Santander 123 standard vs lite for 40% taxpayers

Basically what you're saying is that to earn enough interest to cover the fees of the interest paying account, you need to make at least £80 of interest to be able to cover (after tax) the £48 extra fees. That amounts to a little over £5k of your balance being devoted to pay the fees (£5300 earns only £79.50 and you need £80 income to be able to afford both the extra fees involved and the tax on earning the income to pay those fees).

So if you only have £5k in the account you are making a loss after tax and fees and shouldn't choose the account over the lite version.

If you have £15k in the account you are making £225 gross interest but devoting the first £80 to covering the incremental fees, so only have £145 of "spare" gross interest from your £15k balance (roughly 0.97% achieved).

If you have £20k in the amount you are making (close to) £300 gross interest but devoting the first £80 to covering the incremental fees, so only have (roughly) £220 of "spare" gross interest (after the net interest on that first £80 covers the fees). Getting almost an extra £220 gross interest from £20k is like a 1.1% interest rate.

So in summary I agree with your figures (not bothering to work out the exact AER)

But to be honest, I don't really see the point of coming up with an implied interest rate as you have done.

1) this theoretical interest rate (which differs depending on how much is in the account) is only useful to compare the utility of the 123 account with 123 lite. You can't compare it to other accounts on the market on interest rate alone because another feature of the account is the cashback on your bills - which you have conveniently said covers the £1 monthly fee on 123 lite but in reality for most people will not equate to exactly £12 a year. It might be less or it might be quite substantially more. The cashback is an irrelevance when comparing the two 123 accounts but not when comparing to the wider market. And the cashback effect is a greater percentage of the interest income for different account balances.

So your ever-changing theoretical interest rate can only be used to compare like-with-like, i.e. the 123 normal version vs 123 lite which both generate equal cashback levels.

But then,

2) you don't need an interest rate to do that comparison because the lite doesn't pay any interest at all. You just need to know the crossover point where the interest on the normal version is enough to pay the incremental fees. £5333 generates £80 gross interest which for high rate taxpayer gives them the £48 net income needed to pay the £48 extra fees. For a basic rate taxpayer , they only need £4000 to generate £60 gross income and still get £48 net income needed to pay the fees.

So the "is it worth it" point when considering 123 full version vs 123 lite version is £5333 for high rate tax payer or £4000 for basic tax payer. Whether the 'payoff' is 1.09% or 0.97% in that scenario is not really worth considering. One is better than the other: either way, the payoff is "about a percent, before tax" for high account balances (£15-20k) and "not worth doing" for low account balances (£0-5k).

Trying to impute a specific interest rate is a mess, given there are fixed costs involved, so it's more practical to work with actual pounds.