Pay and Benefits Watch: Why your paychecks don't always add up

Have you ever noticed that your paychecks don't add up to the salary listed for your grade and rank on the government's pay tables?

Take a hypothetical federal executive who makes $118,400 a year, according to the tables. Under the formula Uncle Sam uses to calculate her paychecks, she'll only get $117,998.40 in 1999. What happened to the other $401.60?

To find out, let's break down the government's pay formula.

To determine the executive's hourly rate for the year, Uncle Sam divides her yearly salary by 2,087 hours:

$118,400 / 2,087 = $56.73

To figure out the executive's biweekly rate, the government multiplies the hourly rate by 80 hours:
$56.73 x 80 = $4,538.40

Then the executive's agency pays her $4,538.40 every two weeks. There are typically 26 pay periods in a year:
$4,538.40 x 26 = $117,998.40

Look back over the formula. Can you spot Uncle Sam's secret to making the $401.60 disappear?

The trick is in how many hours a year the government says its employees work. If you work 40 hours a week for 52 weeks, you work a total of 2,080 hours in a year. If you re-calculated the executive's salary at 2,080 hours instead of 2,087 hours, then she would receive just under $118,400. But the government tacks on an additional seven hours to the formula, so employees appear to get shortchanged seven hours' pay each year.

However, there is a method to Uncle Sam's madness. In some years, there are 27 pay days, instead of 26, because of the way our calendar works. Back in 1986, some sharp-eyed budget cutters noticed that the federal pay formula was based on 2,080 hours a year. So our hypothetical executive, under the old formula, would end up with a $4,500 bonus in years with 27 pay days while getting her full salary in years with 26 pay days.

Rather than give federal employees free money every few years, Congress changed the formula to 2,087 hours. So employees are underpaid in years with 26 pay days, and then overpaid in years with 27 pay days. Our hypothetical executive still receives $4,136.80 more than the salary listed in the pay tables in years with 27 pay days, but that's offset by the $401.60 deficit in years with 26 pay days.

Why do some years end up with an extra pay day? It works like this: A biweekly pay period includes 14 days. Typically there are 26 pay periods in a year. Multiply 26 by 14. You get 364. How many days are in a year? Of course, 365 in a normal year and 366 in a leap year. So over the years, those missing days add up to a full pay period, hence the extra pay day in some years.

Pay periods vary by agencies, so the last year with 27 pay days was 1996 for some federal employees and 1997 for others. It happens roughly once every 11 or 12 years, so it will be some time before most federal employees enjoy an overpaid year again.

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