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https://www.gov.uk/apply-tax-free-interest-on-savings
Personal Allowance
You can use your Personal Allowance to earn interest tax-free if you have not used it up on your wages, pension or other income.
Starting rate for savings
You may also get up to £5,000 of interest and not have to pay tax on it. This is your starting rate for savings.
The more you earn from other income (for example your wages or pension), the less your starting rate for savings will be.
If your other income is £17,570 or more
You’re not eligible for the starting rate for savings if your other income is £17,570 or more.
If your other income is less than £17,570
Your starting rate for savings is a maximum of £5,000. Every £1 of other income above your Personal Allowance reduces your starting rate for savings by £1.
Example
You earn £16,000 of wages and get £200 interest on your savings.
Your Personal Allowance is £12,570. It’s used up by the first £12,570 of your wages.
The remaining £3,430 of your wages (£16,000 minus £12,570) reduces your starting rate for savings by £3,430.
Your remaining starting rate for savings is £1,570 (£5,000 minus £3,430). This means you will not have to pay tax on your £200 savings interest.
Personal Savings Allowance
You may also get up to £1,000 of interest and not have to pay tax on it, depending on which Income Tax band you’re in. This is your Personal Savings Allowance.
To work out your tax band, add all the interest you’ve received to your other income.