RBS and NatWest customers who had student accounts dating back to 2002 will learn whether they are owed compensation by 1 November.
The bank said that tens of thousands of customers had been charged for extended overdrafts that were supposed to be interest-free.
They included student customers from 2002 to March this year.
The bank said it would use public databases to find those who have moved home.
These students used up the advertised overdraft allowance and were then granted extra.
They were charged for this, even though the accounts’ terms and conditions clearly stated that arranged overdrafts were interest-free.
David Crawford, head of current accounts at RBS, said it was “very disappointing” that the bank had got it wrong.
He said that the relatively small numbers of customers affected compared with their total customer base meant that the bank had not noticed what was happening.
Those affected will be notified by 1 November that they are due a refund. The redress, typically about £100, will be credited to RBS accounts or sent by cheque.
A statutory 8% interest will be added to the amount.
Mr Crawford said that the bank would use public records to track down those who – as is likely for ex-students – had moved home.
Anyone who believes they have been affected but does not hear from the bank by 1 November, should contact RBS.