### What’s the difference between a percentage, a percentage point, and a basis point?

Three terms—*percentage*, *percentage point* and *basis point*—are widely used in finance. Their meanings are different, and getting them mixed up can lead to an expensive mistake.

A percentage is a way of expressing a ratio as *parts per hundred*. Five parts per hundred can be written as 20%. To convert any ratio to a percentage, simply write it as a fraction and multiply by a hundred. For example: three out of four is three-quarters; multiply it by a hundred and you get three hundred quarters, which is 75. Therefore a ratio of three out of four can be expressed in percentage form as 75%.

Percentages are the usual way to express the yield of an investment. If you invest money at 5% interest per annum (year), you expect to earn $5 each year for every $100 that you invest. Now suppose the interest rate goes up from 5% to 6%. That’s an increase of 20%, because for the same investment you will receive twenty percent more interest each year. If you have $100 invested, you will now receive $6 interest per year instead of $5. That’s an increase of $1 over $5, which is 20%.

It’s confusing when we are dealing with a percentage increase of something that is already a percentage. It’s tempting to say that an increase in the interest rate from 5% to 6% is an increase of 1% (because 6% minus 5% equals 1%). To make it clear that we are talking about a *change in the interest rate percentage*, rather than the *percentage increase in the amount of interest paid*, we use the term *percentage point*.

When the interest rate goes up from 5% to 6%, we can say that the interest rate has increased by twenty percent, or we can say that the interest rate has been increased by one percentage point.

In finance it’s common to set interest rates in fractions of a percent, and to encounter small changes to interest rates. For this purpose we use the term *basis point*, which simply means one hundredth of a percentage point. When the interest rate goes up from 5% to 6%, we can say that the interest rate has been increased by 100 basis points. If the interest rate then goes down from 6% to 5.95%, we can say that the interest rate has been reduced by 5 basis points.

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