Some homeowners are turning down free money.

Many can probably qualify for a government-sponsored refinance program that will reduce their mortgage interest rate and their monthly mortgage payments by hundreds of dollars. Yet many are declining the refinance offers.

Lack of home equity is not a problem. The government's Home Affordable Refinance Program, or HARP, allows eligible homeowners to refinance no matter how deep underwater they are.

Editor's Note: The Truth About the Economy — Government Documents Lead to Eerie Conclusion

Fortune magazine relates a story of a homeowner rejecting a refinance proposal even though it would reduce his interest rate from 6.616 to 4.125 percent and his monthly payments by $630. A streamlined process would require little paperwork, and the application did not depend on an appraisal.

"It didn't make any sense," Quicken mortgage banker Lisa Price told Fortune. "Usually when I call someone with a deal like that they're really excited."

Quicken estimates that half of homeowners don't even respond when told about HARP and only about a fourth who qualify ultimately refinance.

"We get their home number, the business number, their e-mail, we express-mail packages to their house so it looks serious," Quicken CEO Dan Gilbert told Fortune. "We leave messages; we tell them, 'Go look up HARP on Google and you'll see it's real.' We don't quit."

Why don't more refinance?

Homeowners may distrust mortgage lenders. They may feel burned by previous mortgage loans and remember the time-consuming, costly application process.

The latest version of the program, known as HARP 2.0, has helped many homeowners refinance into historically low interest rates, and more are considering program, said Mark Greco, president and founder of 360 Mortgage Group, a mortgage bank in Austin.

“However, less than one in four eligible borrowers under the HARP 2.0 guidelines has taken advantage of this important program," Greco said. "There remains a significant opportunity for HARP 2.0 to benefit additional American homeowners, many whom continue to struggle.”

Lender Processing Services, a real estate data firm, recently reported that about 2.6 million home loans may still be eligible for refinancing under HARP 2.0, Greco noted. These loans fit the general HARP requirements and 50 percent have prime credit scores of 720 or above, including 670,000 with interest rates above six percent.

To qualify, the mortgage must be owned or guaranteed by Freddie Mac or Fannie Mae, and must have been sold to one of those companies before May 31. The homeowner must be current on their mortgage with a good payment history over the last 12 months.

Editor's Note: The Truth About the Economy — Government Documents Lead to Eerie Conclusion