Customers checking their E-Isa balances found they had been updated with just a few pence worth of interest in some cases.
A spokeswoman for RBS/NatWest described the error as an isolated incident and said customers' balances are being updated with the correct amounts as a matter of urgency.
Those who have found a mistake do not need to contact the bank as it will be automatically fixed.
A "relatively small" number of people have been affected, the banking group said.
A statement from the bank said: "We are aware that there is an issue with interest being applied to some customers' RBS and NatWest E-Isas and it is being urgently investigated.
"The missing interest will be applied to the affected customers' accounts as soon as possible and we will ensure that no customers lose out as a result. We apologise for the inconvenience caused."
The bank stopped selling this particular Isa product last year. It has been working to simplify its Isa range and move customers off older products. While migrating customers from the E-Isa, information relating to interest rates on these accounts was incomplete which is why the interest was not properly calculated.
While the latest failure is not IT-related, the bank has been beset by a string of technological errors in recent months, including an IT failure in December which left customers of RBS and its NatWest subsidiary unable to use credit and debit cards for three hours on "cyber Monday" - the day when retailers traditionally expect a huge flurry of online activity in the run-up to Christmas.
Just days after that incident, the bank's websites were the victim of a cyber attack that left some customers unable to access their accounts.
The banking group took a £175 million hit as a result of IT chaos in summer 2012 which left NatWest, Royal Bank of Scotland and Ulster Bank customers locked out of their accounts.