But as it was from AIB current a/c to an AIB deposit account is this reasonable on their behalf?
This is not why you were charged interest.
You lodged a cheque on Day 1.
It does not clear until Day 3 (?) assuming it was an Irish cheque.
So you don't get value for that cheque until Day 3, although it shows up on your account on Day 1.
If you take the cash out on Day 1, you are overdrawn and will be charged interest on your account and surcharge interest if you did not have an overdraft.
I don't think it makes any difference if you transfer the money to another AIB account, a BoI account, or just withdraw cash. You are overdrawn, and so will be charged interest.
If it was €100,000
The rate for a year should be c.10% or €10,000
For one day, it should be €27
So for three days, it should be around €90
If you had an unauthorised overdraft, there would be surcharge interest. The surcharge rate is 12%, presumably on top of the 10%. So for €100,000, you would have been charged around €200 in total.
How much was the amount and how much were you charged?
You can ask them to show you the calculation although it will take them some time to print it off for you.
Brendan