I’ve been exposed to two payroll systems: the once-every-two-weeks kind and the twice-a-month kind. Each has its own nuances and quirks, but only recently did I realize how they could impact my personal finances in *dollars*, not just monthly planning differences. Before moving into my tale, however, allow me to comment on the two systems.

When employees are paid every two weeks, there are 26 nice and equal payments. The issue is sometimes there are three payments in a month, and sometimes only two. To get around this, there is the twice-a-month payment system, which includes 24 (again) equal payments, but this time on an uneven timing basis (i.e., on the 15^{th} and the final day of the month). In the former, you have to deal with being paid different amounts in different months, but your effective hourly rate is always the same. In the latter, you make the same amount every month, but your hourly rate changes.

Which system is better depends on your angle. As an employer, running 24 payrolls is likely cheaper than running 26. As an existing employee, the twice-a-month method might be easier to use in planning if you do not live within your means (i.e., live paycheck-to-paycheck) or can’t do simple multiplication (i.e., every-two-weeks paycheck amount * 26 / 12 = monthly income). As a new or leaving employee, well … that’s where you run into problems.

Take me, for example. I recently changed jobs – from an employer that pays once every two weeks to one that pays twice a month. Unaware of the payroll intricacies or how such might impact me, I was surprised by my first paycheck. I had worked exactly two weeks, but I had been paid less than ^{1}/_{26} of my salary. Why? Because I started in the midst of a long pay period, of course. (Yes, that’s sarcasm.) You see, some half-months have more work days than others. If you prorate ^{1}/_{24} of a salary over a longer period, the effective hourly rate is less than doing the same over a shorter period. And not just a little less, either (depending on the half-month, of course). Let’s compare, shall we?

Given a certain yearly salary (`$YS`

), the resulting average hourly rate is:

`average_hourly_rate = $YS / (40hours/week * 52weeks/year) = $YS/2080`

Being paid every two weeks jives with this just fine. Paychecks would always be the same amount spread over the same number of hours:

`two_week_pay = hours_in_week * average_hourly_rate = 80 * $YS/2080 = $YS/26`

Or:

`two_week_pay = 2 * weekly_pay = 2 * $YS / (52weeks/year) = $YS/26`

When paid every half-month, however, the rate depends on the number of hours in the half-month. For example, in 2007, there are nine working days in the half-month from February 16^{th} to 28^{th}, resulting in a total of 72 working hours. From August 16^{th} to 31^{st}, however, there are twelve working days, or 96 hours.

Let’s look at just how much these differences affect how much you would be paid for 80 hours of work. In the first case (72 hours), the hourly wage and payment amount would be determined as follows:

```
hourly_rate_1 = bi-monthly_payment / hours_1 = $YS/24 / 72 = $YS/1728
payment_for_80_hours_1 = 80 * hourly_rate_1 = 80 * $YS/1728 = $YS/21.6
```

Contrast this with the same calculations for the second case (96 hours):

```
hourly_rate_2 = bi-monthly_payment / hours_2 = $YS/24 / 96 = $YS/2304
payment_for_80_hours_2 = 80 * hourly_rate_2 = 80 * $YS/2304 = $YS/28.8
```

Comparing these with my *actual* hourly rate (`$YS/26`

) reveals the severity of the differences:

```
hourly_rate_2 / average_hourly_rate = ($YS/21.6) / ($YS/26) = 26/21.6 = 1.204
hourly_rate_2 / average_hourly_rate = ($YS/28.8) / ($YS/26) = 26/28.8 = .904
```

Thus, under this system, I could receive a temporary raise of over 20%, or a temporary pay cut of almost 10% – for no reason other than when I start work. That’s quite a swing (and quite a justification).

In addition to the two scenarios above (72 hours in 9 work days, 96 hours in 12 work days), 2007 has some half-months with ten work days (80 hours) and others with eleven (88 hours).

As luck would have it, I started on August 20^{th} (in the midst of the 16^{th} half-month) and was the witless victim of a 10% loss for those two weeks. How nice it would have been to have started on February 16^{th}…

Wait, what am I thinking? How nice it would be *if employers would realize the injustice of the system!* (That’s where I was going with this.) I don’t mind if a company chooses to use a bi-monthly payment period. As I explained earlier, I can see the benefits to personal budgeting and running fewer payrolls. However, when an employee is on the way in or the way out, *why not pay him his average hourly rate?* (Well, either that or only allow employees to start or end their employment on the half-months with exactly 86^{2}/_{3} working hours. You know, the ones that don’t exist?) I mean, it’s not as if the new guy or the retired/fired guy is going to get paid the same amount in that partial working period, anyway – so why insist on pro-rating according to the skewed hourly rate?