(1+nominal annual rateperiods per year)periods per year−1\text{EAR} = \left(1 + \frac{\text{nominal annual rate}}{\text{periods per year}}\right)^{\text{periods per year}} - 1

The periodic rate shown in the results is:

periodic rate=nominal annual rateperiods per year\text{periodic rate} = \frac{\text{nominal annual rate}}{\text{periods per year}}

For continuous compounding, EAR is:

EAR=enominal annual rate−1\text{EAR} = e^{\text{nominal annual rate}} - 1

The one-year future value is:

future value=initial balance×(1+EAR)\text{future value} = \text{initial balance} \times (1 + \text{EAR})

Worked example

With the default inputs, the nominal annual interest rate is 12%, compounding is monthly, and the initial balance is $1,000. Monthly compounding means there are 12 periods per year. The periodic rate is therefore 12% ÷ 12, or 1.00% per month.

EAR compounds that 1.00% monthly rate for 12 months. The result is 12.68% as the effective annual rate. The one-year future value is $1,000 × 1.126825…, which formats as $1,126.83. The output also shows 12 compounding periods per year and the 1.00% periodic rate.

If the same 12% nominal rate is changed to continuous compounding, the periodic-rate line becomes “Continuous” and the formula changes. The EAR becomes 12.75%, and $1,000 grows to about $1,127.50 after one year. The difference is small here, but it proves why the compounding setting cannot be ignored.

EAR versus APR versus APY

EAR is a rate-standardization tool. It strips the comparison down to nominal rate plus compounding frequency. APR is a borrowing disclosure and comparison tool; it may include finance charges, origination fees, or other costs that EAR ignores. APY is the deposit-yield version consumers see on savings accounts and CDs. APY and EAR can match mathematically, but the words signal whether you are evaluating money earned or a general effective rate.

For example, a savings account might quote a 5.00% nominal rate compounded monthly and disclose an APY near 5.12%. An investment text might call that same effective rate EAR. A personal loan with an 8.00% stated rate and fees might have an APR above both the stated rate and the compounding-only EAR. Use the finance charge calculator when the question is the dollar cost for a billing cycle, not the annualized compounding rate.

Tips and limitations

  • Match the compounding frequency to the actual product. Monthly and daily compounding are not interchangeable.
  • Do not add fees to EAR. Fees belong in APR, finance charge, or total-cost analysis.
  • Remember that the future value is only for one year in this calculator.
  • For negative rates, interpret the result as shrinkage of the initial balance over a year.
  • Check day-count conventions for contracts. This tool uses 365.242 for daily compounding, while a loan agreement might use a different basis.

Sources

The EAR formulas use algebra based on those definitions; the continuous option is the mathematical limit of periodic compounding. This is not an APY disclosure and may not match a contract’s day-count basis.

Research correction boundary: 365

Frequently asked questions

What is EAR?
EAR means effective annual rate. It converts a stated annual interest rate into the actual one-year growth rate after compounding. That lets you compare rates with different compounding frequencies on a common annual basis without relying on headline nominal rates.
How is EAR different from APY?
The math can be the same, but the context differs. APY is the consumer deposit yield term commonly used for savings products. EAR is a broader finance term used for loans, investments, and rate comparisons whenever compounding must be standardized.
How is EAR different from APR?
APR is often a borrowing-cost disclosure and may include fees or finance charges. EAR focuses on the compounding effect of a nominal rate. A loan can have a stated rate, an EAR from compounding, and an APR that changes because fees are included.
What does continuous compounding mean?
Continuous compounding is the mathematical limit where interest is added at every instant rather than once per day, month, or year. The calculator uses the exponential formula for that option and labels the periodic rate as continuous rather than showing a normal period.
Can EAR be negative?
Yes, the form allows nominal rates down to just above negative one hundred percent. A negative stated rate produces a negative EAR, meaning the balance would shrink over a year. The initial balance still cannot be negative in the calculator.
Why does daily compounding use 365.242 periods?
The daily option uses 365.242 as an average year length. This is the calculator's Regulation-DD-aligned annualization convention, not a promise that a particular contract uses the same day-count or compounding basis.

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