# Pay periods - Biweekly vs. Annual and why doesn't it add up
**URL:** https://boards.straightdope.com/t/pay-periods-biweekly-vs-annual-and-why-doesnt-it-add-up/151342
**Category:** Factual Questions
**Created:** [January 27, 2003, 9:50pm UTC](https://boards.straightdope.com/t/pay-periods-biweekly-vs-annual-and-why-doesnt-it-add-up/151342 "2003-01-27T21:50:28Z")
**Posts on this page:** 12
**Page:** 1
### Author:  [@BobT](https://boards.straightdope.com/u/BobT)
#### Post date: [January 27, 2003, 9:50pm UTC](https://boards.straightdope.com/t/pay-periods-biweekly-vs-annual-and-why-doesnt-it-add-up/151342/1 "2003-01-27T21:50:28Z")
I’m trying to figure just what I’m missing here when trying to explain to people at work about what our salaries should be.
As an example: (just pulling out a salary schedule at random)
Hourly: $19.96
Biweekly: $1596.80
Annual: $41676.48
If you take the biweekly amount and multiply it by 26, you would get $41516.80. That’s also what you get if you multiply the hourly rate by 2080 (52 weeks of 40 hours/week)
However, if you take the Annual and divide it by 260, you get $160.29. And if you add $160.29 to the (Biweekly \* 26) amount, you get $41677.09. Which is $0.61 off.
If you work this calculation for pretty much every pay schedule, you are always off by this same relative amount.
So just what am I figuring out wrong?
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### Author:  [@bup](https://boards.straightdope.com/u/bup)
#### Post date: [January 27, 2003, 9:53pm UTC](https://boards.straightdope.com/t/pay-periods-biweekly-vs-annual-and-why-doesnt-it-add-up/151342/2 "2003-01-27T21:53:47Z")
The annual is a tad bit more than the biweekly\*26, because a year has one more day than 52 weeks.
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### Author:  [@SmackFu](https://boards.straightdope.com/u/SmackFu)
#### Post date: [January 27, 2003, 10:06pm UTC](https://boards.straightdope.com/t/pay-periods-biweekly-vs-annual-and-why-doesnt-it-add-up/151342/3 "2003-01-27T22:06:13Z")
Annual = Hourly \* 8 \* 261
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### Author:  [@C\_K\_Dexter\_Haven](https://boards.straightdope.com/u/C_K_Dexter_Haven)
#### Post date: [January 27, 2003, 10:15pm UTC](https://boards.straightdope.com/t/pay-periods-biweekly-vs-annual-and-why-doesnt-it-add-up/151342/4 "2003-01-27T22:15:01Z")
I don’t have a calculator, and I’m not thinking through exactly what you’re doing, but I think it is indeed the extra day. If you take the annual and divide by 261 instead of 260 – reflecting 52 weeks of 5 days plus one extra day – you get $159.68 and it works out on the nose… coincides exactly with the daily amount of $19.96 x 8.
And Biweekly X 26 = 41516.80 plus $159.68 (daily amount) = $41676.48.
In short, mathematics is a wonderful thing.
Of course, annual salaries are usually not expressed as $41,676.48, they’re expressed as things like $42,000 which never divides evenly. My salary for teaching a course was divided into 6 equal payments… and then I got a paycheck for $0.02 to reflect the difference between the six payments and the promised amount. Cracked me up. And it was a direct deposit, too.
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### Author:  [@KneadToKnow](https://boards.straightdope.com/u/KneadToKnow)
#### Post date: [January 27, 2003, 10:40pm UTC](https://boards.straightdope.com/t/pay-periods-biweekly-vs-annual-and-why-doesnt-it-add-up/151342/5 "2003-01-27T22:40:44Z")
The bellboy gets the extra money.
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### Author:  [@BobT](https://boards.straightdope.com/u/BobT)
#### Post date: [January 27, 2003, 10:46pm UTC](https://boards.straightdope.com/t/pay-periods-biweekly-vs-annual-and-why-doesnt-it-add-up/151342/6 "2003-01-27T22:46:40Z")
Thanks, I was just being too fancy for my own good when figuring this out.
I knew there was an extra day, but I decided to use the hard way to figure out the difference instead of the easy way.
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### Author:  [@SmackFu](https://boards.straightdope.com/u/SmackFu)
#### Post date: [January 27, 2003, 11:41pm UTC](https://boards.straightdope.com/t/pay-periods-biweekly-vs-annual-and-why-doesnt-it-add-up/151342/7 "2003-01-27T23:41:45Z")
> [@](#):
>
> \*Originally posted by C K Dexter Haven \*
> **My salary for teaching a course was divided into 6 equal payments… and then I got a paycheck for $0.02 to reflect the difference between the six payments and the promised amount.**
Better than mine. I get bimonthly payments, and one is xxxx.76, and the other is xxxx.75. Makes tracking it automatically in Quicken a royal pain.
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### Author:  [@KneadToKnow](https://boards.straightdope.com/u/KneadToKnow)
#### Post date: [January 27, 2003, 11:54pm UTC](https://boards.straightdope.com/t/pay-periods-biweekly-vs-annual-and-why-doesnt-it-add-up/151342/8 "2003-01-27T23:54:42Z")
**SmackFu** , set up one as a monthly payment on the 15th (or whatever) for xxxx.76 and the other as a monthly payment on the last (or whatever) for xxxx.75.
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### Author:  [@FairyChatMom](https://boards.straightdope.com/u/FairyChatMom)
#### Post date: [January 28, 2003, 12:00am UTC](https://boards.straightdope.com/t/pay-periods-biweekly-vs-annual-and-why-doesnt-it-add-up/151342/9 "2003-01-28T00:00:34Z")
You ought to work for the Feds - they take your annual amount and divide it by 2087 to get your hourly. But you only get paid for 2080. So you don’t make as much as the pay charts say.
In 2002: [from this chart](http://www.opm.gov/oca/02tables/gs.htm), you see a GS9 Step4 makes $37895 per year - divided by 2080 hours per work year give you $18.22/hr. But on [this chart](http://www.opm.gov/oca/02tables/gs_h.htm), you see the hourly rate paid is $18.16 - so the actual annual pay is $37772.80 - Government accounting at its finest…
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### Author:  [@don\_t\_ask](https://boards.straightdope.com/u/don_t_ask)
#### Post date: [January 28, 2003, 12:26am UTC](https://boards.straightdope.com/t/pay-periods-biweekly-vs-annual-and-why-doesnt-it-add-up/151342/10 "2003-01-28T00:26:01Z")
In the public service here annual salary rates are converted to hourly rates by dividing the annual salary by 260.89(number working days) and then dividing by hours per day. Working days is 365.25 x 5/7.
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### Author:  [@KneadToKnow](https://boards.straightdope.com/u/KneadToKnow)
#### Post date: [January 28, 2003, 12:37am UTC](https://boards.straightdope.com/t/pay-periods-biweekly-vs-annual-and-why-doesnt-it-add-up/151342/11 "2003-01-28T00:37:27Z")
> [@](#):
>
> 260.89(number working days)
So, you get to leave at like 4:07 one day a year?
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### Author:  [@BobT](https://boards.straightdope.com/u/BobT)
#### Post date: [January 28, 2003, 12:39am UTC](https://boards.straightdope.com/t/pay-periods-biweekly-vs-annual-and-why-doesnt-it-add-up/151342/12 "2003-01-28T00:39:28Z")
Learning more from the payroll people, the key figure in my equation is the hours.
All of my pay is based on hours. So the annual amount will be off in 2004 (although I’m getting a raise before then).