I am grading the final projects of my class, I am trying the clear the backlog of publishing all the class notes, I am way behind on my STOC reviews, and in two days I am taking off for a complicated two-week trips involving planes, trains and a rented automobile, as well as an ambitious plan of doing no work whatsoever from December 20 to December 31.
So, today I was browsing Facebook, and when I saw a post containing an incredibly blatant arithmetic mistake (which none of the several comments seemed to notice) I spent the rest of the morning looking up where it came from.
The goal of the post was to make the wrong claim that people have been paying more than enough money into social security (through payroll taxes) to support the current level of benefits. Indeed, since the beginning, social security has been paying individuals more than they put in, and now that population and salaries have stop growing, social security is also paying out retired people more than it gets from working people, so that the “trust fund” (whether one believes it is a real thing or an accounting fiction) will run out in the 2030s unless some change is made.
This is a complicated matter, but the post included a sentence to the extent that $4,500 a year, with an interest of 1% per year “compounded monthly”, would add up to $1,3 million after 40 years. This is not even in the right order of magnitude (it adds up to about $220k) and it should be obvious without making the calculation. Who would write such a thing, and why?
My first stop was a July 2012 post on snopes, which commented on a very similar viral email. Snopes points out various mistakes (including the rate of social security payroll taxes), but the calculation in the snopes email, while based on wrong assumptions, has correct arithmetic: it says that $4,500 a year, with a 5% interest, become about $890k after 49 years.
So how did the viral email with the wrong assumptions and correct arithmetic morph into the Facebook post with the same wrong assumptions but also the wrong arithmetic?
I don’t know, but here is an August 2012 post on, you can’t make this stuff up, Accuracy in Media, which wikipedia describes as a “media watchdog.”
The post is attributed to Herbert London, who has PhD from Columbia, is a member of the Council on Foreign Relation and used to be the president of a conservative think-tank. Currently, he has an affiliation with King’s College in New York. London’s post has the sentence I saw in the Facebook post:
(…) an employer’s contribution of $375 per month at a modest one percent rate compounded over a 40 year work experience the total would be $1.3 million.
The rest of the post is almost identical to the July 2012 message reported by Snopes.
Where did Dr. London get his numbers? Maybe he compounded this hypothetical saving as 1% per month? No, because that would give more than $4 million. One does get about $1.3 million if one saves $375 a month for thirty years with a return of 1% per month, though.
Perhaps a more interesting question is why this “fake math” is coming back after five years. In 2012, Paul Ryan put forward a plan to “privatize” Social Security, and such a plan is now being revived. The only way to sell such a plan is to convince people that if they saved in a private account the amount of payroll taxes that “goes into” Social Security, they would get better benefits. This may be factually wrong, but that’s hardly the point.