One of my favorite popular math books is called, A Mathematician Reads the Newspaper by John Allen Paulos. In it, the Temple University Mathematics professor has very short, newspaper-like articles which begin with a headline and maybe part of an actual newspaper article. Using math, he then either explains why the headline isn't all that extraordinary or debunks the facts. Professor Paulos is also the author of the book, Innumeracy: Mathematical Illiteracy and Its Consequences.
Both books came to mind the other day when I read an article from Monday's Daily Collegian. In the article entitled, "Direct loan plan could cause debt," the reporter quotes a PHEAA spokesman Keith New as saying that Penn State's decision to join the Federal Direct Student Loan Program would result in a $300 billion debt increase over the next 10 years. In a direct quote, Mr. New said, "Every loan is made from the U.S. Treasury, so every loan adds to the national debt."
When I read the number it just didn't seem right to me, so I did the math (as I assume, the spokesman, Mr. New; the writer, Mr. Weisler; and the copy editor should have done). I based my student numbers on a quote from Melissa Kunes in the article, the "vast majority of the 40,800 Penn State students who receive Stafford Loan funding used PHEAA as their lender."
Let's go to the chalkboard, shall we:
$300 x 10^9 / 10 years = $30 x 10^9/ year
$30 x 10^9 / 40.8 x 10^3 students/year = $735,294.12/student-year
Which means for the numbers to be right, each of our students must borrow over $735,000/year. I checked and while Penn State is expensive, this is about 100 times what a Penn State student can get. Another way to think about it, is that at $30 billion/year, Penn State student loans would be responsible for one tenth of the expected U.S. budget deficit each fiscal year. Somebody should have done the math.
Even if you assume Ms. Kunes is wrong (which I don't), she can only be off by a factor of 2 because there are only about double 40,800 students at Penn State. So something happened here. Let us assume that the Collegian writer misheard the PHEAA spokesman, then the number is only about $3 billion over 10 years or $300 million/year. Would Penn State add $300 million to the national debt/year? Well, only if you assume the default rate on the loans is 100%. If you assume the default rate is more like 3-4% (that's about the Pennsylvania rate, the rates for 4-year colleges are usually lower) and the interest rates on these loans are currently >6%... it's really a wash.
So, I leave the reader with two questions and some homework:
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