WASHINGTON (AP) — Fannie Mae and Freddie Mac posted strong earnings for the July-September period as the housing market continued to recover. The gains will enable the mortgage giants to finish repaying their taxpayer aid or come close to doing so five years after they were rescued by the government.

Fannie reported Thursday that it earned $8.7 billion in the third quarter. Fannie said its earnings were boosted by the rise in home prices during the period, which enabled it to reduce its reserves set aside for losses on mortgages. Fannie will pay a dividend of $8.6 billion to the Treasury next month, bringing its payments to about $114 billion.

Freddie posted net income of $30.5 billion for the July-September period. It will have repaid its full $71.3 billion bailout after paying a dividend of $30.4 billion.

The government rescued Fannie and Freddie at the height of the financial crisis in September 2008 when both veered toward collapse under the weight of losses on risky mortgages. Together the companies received taxpayer aid totaling $187 billion.

The gradual recovery of the housing market has made Fannie and Freddie profitable again. Their repayments of the government loans have helped make this year's federal budget deficit the smallest in five years.

Freddie said Thursday its third-quarter profit was boosted by an accounting move that allowed it to capitalize on tax benefits it had accumulated as a result of its losses on mortgages during the crisis. The benefit to Freddie's bottom line from that tax accounting amounted to $23.9 billion, the company said.

Its third-quarter net income of $30.5 billion compares with $2.9 billion in the same period last year.

Fannie's earnings of $8.7 billion in the latest period was up from $1.8 billion in the third quarter of 2012. Washington, D.C.-based Fannie said it expects to remain profitable "for the foreseeable future."

Fannie and Freddie, which is based in McLean, Va., own or guarantee about half of all U.S. mortgages, worth about $5 trillion. Along with other federal agencies, they back roughly 90 percent of new mortgages.

The two companies don't directly make loans to borrowers. They buy mortgages from lenders, package them as bonds, guarantee them against default and sell them to investors. That helps make loans available.

President Barack Obama has proposed a broad overhaul of the U.S. mortgage finance system — including winding down Fannie and Freddie.

The goal is to replace them with a system that would put the private sector, not the government, primarily at risk for the loans. The government would still be involved, both in oversight and as a last-resort loan guarantor. Obama also wants a guarantee that private lenders will make sure homeowners have access to 30-year fixed mortgages.

A fix to the housing finance system is unlikely to be easy, however. The Obama plan is in line with bipartisan Senate legislation. But most Republicans in the House of Representatives want the market almost completely privatized, while many Democrats insist on government having a larger role.