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About 2.4 million borrowers with Federal Housing Administration loans could lower their mortgage costs by refinancing because the FHA reduced its insurance premiums in late January, finds a new study conducted by the Housing Finance Policy Center at the Urban Institute.

In late January, FHA reduced its annual mortgage insurance premiums by 0.5 percentage points. The reduction in premiums is expected to save the average borrower $900 per year. Since its move, government-backed FHA loans have risen dramatically, surging 76.5 percent the first week after FHA made the cost cuts.

Borrowers could save money by refinancing if the combination of the new mortgage rate and the new FHA premiums result in at least a 0.75 percent reduction in annual mortgage costs, researchers found. This represents more than a third of the 6.6 million FHA borrowers.

“Our estimates are also based on the current FHA mortgage rate,” the study’s researchers noted. “A continued decline in rates could make refinancing appealing to a greater number of borrowers and would raise our estimates, whereas an increase in rates would lower them.”

The study excluded FHA mortgages originated before June 2009 (because they’re eligible for the Streamlined Refinance program and these rates are lower than FHA’s current premiums) as well as delinquent mortgages, modified mortgages, and those with a maximum term of 15 years. Including these borrowers, researchers estimated that about 4.4 million FHA borrowers could be candidates for refinancing.