The payments are normally due in each January and July in each 50% installments. If the total tax liability is less than £1,000 it is all due the following January, and no Payments on Account are due. This is the lower (de minimus) limit.
The next rule is that the Payment on Account is 50% of the previous years liability, with any further balance due the following January.
As Mr A has a £2,000 liability in year 1 his payments on account for year 2 will be £1,000 each and as the total tax liability is £3,500 for year 2, the balance of £1,500 is due the following January.
In year 3 the Payments on Account are £1,750 each, but this results in an overpayment of £500 for year 3.
This is best demonstrated in a simple table:
As you can see, the first payment due is the whole of the tax for year 1 plus 50% for year 2. Because of this, there is an 18-month tax bill in one go, which surprises most tax payers. As the tax is unhelpfully due in January, this can cause cash flow issues.