Subject: Calculating Fortnightly rates of pay - A few responses
From: Seenikatty, Serena (Serena.Seenikatty@health.wa.gov.au)
Date: Fri Jul 16 1999 - 11:03:24 WST
To quench the curiosity it has raised ..... here are a few of the many responses received explaining how the formula is derived. Thanks again to everyone who responded!!!
Serena
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ORIGINAL MESSAGE: Thursday, July 15, 1999 9:36:47 AM
RE: Calculating Fortnightly Rates of Pay
ATTENTION MATHEMATICAL WIZARDS!!!
Can someone please explain how the formula for the divisor of 26.08333 for the fortnightly rate of pay is historically derived. I understand that the divisor itself is derived from multiplying the annual rate by 12 and dividing the result by 313 to calculate the fortnightly rate (examples of this formula can be found in the Public Service Award and TI 505). I am aware that the calculation factors in leap years and that it is based on a 6 day working week.
Your explanations will be greatly appreciated.
Kind regards
Serena (AKA mathematically challenged??)
SERENA SEENIKATTY
Employee Relations Officer
Sir Charles Gairdner Hospital
phone: 9 346 3778
fax: 9 346 2560
email: Serena.Seenikatty@health.wa.gov.au
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Hello Serena,
The formula for 26.08333 recurring comes from 313 divided by 12.
This is to take into consideration leap years, and the fact that about once in every 11 years, a financial year will have 27 fortnightly pays instead of the usual 26.
So if you have a fortnightly pay, to determine the per annum amount:
$ fortnightly x 313 / 12 = per annum.
OR if you have a per annum amount and you require the fortnightly, just reverse the mathematical symbols:
$ per annum / 313 x 12 = fortnight.
Hope this makes sense - enjoy your maths!
Regards - Sharon Kruger Human Resource Officer Dept of Transport
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Hi Serena
I guess you will get lots of answers on this one, but just in case you don't, the formula is quite simple.
Basically every year there are 26 pays and in the 12th year there are 27 pays.
Therefore 26 x 12years = 312 plus the extra pay in the 12th year 1 = 313
313 divide 12 years is 26.08333 recurring.
This figure therefore factors in the extra pay every 12 years. Hope this helps.
Karlyn
Karlyn Cucuzza
Executive Officer
Public Health & Purchasing
PH: 9222 2067
Fax: 9222 4142
Email: Karlyn.Cucuzza@health.wa.gov.au
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Serena
The following information is a response to a recent employee's statement that we (Main Roads) were robbing him.
The information you want is at the end under MAIN ROADS CALCULATION.
I also had problems finding the answer and DOPLAR said it was just "Computer Rounding errors" that gave the figure, and to just use 26.
Hope all this helps
FORTNIGHTLY PAYRATE CALCULATION
CURRENT CALCULATION
The F/N rate is the Annual salary divided by 26.08333 derived from 313 / 12)
An explanation is given at the end of this document.
ASSUMPTIONS
For the purposes of this discussion, the following
assumptions have been made.
365 days per year
52 weeks plus 1 day per year
26 fortnights plus 1 day per year
1 leap year every 4 years
Annual salary of $26,000, gives
Current F/N rate equal $998.81, or gives
Currently $71.34 per day (14 days)
OPTIONS
Divide annual salary by 26 (using assumptions)
This gives $1000 per F/N ($1.19 over current rate) but does not cover the extra day per year which would be 1 work day without pay.
The extra $1.19 per F/N times 26 equals $30.94 which is $40.40 less than the full amount per day.
This option robs you of $40.40 per year, and could also mean 2 work days without pay in a Leap Year.
Divide year by 14 days (using assumptions)
This gives divisor of 26.0714 (365 / 14)
This then gives $997.26 per F/N ($1.55 below current rate) but it covers the extra day per year.
The $1.55 less per F/N equate to $40.30 per year which is $31.04 less than the full amount per year.
This option robs you of $31.04 per year which will rise to $102.38 in every Leap Year.
Divide year by 14 days allowing for leap years (using assumptions)
This gives divisor of 26.0893 (365.25 / 14)
This then gives $996.58 per F/N ($2.23 below current rate) but it covers the extra day per year.
The $2.23 less per F/N equate to $57.98 per year which is $13.36 less than the full amount per year.
This option robs you of $13.36 per year which will rise to $84.70 in every Leap Year..
MAIN ROADS CALCULATION
This is based on what we believe is a fairer method for the employee.
There is 26 F/N's plus 1 day per year.
Therefore after 14 years you have 364 F/N's (14 * 26) plus an extra F/N due to 14 extra days. This would normally give 365 complete F/N's every 14 years.
But
Due to Leap Years (every 4 years) the 14 year period is reduced to 12 years.
Therefore after 12 years you have 312 F/N's (12 * 26) plus an extra 12 days, plus an extra 3 days for Leap Years.
This totals 313 F/N's plus 1 day every 12 years, which gives the formula 313 / 12 or 26.08333.
Due to rounding the F/N amounts, the 1 day extra every 12 years becomes irrelevant.
(If the 1 day is considered, then all rounding errors should be taken into account, and this is very likely to reduce the overall amount the employee gets every 12 years.)
As can be seen, the rate of 26.08333 is a fairer method of calculating the F/N rate and gives more money to the employee, compared to other options..
Wayne STORRIE (HRISC)
Phone 9323-4665 Room G10
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