A total of €729m has so far been paid into the High Court administered Insurance Compensation Fund to cover losses at Quinn Insurance.
The Dáil Finance Committee today heard that a further €272m will be advanced next year.
The Fund derives its income from a 2% levy on non-life insurance policies written in the State.
The Committee has been hearing from joint administrator Michael McAteer, of Grant Thornton, about the financing of the insurer, including its reserving for claims, in the years prior and since his appointment.
The Finance Committee heard that €936m worth of insurance claims against Quinn Insurance Limited were under-reserved in the years prior to the company being placed into administration in 2010.
In July, a tenth report from the joint administrators was presented to the High Court which controls the state's Insurance Compensation Fund. It heard that the final call on the Fund arising from the administration of Quinn Insurance was estimated at €1.65 billion.
That compared to an estimate from the administrators of €600m during the first year of the administration.
TDs and Senators heard that around €1.1 billion of the €1.65 billion would be raised via the Insurance Compensation Fund.
Quinn Insurance has since been sold to Liberty Mutual but the state remains liable for prior history claims.