Ulster Bank has apologised for failing to put 1,300 customers on the correct mortgage repayment schedules.
The bank had offered clients the option of paying only the interest and not the capital on loans for between two and five years.
However, in a number of cases it failed to convert the repayments to interest and capital at the date when that was supposed to happen.
The under collection of capital was €40m. The bank accepts it made a mistake.
In a statement, the bank said it had identified the error and reported it to the Central Bank.
Ulster Bank has given clients four options to the deal with the underpayment.
The first is to avail of an interest-free loan equal to the under-collected sum, which would be paid over time.
The second is an extension to the term of the mortgage.
The third is to repay capital and interest over the current term, and the final option is to repay the amount owed in a lump sum.
In a statement, the Central Bank said: "Any impacted consumers who experience difficulty making revised repayments will be treated sympathetically."
It added customers should be offered all protections under the code of conduct on mortgage arrears where relevant.
The Consumers' Association of Ireland said: "The lender must take responsibility for any and all costs associated with recouping of the primary sum involved both past and future."
Meanwhile, it has emerged that the Financial Services Ombudsman ruled against Ulster Bank in a case where the bank miscalculated mortgage repayments and attempted to have the customer pay for the bank's error.
RTÉ News has learned that in the summer of 2009 the Ombudsman ruled against the bank and directed, not only that it waive the outstanding repayment, but also pay compensation to the customer.
The Ombudsman found that the bank had "breached the duty of care owed to the complainant", which it said has been recognised by the Supreme Court in the case of National Irish Bank v's RTÉ.
The case rose after the customer noticed their monthly mortgage payments had increased in 2008 even though the interest rates on the mortgage had dropped.
The customer contacted the bank and the bank discovered the error had been undetected for over a year.
The bank subsequently demanded that the customer pay the difference of almost €5,000.
In his ruling, Ombudsman Joe Meade said he did not feel the customer "should be faced with this substantial bill in circumstances where the errors were made by the bank itself".
The ruling was legally binding on Ulster Bank as the customer's complaint was upheld under the Central Bank Act for 2004 and Ulster Bank did not appeal the ruling to the High Court.
A spokesperson for Ulster Bank said that without having the opportunity to review the case in 2009, there was a difference between correcting the interest and capital repayments for the 1,300 customers and the calculation of interest on a mortgage.