Trying to understand Tax on SIPPS paid net

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Am I wrong, you pay tax on gross amounts, not on the net. Was reading the III web info on SIPPs and they say with a net contribution into a SIPP of £1000, they will claim £250 (20% tax) for a total of £1250. For a higher rate tax payer (40%) you can claim a further 20%, which they state as £250. I don't think that is correct.
So for the III example, if I earn £1667.67, I pay tax of £667.67, invest the £1000 into a SIPP net, claim £250 via the provider, and the difference £416.67 via my tax return?
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It isn't correct. If you contribute £1,000 then basic rate tax relief of £250 will be added.
But there is no fixed further 20%. Any additional tax relief (which saves you money, it doesn't get added to the pension fund) depends on your own tax position for the tax year in question.
Say you pay higher rate tax on £1 then the higher rate relief (given by increasing your basic rate band by the gross contribution) will only be 20p, not £250.
In some scenarios though it could be more than £250.
The above is worded in a way that just asks for confusion.
A pension contribution is the gross contribution. So, in the example above, the pension contribution is £1250.
You receive basic rate tax relief at source. That is £250.
You pay the net of basic rate contribution of £1,000. The provider will either immediately give you the tax relief if they prefund or you wait for the tax relief if they do not.
If you are a higher rate taxpayer, you can claim the further 20% relief via self assesemnt which is £250.
You receive £225 relief at source.
You can claim a further £225 relief via self-assessment
My question was based on the fact that SIPP providers assume that you are a 20% tax payer and base their reclaim on that hence, the 25% of the net contribution, in the example 250 of 1000. As a 40% tax payer you actually paid 666.67 tax on the 1666.67, and therefore you would expect the HMRC system to understand that and refund the difference, 666.67 - 250 = 416.67
To understand after-tax pension payments you will avoid confusing yourself if you always think in terms of gross contribution. So if you want to make a £1250 gross contribution as a higher rate tax payer you will have paid £500 tax on that amount, £250 basic rate and £250 extra for the higher rate tax.
So you actually pay £1000 into your pension and get the missing £250 added on by HMRC through the provider. That leaves the £250 higher rate component. HMRC refunds this to you personally, not to your pension.
I have a SS pension.
I've decide to increase my pension contribution by £1666.67 pcm and reduce my gross pay by the same amount.
When I compare my pay slip to the month before, I can see that my tax has reduced by £667.67 (40%) and my net sum by £1000 (60%) . Glad I didn't decide to open a PP SIPP and contribute the net £1000