8.3.5 Percentage Points

Percentage Points

When comparing percentages, the difference between the percentages is described in terms of “percentage points.” Subtracting percentages gives percentage points.

[ A mortgage point is 1% of the amount you borrow for the purchase of your house. It is an additional fee that the bank may collect in return for offering a reduction on the annual percentage rate (APR) of the mortgage—in other words, paying this fee entitles you to a cheaper loan term. ]

Note that this is not the same as the percent increase or decrease. This distinction is something to be aware of in media reports, particularly when interest rates or buying mortgage rate points are discussed.

For example: If 72% of students starting at a community college were placed in a noncredit math course one year, but only 63% the next, the college had a decrease of 9 percentage points in students not being ready for credit math courses.

The next activity illustrates the difference between percentage points and percent change.

Notepad iconActivity: Student Loans

You took out a private student loan for college fees. You see a headline reading, “Interest rates jump 2%.” Should you be worried?

Hint icon

Comment

Most people read this headline to mean that the interest rate on the loan increases by 2 percentage points. What would that mean for you?

Is there another way to think about the headline that isn’t as sensational?

Solutions icon

Answer

The headline is ambiguous. It could mean “Interest rates increase by 2 percentage points”—for example, from 10% to 12%. This is a big deal. Your interest rate just went up 20%: open .12 minus .10 close divided by .10 multiplication 100 percent equals 20 percent.

On the other hand, the headline could mean “Interest rates increase by 2% based on your previous interest rate.” In our example, that would mean rates go up from 10% to 10 percent prefix plus of two percent of 10 percent equation sequence equals .10 plus .02 multiplication .10 equals .10 plus .002 equals .102 equals 10.2 percent

Well, OK, not great news, but hopefully manageable and much better than our first interpretation.

When people mean percentage points, they should say so! Unfortunately, many news articles do not. It’s up to you to find out from the article itself what it is about.

In newspapers and magazines, you will often run into articles that contain percentages. The exercise below illustrates the importance of interpreting this information correctly.

Notepad iconActivity: Percentage Points

A newspaper headline reads “Exam pass rate increases from 50% last year to 75% this year.”

Does this mean that the pass rate has increased by 25%? Explain why or why not.

Hint icon

Comment

Did you convert the percentages to their decimal values before using the percent increase formula?

Solutions icon

Answer

Writing the pass rates in decimal form as 0.5 and 0.75, the percent increase is:

100 percent equation left hand side equals right hand side 0.75 minus 0.5 divided by 0.5 multiplication 100 percent equation left hand side equals right hand side 0.25 divided by 0.5 multiplication 100 percent equals 50 percent

So, the pass rate has increased by 50%, not 25%. However, it would be correct to say that there was a 25 percentage point increase in the exam pass rate.

The bottom line is to be sure that you pay attention when you run across percentages. A statistic might not mean what you initially think it does. Keep your eyes open and your brain turned on!

8.3.4 Fact or Fiction?

8.3.6 The Golden Ratio