He said if the tax credits are extended, additional apartments could be renovated.
The 10th-floor apartment, which they rented for $2,995 a month, had high ceilings and was newly renovated.
Both the store and the apartment have been fully renovated.
The five-room apartment, on the fourth floor, was large and had been well renovated.
Fames's apartment was on the fifth floor of a building renovated a year or so ago.
In all, he said, the 4,000 apartments could be renovated over the next 18 months at a cost of $78 million.
Their apartment will be renovated and put up for sale at $441,000.
He said that although the apartment they will be buying has been renovated, the work was done in what he called a traditional style.
Housing officials estimate that 1,498 more apartments could be renovated under the program by 2007.
The complex has also changed ownership, and apartments have been renovated.