# Is There A Flaw In This Paycheck Calculation?

I work at a company that pays their employees every other Friday. In other words, paychecks are distributed every 14 days, ending on Friday.

Upon being hired, I was told that I will make \$300 every two weeks. (I am a part-time student employee, which is why my salary is so low). In fact, for the first year, I was paid exactly \$300 every two weeks. However, in the past month I noticed that my gross pay had decreased from \$300 to \$276.92. I contacted payroll about this, and they gave me the following response:

Salaries are calculated according to the following formula: G=(P*2*12)/26, where "G" is your gross pay, and "P" is your two-week salary." In my case, "P" is \$300.

I interpreted their formula as this:

• If I make "P" (\$300) every two weeks, and we assume that there are two paychecks per month, then my monthly salary is P*2 = \$600.
• If there are 12 months in one year, and I make P*2 every month, then my yearly salary is (P*2)*12 = \$7200.
• If there are 52 weeks in one year, and we are paid every two weeks, then my biweekly paycheck should be my yearly salary divided by 26, or ((P*2)*12)/26 = \$276.92

The problem I am having with this though, is that the first bullet assumes we are paid two times per month, when in fact we are paid every 14 days. This means that for months with 31 days, I don't receive two paychecks, but I actually should receive 2.21 paychecks. Similarly, for months with 30 days, I should receive 2.14 paychecks, and for months with 28 days, I should receive 2.00 paychecks.

If my reasoning is correct, I come up with the following conclusion:

• There are 7 months with 31 days, 4 months with 30 days, and 1 month with 28 days.
• The number of paychecks I should receive in one year is equal to: 7*2.21 + 4*2.14 + 1*2.00 = ~26
• However, payroll's assumption seems to be that we receive exactly 2.00 paychecks each month, which comes out to 12*2 = 24 paychecks per year.
• In conclusion, I am now losing two paychecks each year, or in my case, I am making \$600 less per year.

Can anyone comment on this? I would like to meet with my payroll department, but I want opinions on if my reasoning is sound or not first.

Thanks.

Update:

Perhaps some of my confusion stems from my inexperience/ignorance. I have always been under the impression that people who are paid "semi-monthly" (twice per month) typically get paid on the 15th of each month and the last day of each month. And, for example, their pay stubs would show: "Pay Period: Aug. 1 - Aug. 15" and "Pay Period: Aug. 16 - Aug. 30".

However, my pay stubs say things like: "Pay Period: Aug. 24 - Sept. 6" and "Pay Period: Sept. 7 - Sept. 20"

I guess it doesn't make sense (to me) that I would be paid "semi-monthly," yet my pay periods are spanning across the middle of months. Is this possible?

• Don't depend on your memory of what someone told you when you were hired. Either one of you (or both) could be wrong. Instead, look at the contract that you signed before you started. That should explain exactly what you are being paid (\$150/week, \$600/month, etc). Also look at you paystub to see if any deductions have been added (social security, etc.) Sep 26, 2011 at 13:08
• To respond to your update: I think it is all still irrelevant. You are clearly being paid every two weeks (7-20 is 14 days, not 15). However, that doesn't mean that they aren't measuring salaries in terms of half-months. Those are two different things. Sep 26, 2011 at 17:31

The math in your question (and their "formula", to be honest) is complicating something rather simple:

• Are you paid \$300 for two weeks' work or \$300 for 1/2 months' work?

You don't need to know how many fractions of a paycheck you get per month, or anything else. (In fact, that first bullet point of your top section essentially creates a loop that would continually reduce your paycheck by 2/26 as long as you keep calculating it. Even the worst accounting systems wouldn't be based on such flawed logic.)

All you need to know is whether the "\$300" you were supposed to be paid when you were hired originally meant every two weeks or twice per month.

• Every two weeks: \$300 × 26 paychecks per year = \$7800 yearly salary.

If the company originally intended this and converted to a twice/month paycheck, you would get 7800/24 or \$325 per paycheck.

• Twice/month: \$300 × 24 paychecks per year = \$7200 yearly salary.

If the company meant this and converted to a biweekly paycheck, you would get 7200/26 or \$276.92 per paycheck.

As you can see, the second scenario matches the paycheck you get now. According to the information you've given us, you are 100% sure you used to be paid \$300 every two weeks. In that case, they have committed an accounting error. The error is either:

• You used to be paid too much (salary intended to be \$600/month)
• They misread your contract (when switching systems or something) and are now paying you too little (salary intended to be \$300/two weeks or \$650/month).
• Thank you for your response. I like the way you put it, and I really need to find out if I'm being paid for 2 weeks or 0.5 months. My biggest concern is that the formula they gave me seems to indicate one system (0.5 monthly), whereas the issuance of paychecks every 14 days seems to indicate the other system (biweekly). Sep 26, 2011 at 17:25
• Thanks...there was a confusion when reactivating my employment for the Fall semester. Sep 28, 2011 at 4:11

There is a difference, as you noted, between bi-weekly (every two weeks) and semi-monthly (twice per month.) The former results in 26 check per year while the latter, 24.

Do you have some written confirmation of what your promised salary is? It's odd to me that you be told a rate different than the pay period. If I read this correctly, payroll is tell you, "your pay is \$600/mo, but since you are paid 26 checks per year, it divides to \$276.92 per pay period."

This may be so, but to me it sounds odd. I have an annual salary, and my check*26=salary within a few cents. In your position, I'd think you would have an hourly rate, and the math should work for the number of hours per period.

This may not be a payroll issue but an HR (human resources) issue, or discussion with whoever hired you.

• Thank you for your insight and response. I definitely agree that I should be paid hourly given my situation. Unfortunately, I didn't have much in the way of paperwork, however I really need to track that down. Could you read my update and provide any comments (if you have any)? Thanks. Sep 26, 2011 at 17:21
• If your check pay periods increment by 14 days, you are bi-weekly. So, it seems odd that someone would tell you your monthly salary. Sep 26, 2011 at 18:46