In a letter to Fianna Fáil's finance spokesman Michael McGrath, AIB Chief Executive David Duffy said customers would pay the existing tracker rate, plus a further 1% for the duration of the mortgage if they move home.
The development will take effect from the summer. It will be available to customers of EBS and AIB.
If a customer is moving home and wants to borrow further money, they would have to do so at the higher interest rate that applies to new business.
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The new tracker arrangement will be available for customers trading up or down from their current residential property.