Free Financial Calculator Online

Effective Annual Interest Rate Calculator

Convert a nominal interest rate (APR) to the effective annual rate (EAR or APY) for any compounding frequency, including continuous compounding.

%
Effective annual rate (EAR / APY)
12.6825%
CompoundingEAR at 12.00%
Annually (1)12.0000%
Semi-annually (2)12.3600%
Quarterly (4)12.5509%
Monthly (12)12.6825%
Weekly (52)12.7341%
Daily (365)12.7475%
Continuously12.7497%

How it's calculated

EAR = (1 + r ÷ n)n − 1, and for continuous compounding EAR = er − 1.

r is the nominal annual rate as a decimal and n the number of compounding periods per year. Enter the rate as a percent; the calculator converts it.

Need to calculate the effective interest rate of an investment or loan payment? Use our free calculator above!

The Effective Interest Rate Calculator is a tool designed to help you understand the impact of the frequency of interest compounding on the actual annual interest rate you earn on an investment or pay on a loan. Nominal interest rate, also known as the quoted or stated rate, is the rate that doesn’t take into account the effect of compounding. However, in reality, the interest you earn or owe can be compounded on various intervals such as annually, semiannually, quarterly, monthly, or daily. The effective interest rate, also known as the annual equivalent rate (AER), reveals the true return on an investment or the true cost of a loan, which is typically higher than the nominal rate due to the effects of compounding.

The nominal interest rate is the interest rate before taking inflation or compounding into account. It’s the rate that’s quoted in loan agreements or investment descriptions. However, the nominal interest rate doesn’t provide a complete picture since it doesn’t account for the effects of compounding. Compounding periods refer to the frequency with which interest is added to the principle over a set period of time. The more frequently interest is compounded, the greater the overall interest will be. For instance, if interest is compounded annually, n would be 1; for semiannually, n would be 2; for quarterly, n would be 4; for monthly, n would be 12; and for daily, n would be 365. The Effective Interest Rate Calculator takes these two inputs (the nominal interest rate and the number of compounding periods) and uses them to calculate the effective interest rate, giving a more accurate measure of interest.

How To Use Our Effective Interest Rate Calculator

Input the Nominal Interest Rate

In the field labeled “Nominal Interest Rate (as a decimal)”, input your nominal or stated interest rate as a decimal (for example, input 0.05 for a 5% interest rate).

Input the Number of Compounding Periods per Year

In the field labeled “Number of Compounding Periods per Year”, input the number of times your interest is compounded annually. For instance, if your interest is compounded monthly, input 12; if it’s compounded quarterly, input 4.

Calculate the Effective Interest Rate

Once you’ve inputted the nominal interest rate and the number of compounding periods, click on the “Calculate” button. The calculator will use these inputs to compute the effective interest rate and display the result. The output will give you the actual annual interest rate that reflects the impact of compounding.

Frequently Asked Questions

›What is the effective annual rate?

The effective annual rate (EAR) is the interest you actually earn or pay in a year once compounding is included. It is always at least as high as the nominal rate, and higher the more often interest compounds.

›How do you calculate EAR?

EAR = (1 + r/n)^n − 1, where r is the nominal annual rate as a decimal and n is the number of compounding periods per year. A 12% rate compounded monthly: (1 + 0.01)^12 − 1 = 12.68%.

›Is EAR the same as APY?

Yes. Banks call it annual percentage yield (APY) on savings accounts. APR, used for loans, is usually the nominal rate and does not include compounding.

›What is continuous compounding?

The limit as compounding becomes infinitely frequent. EAR = e^r − 1, so 10% compounded continuously is 10.52%, barely more than daily compounding.

Browse all financial calculators