SIPP and Higher Rate Tax Relief

Hi, Struggling with my maths…grateful for any assistance. [oversimplified] I’m a higher rate tax payer and take home £6,000 of £10,000 because I pay 40% tax. I pay that £6,000 into my SIPP My SIPP provider automatically adds basic rate tax relief at 20% (£6,000 x 0.25 = £1,500) I claim back higher rate tax relief via my tax return ((£6,000 + £1,500) x0.25) = £1,875 £6,000 + £1,500 + £1,875 = £9,375? Where has the £625 gone? Sure I’m being thick. Thanks all for your help.

Hi Redgiant Buckland,
When you pay £6000 into your pension, your pension provider claims tax relief of 20% from HMRC (£6000/80*100) = £1500.
Overall £7500 is paid into your pension scheme.
When you claim higher rate tax relief from HMRC, the basic rate band is increased by £7500, so that you pay £7500 more at 20% and £7500 less at 40%.
This reduces your tax liability by £1500 (£7500 @ 20% = £1500.00).
Thank you.