What does π have to do with exchange rates, much less pie?

First a disclaimer: an over-educated family member said that puns are the lowest form of humor.  She meant that puns are “crude”, and are not to be used.

Exchange rates convert values denominated in one currency into another currency.  Boring, right? To buy a piece of pie that costs €2.00 (two euros) today, when you have only dollars, you need exchange rates to convert that euro value into dollar equivalents. 

Simple math. At today’s rate of $1.30 per €1, two euros equals $2.60 (2 x 1.30).  Just multiply the euro value by the exchange rate.  If the pie is priced in dollars instead of euros, it’s just division using the same exchange rate (2.60 / 1.30 = 2.00).

It works as simply as the colloquial idioms “piece of cake” and “easy as pie” are interchanged with each other.

Getting to Pi

If the exchange rate is an irrational number, like π, what do you do? Pi has an infinite number of digits to the right of the decimal point.  Worse, unlike 1/3 which can be written as 0.333…, the digit isn’t a repeating “3”; it changes.  One computer calculated the value beyond 200 billion digits.

Exchange rates get no exemption from Mathematics.  What to do with the extra decimal places?

Peter, Michael, and Samir, computer programmers in the 1999 movie Office Space had a brilliant idea: insert code into a program to round down the fractions beyond the cent on each bank transaction.  The difference then was sent to a bank account of their own.  Since these rounding differences were so small, by their calculations it would take some time for a substantial balance to accumulate in their account and the scheme would go unnoticed.  To their surprise within a few days the account accumulated more than $350,000 USD.

Was it a programming error on their part or does rounding lose that much money?  A better understanding of exchange rates provides an answer.

Robert Rowan is an International Finance Controller for SAS and the author of Foreign Currency Financial Reporting from Euro to Yen to Yuan: A Guide to Fundamental Concepts and Practical Applications.