Effective Annual Rate (EAR) Calculator

The Effective Annual Rate (EAR), also called the Effective Annual Interest Rate or Annual Equivalent Rate (AER), is the actual interest rate earned or paid on a loan or investment after accounting for compounding within the year. Unlike the nominal rate, EAR reflects the true cost or return when interest is compounded more than once annually.

For standard compounding, EAR = (1 + r/m)^m − 1, where r is the nominal annual rate expressed as a decimal and m is the number of compounding periods per year. For continuous compounding, the formula becomes EAR = e^r − 1, where e is Euler's number (≈ 2.71828).

Two financial products can have the same nominal rate but very different true costs if their compounding frequencies differ. EAR standardises this by expressing each product's rate on the same annual basis, making it straightforward to pick the better deal — whether you're comparing savings accounts, mortgages, or credit cards.

The more frequently interest is compounded, the higher the EAR relative to the nominal rate. For example, a 12% nominal rate compounded monthly produces a higher EAR than the same rate compounded quarterly. With continuous compounding, EAR reaches its theoretical maximum for a given nominal rate.

The nominal rate (also called the stated rate) is the advertised interest rate before compounding effects are considered. The EAR accounts for the fact that interest is compounded within the year, making it the true rate you actually earn or pay. The EAR is always equal to or greater than the nominal rate.

Continuous compounding assumes interest is calculated and added to the principal at every infinitely small instant, rather than at discrete intervals like monthly or daily. The EAR formula for continuous compounding is EAR = e^r − 1. This produces the highest possible EAR for a given nominal rate.

Enter the nominal rate for each loan separately and set the appropriate compounding frequency. Compare the resulting EAR values — the loan with the lower EAR is cheaper regardless of how the nominal rates are quoted. This approach eliminates confusion caused by differing compounding schedules.

Yes, in most contexts. Annual Percentage Yield (APY) — commonly used for savings accounts and deposits — is the same concept as EAR. Both express the true annual rate after compounding. Annual Percentage Rate (APR) on the other hand is typically a nominal rate and may not reflect compounding, so it should not be confused with EAR or APY.