## 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:

Next Up

## 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 semi-annually, 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 semi-annual 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:

Semi-annual = 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.

RELATED TERMS
1. ### Periodic Interest Rate

The interest rate charged on a loan or realized on an investment ...
2. ### Compound Interest

Compound Interest is interest calculated on the initial principal ...
3. ### Discrete Compounding

Discrete compounding refers to the method by which interest is ...
4. ### Continuous Compounding

The process of earning interest on top of interest. The interest ...
5. ### Compound Return

The rate of return, usually expressed as a percentage, that represents ...
6. ### Stated Annual Interest Rate

The return on an investment that is expressed as a per-year percentage, ...
Related Articles
1. Investing

### Accelerating Returns With Continuous Compounding

Investopedia explains the natural log and exponential functions used to calculate this value.
2. Investing

### 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 ...
4. 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.
5. Managing Wealth

### Dissecting the Simple Interest Formula

Simple interest ignores the effect of compounding: it's only calculated on the principal amount. This makes it easier to calculate than compound interest.
6. Investing

### How to Calculate Your Investment Return

How much are your investments actually returning? Find out why the method of calculation matters.
7. 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.
8. Investing

### The Interest Rates: APR, APY And EAR

When most people shop for financial products, all they focus on is the listed interest rate. Human eyes instinctively dismiss the fine print, which usually includes the terms APR (annual percentage ...
RELATED FAQS
1. ### What formula can I use to calculate interest on interest?

Find out more about compounding interest, what it measures and how to calculate the amount of compound interest accrued using ... Read Answer >>
2. ### How do I calculate compound interest using Excel?

Learn what compound interest is, the formula used to calculate it, and how to calculate it using three different techniques ... Read Answer >>
3. ### 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 >>
4. ### 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 >>
5. ### How can I tell if a loan uses simple or compound interest?

Learn the differences between simple and compound interest and how you can use mathematical calculations and lender disclosures ... Read Answer >>
6. ### What is the difference between continuous compounding and discrete compounding?

Learn to differentiate between and calculate the continuous and discrete compounding formulas for interest-generating investments ... Read Answer >>
Hot Definitions
1. ### Investing

The act of committing money or capital to an endeavor with the expectation of obtaining an additional income or profit.
2. ### Stagflation

A condition of slow economic growth and relatively high unemployment - a time of stagnation - accompanied by a rise in prices, ...
3. ### Notional Value

The total value of a leveraged position's assets. This term is commonly used in the options, futures and currency markets ...
4. ### Interest Expense

The cost incurred by an entity for borrowed funds. Interest expense is a non-operating expense shown on the income statement. ...
5. ### Call Option

An agreement that gives an investor the right (but not the obligation) to buy a stock, bond, commodity, or other instrument ...
6. ### Pro-Rata

Used to describe a proportionate allocation. A method of assigning an amount to a fraction, according to its share of the ...