Question re understanding of tax on savings interest

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Hello - just wanting to check that my understanding here is correct.
In a scenario where someone earns £15,500 - am I correct in thinking that they then get benefit of just over £2k of the Starter Savings rate, PLUS the personal savings allowance of an additional £1k - meaning that just over £3k of savings interest could be earned before tax would become payable on that interest? Apologies if any of the terminology I'm using here isn't entirely correct - hopefully the premise of the question is clear though!
In a scenario where someone earns £15,500 - am I correct in thinking that they then get benefit of just over £2k of the Starter Savings rate, PLUS the personal savings allowance of an additional £1k - meaning that just over £3k of savings interest could be earned before tax would become payable on that interest? Apologies if any of the terminology I'm using here isn't entirely correct - hopefully the premise of the question is clear though!
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£2,070 - savings starter rate (0%)
£1,000 - savings nil rate (0%)
Much appreciated!