AIB will continue to allow consumers to open new accounts with Anglo Irish Bank -- and let them benefit from Anglo's high deposit rates.
Anglo's demand deposit account pays 3.1pc, compared with just 0.025pc paid by AIB.
Over a year, this means AIB's demand account pays just 25c, compared with €31 paid by Anglo for every €1,000 saved. This is before tax.
AIB said it would continue to honour the terms and conditions of the 120,000 accounts it is taking over from Anglo.
Anyone who wants to avail of the high rates paid on savings by Anglo Irish would have to open an account through Anglo, by going into its head office or by going online.
As well as having one of the highest demand deposit rates -- where money can be withdrawn without notice -- Anglo also offers one of the best one-year fixed rates at 3.5pc.
This compares with AIB Access 30, where 30 days' notice has to be given before money can be withdrawn, which has a rate of 1.75pc.
A spokesman for AIB said: "We have no plans to alter the deposit rate offers provided by Anglo Irish Bank."
The spokesman added that AIB would be able to continue to provide the much higher-interest Anglo accounts because Anglo has no branches which meant "that channel was a low-cost one".
AIB was anxious to keep the existing Anglo savings products and even expand them. Some 120,000 accounts, worth €9bn, are moving to AIB from Anglo.
Permanent TSB is taking over €3.6bn -- 160,000 accounts -- of Irish Nationwide deposits. But Permanent TSB said last night it would not offer new customers of Irish Nationwide the existing high rates.
Irish Nationwide pays 3.25pc on its demand deposit account to its existing customers, the highest in the market. Its one-year fixed rate is 3.5pc.