A calculation by a Brookings Institution economist narrowed down the pool of underwater homeowners to 500,000 who could qualify for principal reduction from the $25 billion mortgage settlement.

Using the parameters of the settlement, Ted Gayer found just 5% of the nation's 11.1 million underwater borrowers could get the principal reduced on their mortgage, first reported by The Washington Post.

About $10 billion of the settlement, in the form of credits, will go toward principal write-downs made by the five banks. Only homeowners delinquent on their mortgages are eligible.

Gayer eliminated others according to underlying requirements, including Fannie Mae or Freddie Mac loans and homes not owner-occupied.

It's a rough calculation, Gayer warned, and he made some assumptions in the process. He eliminated any loans not held on the banks' balance sheets, as well as any with a second loan. Mortgage bondholders may not take kindly to principal write-downs, he said.

The Office of Iowa Attorney General Tom Miller, which played a key role in the mortgage servicing settlement, said the report issued a "very rough estimate, which is likely based on additional layers of rough estimates and assumptions."

A spokesperson for Miller said, "While we understand that there is an interest in a definitive number of borrowers who might quality for principal reduction, we don't yet have that solid number and cannot confirm the author's estimate. I also note that there are other elements to the settlement that the author has not taken into account." 

(For more on Gayer's math, read his entry on the Brookings website.)