Tax on savings - fixed vs ISA

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Hi all
I'm just trying to get my head around the tax rules on interest on savings and the best savings account to use to give the best return. I'd appreciate someone checking my working out
. Let's say I have £30,000 in savings, and am a basic rate tax payer. Let's also say that the interest rate on a fixed rate savings account is 4.5%, and the interest rate on a cash isa is 3.8%.

Interest gained on fixed rate savings account: £1,350
Interest gained on cash ISA: £1,140
I would then have to pay tax on £350 of the fixed account scenario, which would be £70. Then I would subtract that £70 from the £1,350, which would be £1,280. So, if I were to invest 100% of my savings in one or the other of those accounts, I should still go for the fixed account, as despite the tax that would be owed, £1,280 is more than £1,140. Have I got that right?
I suppose the smart thing to do (assuming the above calculations are correct), is to open up both accounts and bung as much as possible into the fixed before getting taxed, and the rest in the isa.
Thanks for any help and advice all
Andrew
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You can have a fixed rate cash ISA, so to avoid confusion best to refer to Cash ISA savings and non ISA savings.
Is there a more savvy way to save (yes I know investing should come into play at these sorts of figures but I don't want it) this at the moment than taking out the Virgin EA ISA at 3% sticking 20k in there and then putting the rest in the highest possible monthly paying 'normal' fixed (1 or 2yr as that's all i want) rate account?
Or would it be better to go with a fixed ISA instead? It just seems to me by doing this I'd get both the highest possible EA rate (with the added tax benefit of being an ISA) and also the highest possible Fixed rate as well, and if the latter paid monthly would still not generate enough interest to pass the savings allowance in current tax year or next tax year.
Or am i getting this horribly wrong and theres a better way of doing this?
But if you can't utilise that then it's relatively straightforward.
The first £1,000 is taxed at 0% and the reminder at 20%.
Where it gets trickier is if you are affected by HICBC, tapered Personal Allowance or tapered Married Couple's Allowance as the £1,000 taxed at 0% is still taxable income and forms part of your adjusted net income which can impact other parts of your tax liability.