Washington ? Just over a week remains for the families of Sept. 11 victims and injured survivors to apply for money from the government’s compensation fund.

So far, 4,443 claims have been filed by relatives of those who died and by people injured in the attacks. The average payout is $1.77 million. The deadline to apply is Dec. 22.

The total payout should be $2 billion to $3 billion — “well under what had been estimated,” said Kenneth Feinberg, the fund’s special master. When the fund was started, the price was pegged at $6 billion by the Congressional Budget Office and some believed it could climb higher.

Feinberg said officials initially thought many more people had died on Sept. 11 than the actual totals. Because there were fewer victims, there were fewer claims on the fund, he said.

The fund was created by Congress soon after the attacks to aid the families of those killed or injured, and to protect the airline industry and government entities from lawsuits. Families who receive money from the fund agree not to sue.

Lawyer Justin Green, whose firm represents hundreds of Sept. 11 families, said his chief worry was that some believed the deadline was “like taxes — that you can file late and only pay a small penalty. In the case of the fund, the penalty is that you get nothing.”

To date, 1,300 payments totaling $1.4 billion have been paid.