Lenders continue to refuse to reduce the principal balances of mortgages.  As a result, the Hope for Home Owners program is not working.  Early projections indicate that only 20,000 troubled homeowners will apply for the "Hope for Homeowners" program, a considerable reduction from the previously estimated 400,000 homeowners who were expected to apply. The $300 billion program was launched Oct. 1 and is designed to help troubled homeowners rewrite a "risky" mortgage loan into a 30-year, fixed-rate loan with a lower interest rate. During the first two weeks of the program, the Federal Housing Administration, which oversees Hope for Homeowners, reported receiving only 42 applications. Some housing experts believe the low application rate is due to the program being voluntary for lenders and provisions requiring homeowners to agree to an equity share with the government.