Effective Annual Rate (EAR) Calculator

Convert a nominal annual rate into the effective annual rate for any compounding frequency, including continuous compounding.

Result

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How to use this calculator

Enter the nominal annual rate (the stated APR).
Choose how often it compounds, or select continuous.
Read the effective annual rate (EAR/APY).
Use the side-by-side table to compare frequencies.

About this calculator

The nominal annual rate (APR) on a loan or savings account does not, by itself, tell you how much interest actually accrues in a year — that depends on how often it compounds. The effective annual rate (EAR), also called the annual percentage yield (APY) for deposits, captures the real yearly cost or return by accounting for compounding within the year. This calculator converts a nominal rate to its EAR for any frequency — annual, semiannual, quarterly, monthly, weekly, daily, or continuous — using EAR = (1 + nominal/m)^m − 1, with the continuous case given by e raised to the nominal rate, minus one. The more frequently interest compounds, the higher the EAR climbs above the nominal rate, approaching the continuous limit. The tool also shows the EAR at several common frequencies side by side, so you can compare offers on an apples-to-apples basis — always EAR to EAR, never APR to APY.

How it works — the formula

EAR = (1 + nominal/m)^m − 1     (m compounds per year)
Continuous: EAR = e^nominal − 1

Compounding the nominal rate m times a year and annualizing gives the effective rate; infinite compounding yields the continuous formula.

Source: Investopedia — Effective Annual Interest Rate

Worked examples

Example 1

6% nominal, monthly

Inputs:: nominal=6, freq=12
Output:: EAR 6.1678%

Example 2

6% nominal, daily

Inputs:: nominal=6, freq=365
Output:: EAR 6.1831%

Example 3

6% nominal, continuous

Inputs:: nominal=6, freq=0
Output:: EAR 6.1837%

Limitations

Assumes a constant nominal rate.
Ignores fees that change the true cost (APR with fees differs).
Continuous compounding is a theoretical limit.

Rate conversion; compare like-for-like (EAR to EAR).

Frequently asked

What is the effective annual rate?+

The EAR is the actual annual interest rate after accounting for compounding within the year. A 6% nominal rate compounded monthly has an EAR of about 6.17%, because interest earns interest each month.

What is the difference between APR and APY?+

APR (the nominal rate) does not include intra-year compounding; APY (the same as EAR) does. For the same nominal rate, APY is higher the more frequently interest compounds. Compare loans by APR-vs-APR and savings by APY-vs-APY, and convert when mixing.

How does compounding frequency affect the EAR?+

More frequent compounding raises the EAR. At 6% nominal: annual gives 6.00%, monthly 6.17%, daily 6.18%, and continuous 6.184%. The increases shrink as frequency rises, converging to the continuous limit.

What is continuous compounding?+

It is the theoretical limit of compounding infinitely often. The EAR is then e raised to the nominal rate, minus one. It is only marginally higher than daily compounding and is used mainly in finance theory and options pricing.

Why do banks advertise APY for savings?+

Because APY (the EAR) shows the true annual return including compounding, making it the honest, comparable figure. U.S. regulations require deposit accounts to disclose APY so consumers can compare offers directly.

How do I convert EAR back to a nominal rate?+

For m compounds per year, nominal = m × ((1 + EAR)^(1/m) − 1). This calculator goes from nominal to EAR; reverse the formula if you have the EAR and need the nominal rate for a given frequency.