What is an 'Effective Annual Interest Rate'
The effective annual interest rate is the interest rate that is actually earned or paid on an investment, loan or other financial product due to the result of compounding over a given time period. It is also called the effective interest rate, the effective rate or the annual equivalent rate. Calculated as:
BREAKING DOWN 'Effective Annual Interest Rate'
The effective annual interest rate is an important concept in finance because it is used to compare different products that calculate compounded interest differently. For example, if a investment A pays 10%, compounded monthly, and a investment B pays 10.1% compounded semiannually, the effective annual interest rate can be used to determine which investment will actually pay more over the course of the year.
Effective Annual Interest Rate Calculation
The nominal interest rate is the stated rate on the financial product. In the example above, the nominal rate for investment A is 10% and 10.1% for investment B. The effective annual interest rate is calculated by taking the nominal interest rate and adjusting it for the number of compounding periods the financial product will experience in the given period of time. The formula is as follows:
Effective annual interest rate = (1 + (nominal rate / number of compounding periods)) ^ (number of compounding periods)  1
For investment A, this would be: 10.47% = (1 + (10% / 12)) ^ 12  1
And for investment B, it would be: 10.36% = (1 + (10.1% / 2)) ^ 2  1
As can be seen, even though investment B has a higher stated nominal interest rate, because it compounds less times over the year, the effective annual interest rate is lower than the effective rate for investment A. It is important to calculate the effective rate because is an investor were to invest, for example, $5,000,000 into one of these investments, the wrong decision would cost over $5,800 per year.
As the number of compounding periods increases so does the effective annual interest rate. Quarterly compounding produces higher returns than semiannual compounding, monthly compounding more than quarterly, and daily compounding more than monthly. Below is a breakdown of the results of these different compound periods with a 10% nominal interest rate:
Semiannual = 10.250%
Quarterly = 10.381%
Monthly = 10.471%
Daily = 10.516%
There is a limit to the compounding phenomenon. Even if compounding occurs an infinite amount of times, not just every second or micro second, but continuously, the limit of compounding is reached. With 10%, the continuously compounded effective annual interest rate is 10.517%. The continuous rate is calculated by raising the number "e" (approximately equal to 2.71828) to the power of the interest rate and subtracting one. It this example, it would be 2.171828 ^ (0.1)  1.

Discrete Compounding
Discrete compounding refers to the method by which interest is ... 
Stated Annual Interest Rate
The return on an investment that is expressed as a peryear percentage, ... 
Compounding
The ability of an asset to generate earnings, which are then ... 
Nominal Interest Rate
The interest rate before taking inflation into account. The equation ... 
Nominal Rate Of Return
The amount of money generated by an investment before expenses ... 
Front Fee
The option premium paid by an investor upon the initial purchase ...

Investing
Overcoming Compounding's Dark Side
Understanding how money is made and lost over time can help you improve your returns. 
Financial Advisor
Compound Annual Growth Rate (CAGR)
The compound annual growth rate is an important tool for measuring investment performance and comparing it across asset classes. Discover how it is calculated and how it can inform your investment ... 
Investing
Interest Rates Explained: Nominal, Real, Effective
Interest rates are divided into subcategories. Smart investors look beyond the nominal or coupon rate of a bond or loan to see if it fits their objectives. 
Retirement
Using Compounding to Boost Retirement Savings
Allowing growth on your investments to compound over time gives you immense returns when saving for retirement. 
Investing
Calculating Future Value
Future value is the value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today. 
Investing
4 Ways Simple Interest Is Used In Real Life
Simple interest works in your favor when you're a borrower, but against you when you're an investor. 
Investing
How to Calculate Your Investment Return
How much are your investments actually returning? Find out why the method of calculation matters. 
Personal Finance
Simple Interest Loans: Do They Exist?
Yes, they do. Here is what they are â€“ and how to use them to your advantage.

How do mutual funds compound interest?
Learn how mutual funds can grow wealth over time through the magic of compound interest by reinvesting dividends back into ... Read Answer >> 
How do I use the rule of 72 to calculate continuous compounding?
Find out why the rule of 72 does not accurately reflect the growth caused by continuous compounding, and which number can ... Read Answer >> 
What is the rationale behind the effective interest rate?
Read about the reasons why market actors identify the effective interest rate as it pertains to investing, lending and accounting. Read Answer >> 
How can I tell if a loan uses simple or compound interest?
Learn the differences between simple and compound interest and how you can identify which one a loan uses. Read Answer >> 
What is the difference between continuous compounding and discrete compounding?
Learn to differentiate between and calculate the continuous and discrete compounding formulas for interestgenerating investments ... Read Answer >>