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Your monthly pay was worked out as 1/12th of your pro-rata annual pay. It sounds as though payroll have divided your july gross pay by 62 (62 half days in July) instead of dividing the full-time equivalent of your monthly pay by 62 . Contract pay means that they employ you throughout the month/term/year so I think that finishing part way through a month involves pay being work out based on how many days in that month you were still employed. Thus you'd get more for each day of employment in short months like February. Had your one day of work been on the 6th of July, for instance, you'd have been paid more, even though you didn't work from 1st-5th! Work out how many half days you would have worked if school had been in session for the whole of July. Your gross pay should probably have been about a quarter of your usual monthly pay. When you know that employment will cease before the end of the summer term, it's usually better to be on supply daily pay as that includes a pro-rata amount for holiday pay. You sometimes lose out if you are off sick on a sceduled work day, though, as you get no pay at all when not at work.
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