so 0.045 x N = 1000

: N=1000/0.045 = £22,222.22

now that's when the interest will exceed £1000 other factors may be relevant but at that rate she can have around £22k before she has to pay tax on interest. 

Any answer you get should come with 'I'm not a tax expert'

they should ring hmrc.

As well as her £1,000 personal allowance for savings interest income she also has (£17,570 - £13,688) which equals £3,882 additional allowance for those on low income. His means she can received £4,882 in interest before being subject to tax.

It would require £108,489 in the bank to earn this sum in interest at 4.5%.

no I was not aware of the £5k rule but I set the example

so 0.045 x N = 5000

: 5000/0.045 = £111,111.11 if 5k is allowed. 

Yes I was just doing the interest, the personal allowance is dependent on total income from all sources. 

I was not aware of this 5k rule. Could come in handy.

I agree with NJ's calculation and you can confirm there would be no tax due by using his figures in this link,

https://www.tax.service.gov.uk/guidance/work-out-tax-on-your-savings-or-dividend-income/start/tax-year?c=1

An aside - but related:

Having several savings accounts with different providers all on-line I find it difficult to keep track of how much interest I actually get and in what time periods (some monthly/some annually.

The banks etc. are supposed to provide the details to HMRC but that system doesn't appear to work.

I think I should tell HMRC that I may be (am) liable but if I do & can't provide exact details I'm unsure what will happen.

If I don't tell them they say penalties may be incurred!

If only we still had paper!🙄

^^^^ one account is with National Savings - you would think they should have established & working arrangements for reporting interest to HMRC!

I'm not that organised Barry - in fact I've swapped accounts around so much I'm not even sure of the providers I've had interest from in the past for me to be able to check back!

But I read in a newspaper fairly recently that not all the systems are compatible & £billions (yes £billions!) of such interest is going untaxed. It said Ms Reeves was going to crack down on it (once her desk is clear of complaints🤣).

We can assume she's maxed out her stocks and cash ISA allowances?