Joanna,
I think that you are getting this a wee bit muddled... Don't worry though, Ctax can be really confusing once you delve into its mucky innards... (CTB is calculated to 6 decimal places, try explaining to your average lay person how they have been paid fractions of pennies, and that is why the overpayment does not add up to the ‘weekly’ figure notified in the award letter, because we add up all these fractions of pennies, and then ask you to re-pay them!).
The basic premise of Ctax is that it is a mixture of old 'rates' and 'poll tax' (yes it lives on in spirit, if not by name!). Ctax is in fact 2 separate taxes in one... 50% of the Ctax demand is for the property element (rates), and 50% is for the number of adults living in the property (poll tax). When getting into 2AR it is important to remember that there are these two separate taxes...
However, the poll tax being the nightmare that it was, it was decided that all properties would automatically be treated as having two occupants. This disadvantaged households with only one occupant. So to erase that anomaly in single households, the 25% attributable to the 'missing' adult would be refunded (this is called the SPD). This 25% is in fact a 50% reduction in the poll tax element.
As however is the way with these things, the government went further and said that it would not be fair to treat all people as being liable to ‘pay’ the additional 25% of the charge if they could not afford it, or were carers of the householder, or were students or as I recall members of religious orders... People in these groups were to be treated as if they were not resident, and invisible, thus allowing the 25% SPD reduction (50% of the poll tax element) to remain in place...
So with that in mind, there is no such thing as a single person rebate that you have referred to. Single Person Discounts (SPD's) are part of the statutory Ctax scheme. The SPD is not subject to any form of means test, and to qualify, all a person has to do is to tell the council's Ctax dept. that they live alone, or that they live with one or more 'invisible' people. There is no end to the number of invisible people that can be in the household (if all occupants are invisible, then the 'poll tax' side is removed completely allowing a 100% reduction in the personal element, and in the case of students and most others, it also brings with it a 100% reduction in the ‘rates’ side too, giving a total exemption to the Ctax. Again this exemption is part of the statutory Ctax system, and is not part of the benefit system).
Also, if a householder lives with someone who is 'invisible', that householder is treated as living alone. Full-time students are invisible so long as they have the all important 'Council Tax Student Exemption Certificate' issued by the relevant college/university. No Exemption cert, no invisibility…
There would be absolutely no need for 2AR in any circumstances where the SPD should apply. 2AR however is claimed in circumstances where for instance there are e.g. three people in a property (e.g. householder and 2 non-deps). Say one is a student (invisible), leaving two people. There would be no SPD (as there are two 'visible' people living in the property), but one of the non-deps is unemployed, or on a low income. 2AR can be used to claim back the 25% that would have been awarded by way of the SPD. The same applies even with 1 householder and 1 non-dep, or 1 householder and dozens of non-deps if all the non-deps are unemployed or have sufficiently low incomes).
2AR is paid in the name of the householder (with their NINo. etc.) although it is in respect of the non-dep. The householder might also be on a low income, and might claim 'Main' CTB. Councils should undertake a 'better buy' calculation and award whichever is the highest award. However, as CTB can cover both taxes (100% of the total charge), it is possible to claim a DHP on the remaining Ctax liability after CTB has been awarded.
It is possible for 2AR to be awarded at (from memory), 12.5% and lesser figures, of the total demand (or 25% and 12.5% of the ‘poll tax’ element), but I won’t go there in this post, as it really is potentially awfully complicated at that stage, and I have said to much already!!!.
Does this help, (I hope so because my fingers now hurt!)...
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