## Taking advantage of pay frequency

— Arvada, Colorado UNITED STATES

A while back, my employer tried to switch from paying us monthly to paying us biweekly. It had to do with lower administration costs or some bureaucratic procedural details. The plan didn't go over well with the employees to the point where, eventually, the idea was scrapped. Overall, employees weren't happy with the change, but I was actually in favor of making the change. I had figured out that, considering the details in the implementation, once you added up all the paychecks, it meant that the employees actually got **more** money being paid biweekly. On the surface, it's natural to assume that the pay would be the same either way. Let's use some examples. Mike and Brittany both get hired with the same company on the same day. (For convenience sake, we're going to say 2019 December 1 since that month began on a Sunday.) Both Mike and Brittany have negotiated their payrate to be $58,500.00 annually. The difference is that Mike elected to get paid every month on the last day of the month while Brittany elected to get paid biweekly (i.e., every fourteen days). For Mike's monthly salary, the employer naturally divided his annual rate by twelve. $$\mathrm{\$}\mathrm{58,500.00}\xf712=\mathrm{\$}\mathrm{4,875.00}$$ For Brittany's biweekly salary, since (naturally) there are fifty-two weeks in a year, there should be twenty-six paychecks. $$\mathrm{\$}\mathrm{58,500.00}\xf726=\mathrm{\$}\mathrm{2,250.00}$$ Let's suppose that both Mike and Brittany continue to work at this job (without getting a raise) until 2049 July 31—which, conveniently, is a payday for both of them. How much have each of them been paid total over the years if we were to count up each of their *individual* paychecks? We could either put the numbers on a spreadsheet or chalk up six lines of code in a scripting language and run it. If we were to do that, the results would be that Mike got a total of $1,735,500.00 over the course of his career while Brittany was paid $1,741,500.00 over that same course of time. Go ahead and try it yourself and see. Brittany got paid **six thousand dollars** more than Mike did over the same course of time when they were supposed to have the same salary. Now sure, over approximately thirty years, six thousand dollars comes out to just two hundred dollars each year (which is what Mike is saying to himself to psychologically minimize the discrepancy), but, hey… more money is more money. The question is: how did that happen. Okay, earlier I said that there are fifty-two weeks in a year. That was… a lie. A fifty-two-week year has 364 days in it. However, actual years have 365 days or 366 days if it's a leap year. Brittany gets paid **every** fourteen days. Period. Every time another fourteen days pass and if Brittany hasn't managed to die, retire, do something to get herself fired or ragequit in frustration, she gets another paycheck. Mike, on the other hand, gets paid at the end of every month. Sometimes, that month can be as short as twenty-eight days; othertimes, it can be as much as thirty-one days. Mike gets paid the same amount regardless of the length of time. That still shouldn't make a difference, right? Even though Mike gets paid monthly, at the end of the year it should even out. However, Mike's years are 365 or 366 days; Brittany's years are 364 days. Every year there is at least one day that Brittany gets paid for that Mike doesn't. In leap years, it's two days. Over a significant length of time (e.g., thirty years, perhaps?), that comes to a six-thousand-dollar discrepancy. Brittany and Mike's employer could have also calculated the amounts better. Instead of dividing Brittany's annual rate by 26, a number of 26.08875 (i.e., the number of biweekly pay periods in a mean Gregorian year) would have closed the gap much more significantly and saved the employer some money. While my employer ultimately chose not to implement the switch, their course of action at the time was to stick with 26. If you find yourself in this situation, I say take every advantage you can get.

Tags: Calendars, Mathematics

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