Next video:
Loading the player...

The effective annual interest rate is a way of restating the annual interest rate so that it takes into account the effects of compounding. 

The formula is:

R = (1+ i / n)  ^ n – 1. 

In this formula, R is the effective annual interest rate, i equals the stated annual interest rate and n equals the compounding period (which is usually semiannually, monthly or daily).

The focus here is the contrast between R and i. If i, the annual interest rate, is 10%, then with monthly compounding where n equals the number of months in a year (12), the effective annual interest rate is 10.471%

The formula would appear as:

(1+10 % / 12 ) ^ 12 – 1 = 10.471%

Why bother with effective annual interest? Using the effective annual interest rate helps us understand how differently a loan or investment performs if it compounds semiannually, monthly, daily or in any other timeframe.

From the previous example, if we had $1,000 in a loan or investment that compounds monthly, it would yield $104.71 of interest in one year (10.471% of $1,000), which a higher amount than if we had the same loan or investment compounded annually. Yearly compounding would only generate $100 of interest (10% of $1,000), a difference of $4.71.  

If the loan or investment compounded daily (n = 365) instead of monthly (n = 12), the interest for that loan or investment would then be $105.16. As a rule of thumb, the more periods (n) the investment or loan compounds, the higher the effective annual interest rate will be. 

Related Articles
  1. Investing

    Learn Simple and Compound Interest

    Interest is defined as the cost of borrowing money, and depending on how it is calculated, it can be classified as simple interest or compound interest.
  2. Personal Finance

    APR and APY: Why Your Bank Hopes You Can't Tell The Difference

    Banks use these rates to entice borrowers and investors. Find out what you're really getting.
  3. Investing

    How to Find Quality Stocks Amid the Wreckage

    Finding companies with good earnings and hitting on all cylinders in this environment, although possible, is not easy.
  4. Investing

    Explaining Interest

    Interest is the price charged to borrow money, and is typically expressed as a percentage of the principal, or the amount loaned.
  5. Personal Finance

    Simple Interest Loans: Do They Exist?

    Yes, they do. Here is what they are – and how to use them to your advantage.
  6. 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.
  7. Insights

    Simple Interest

    Simple interest is a quick method of calculating the interest charged on a loan. Simple interest is determined by multiplying the interest rate by the principal by the number of periods.
  8. Trading

    How Do You Use the Stochastic Oscillator?

    A stochastic oscillator is a technical momentum indicator that compares a security's closing price to its price range over a given time period.
  9. Retirement

    Using Compounding to Boost Retirement Savings

    Allowing growth on your investments to compound over time gives you immense returns when saving for retirement.
  10. Insurance

    Top Healthcare, Medical Equipment Stocks of 2015

    A short list of the top healthcare and medical equipment stocks of 2015.
Hot Definitions
  1. Turkey

    Slang for an investment that yields disappointing results or turns out worse than expected. Failed business deals, securities ...
  2. Maintenance Margin

    The minimum amount of equity that must be maintained in a margin account. In the context of the NYSE and FINRA, after an ...
  3. Salvage Value

    The estimated value that an asset will realize upon its sale at the end of its useful life. The value is used in accounting ...
  4. Cryptocurrency

    A digital or virtual currency that uses cryptography for security. A cryptocurrency is difficult to counterfeit because of ...
  5. Promissory Note

    A financial instrument that contains a written promise by one party to pay another party a definite sum of money either on ...
  6. SEC Form 13F

    A filing with the Securities and Exchange Commission (SEC), also known as the Information Required of Institutional Investment ...
Trading Center