Re: salary conversion question

Re: salary conversion question   (09/17/2014, 11:49 PM)

First, assuming you're calculating it for 2014, there are 365 days in the year.

So if you work every day and you don't get overtime pay, you would have worked 8,760 hours total. With an annual salary of $45,000 the hourly rate would then be $5.14 per hour.

Now the overtime is trickier since you have to figure out how many of your total hours are time and a half. It also depends if your week starts on a Monday, or if you can just count every 7 days as a week.

So looking at 2014, January 1 was on a Wednesday. Let's say you start working on Jan 1 and work 24 hours a day. That means before Tuesday, Jan 2, has even ended, you've already worked 48 hours. So the first 40 hours are regular pay, and the rest of the week is time and a half.

Jan 1 = 24 hours * X where X is regular pay rate
Jan 2 = 16 hours * X + 8 hours * Y

Y is then the time and half pay, so:

Y = 1.5 * X

Now Jan 3 = 24 hours * Y
Same thing for Jan 4, 5, 6, and 7.

The total for the first 7 days of the year is:

24X + 16X + 8Y + 24Y + 24Y + 24Y + 24Y + 24Y

That's equal to 40X + 128Y for each week of the year, which equals 232X each week.

January 8 is the following Wednesday and you're starting a new week, so you'll make 232X for the week of Jan 8-14. Now just add up all the weeks in the year. After 52 weeks, the very last week ends on Tuesday, Dec 30.

Then you have 1 more day on Dec 31 that could be considered the 53rd week. So Dec 31 pay = 24 * X.

So the total pay is now:

52 weeks * 232X + 24X = 12,088 * X

Now just divide:

$45,000 / 12,088 = $3.72 per hour

So your regular pay is $3.72 an hour and your overtime pay is then $5.58 and you work a total of 8,760 hours in 2014. Of those hours, 2,105 hours were paid at the regular pay rate, and 6,655 hours were paid at the overtime rate.

So just to reiterate:

2,105 hours * $3.72 per hour = $7,830.60
6,655 hours * $5.58 overtime = $37,134.90

So the total adds up to $44,965.50 which is your annual salary of $45,000 per year. The slight difference is due to rounding the exact hourly rate to the penny, since it's really $3.7227 per hour.