June 20, 2011
I hope you had a perfect score in my quiz below. You’ll find the answers at the end of the column.
Many people are poor with percentages, even if they had great math marks in school.
Even large companies can make mistakes. Check out a computer ad published in the late 1990s.
“Why cruise at 60 when you can speed at 75?” the headline said, referring to the new Dell Dimension 75 MHz Pentium-chip based system.
“You get 15 per cent more processing power than a 60 MHz system. That’s one heck of a machine for under $2,000.”
Dell’s processing speed was impressive at the time, says Jack Weiner, a mathematics and statistics professor at the University of Guelph.
However, going from 60 MHz to 75 MHz was a 25 per cent increase — not 15 per cent, as the ad said.
Today, you can buy a $450 Dell laptop with 2.5 GHz of processing power. One MHz (or megahertz) equals one million cycles per second, while one GHz (or gigahertz) equals one billion cycles per second — or 1,000 MHz.
To calculate the increase in this case, you subtract the earlier amount (60) from the later amount (75). That’s 15.
Then, you divide 15 by 60 and multiply it by 100. The result: A 25 per cent increase.
A common mistake is to divide 15 by 75 and multiply by 100, producing a 20 per cent increase.
You have to use the earlier amount, not the later amount, as the divisor.
(The divisor is the number used to divide another. In the equation 15/3 = 5, the number 3 is the divisor.)
Confusion about calculating percentage increases and decreases is common. This can lead to money management problems.
Here’s a real case, involving mortgages sold to low-income U.S. consumers before the 2008 market crash.
Many subprime mortgages, not available in Canada, had low “teaser rates” in the first year, followed by stiff increases in subsequent years.
Sellers often exploited a common misunderstanding of “per cent” and “percentage point” to bamboozle borrowers about the increases they faced.
Suppose you started with a 2 per cent mortgage rate. The bank has told you that rates would be going up 10 per cent in the next year.
That could mean two things:
1) Your rate would go from 2 per cent to 2.2 per cent (an increase of one-tenth of a percentage point).
2) Your rate would go from 2 per cent to 12 per cent (an increase of 10 percentage points or 500 per cent).
Scenario one was comfortable. Scenario two was catastrophic.
The widespread confusion about calculating percentages helped bring about a collapse in the U.S. real estate market. Luckily, Canada’s banks never entered subprime territory.
Percentage points are used to show the arithmetical difference between rates. For example, if a rate jumps from 2 per cent to 10 per cent, that’s an increase of 8 percentage points.
We in the media find it easier to use per cent instead of percentage point. If the Bank of Canada rate goes from 2 per cent to 3 per cent, that’s an increase of one percentage point — not 1 per cent, as reporters often say.
By downplaying an actual rate increase of 50 per cent, we create a climate of misunderstanding and possible disaster.
The difference between per cent and percentage points was a mystery to me until I became a full-time business writer. Now I’m aware of how often they’re confused.
I asked Alan Goldhar, who teaches business at York University, if students know the difference.
“For business students, I’d guess about half would understand the concepts right away,” he said.
“For non-business majors, I suspect one in five students would understand without explanations or examples by me. I’m usually amazed at how little most of them know about finance concepts.”
Let’s hope practical life skills are added to school curricula, so that students learn the skills needed for successful money management at a younger age.
Here are the questions
a) 10 per cent
b) 11 per cent
2. You hope to buy a $30,000 car, but end up with a $45,000 model. You blew your budget by how much in percentage terms?
a) 33 per cent
b) 45 per cent
c) 50 per cent
3. You have a mortgage with a 3 per cent interest rate for one year. The rate goes up to 6 per cent in the second year. What is the percentage increase?
a) 3 per cent
b) 50 per cent