Can you reduce UK income tax to zero by paying into SIPP when moving abroad?

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in Cutting tax
Hi all, please can I sense-check this?
Say someone left the UK to work overseas on 31st August 2022.
From 1st September they are not liable to pay UK.
Their UK income this year for tax purposes will be £15973
Personal allowance of £12570 means they will owe basic rate tax on £3403, which is £680.
How much do they need to pay into a SIPP to gain £680 of tax relief?
Is it 80% of £3403 = £2722?
Thanks
Say someone left the UK to work overseas on 31st August 2022.
From 1st September they are not liable to pay UK.
Their UK income this year for tax purposes will be £15973
Personal allowance of £12570 means they will owe basic rate tax on £3403, which is £680.
How much do they need to pay into a SIPP to gain £680 of tax relief?
Is it 80% of £3403 = £2722?
Thanks
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(Ha sido divertido)
Under the personal pension regime, the taxpayer pays £2,722 into the pension scheme, and the government pays £360 into the pension scheme, so the taxpayer is £2,722 worse off and the pension scheme is £3,403 better off. Exactly the same result, because effectively the government is simply paying the pension scheme the £680 tax suffered by the individual.
Assuming at least £15k of the earnings qualify for pension contribution purposes.