The administration is completing work on a $7 to $10 billion program designed to keep private businesses in cities and other depressed areas such as Apalachia as well as to attract new firms.

The 3-year-plan, expected to go to Congress next January, also is designed to created 250,000 or more jobs in areas where unemployment is particularly high.

An interagency task force has been at work on the project for several months. The final plan will be a central part of President Carter's strategy to revitalize the nation's decaying cities, the major new initiative the administration will propose next year.

The program is expected to work as follows:

It will provide federal grants and loans to firms that decide to improve or build their facilities in cities. This is designed to stop the move of industries from major cities to less populated areas.

It will encourage banks to make loans to these businesses by pumping federal funds into banking institutions making such loans.

It would quadruple the amount of tax-free development bonds that can be sold to finance urban industrial projects.

Officials concede that it will take several years for these proposals to have a major impact. In the meantime, short-term programs such as public service jobs and continued fiscal relief to cities will have to be maintained and increased to keep cities afloat.

The special interagency task force empowered to devise the administration's urban strategy includes representatives from the Departments of Housing and Urban Development, Transportation, Health, Education and Welfare Commerce, Labor and Treasury.

Roger Altman, Assistant Secretary of the Treasury for Domestic Finance, said that the task forcee agrees that the urban financing mechanism as the proper approach to create jobs in the inner city.

While the actual division of the $7 to $10 billion is not final, at least $1 billion would be available for outright grants.

A business would get up to 15 percent of the actual investment cost. The firm then could obtain government loans for up to 75 per cent of the cost of the rest of the project. It would have to get private financing for the remainder.

This "market test" helps insure that the government is financing projects with a reasonable chance for success so that the jobs created are permanent ones, Altman said.

For example, a manufacturer with a $10 million project could get a grant for 15 per cent, or $1.5 million. He could obtain a government loan for up to 75 per cent of the remaining $8.5 million, or almost $6.4 million. The manufacturer would have to get the remaining $2.1 million from a bank or some other private source.

By providing the employer with grants and easily accessible, relatively low-cost loans, the federal government would be seeking to offset the energy, labor and tax advantages of locating elsewhere - such as in the South or Southwest.

Another key element of the plan is creation of a "secondary market" in which banks can resell loans they made to businesses investing in distressed areas.

Such a secondary market would make it easier for banks to make inner-city investment loans to businesses. The government would not buy a loan from a bank unless the bank agreed to use the funds to make the same kind of loan to another business.

The government has similar experience in secondary markets, buying markets, buying mortgage loans, for example, from savings and loan associations who then can take the proceeds and make loans to other home buyers.

The proposals also would raise from $5 million to $20 million the ceiling on the amount of tax-free development bonds local governments could sell to help finance inner-city projects, but would keep the $5 million ceiling for other areas.

The higher ceiling on these bonds would help to attract bigger companies with national reputations to locate plants in the inner city, Altman said.

Although the overall program and funding will be federa, there will be a strong emphasis on doing most of the work - such as generating business interest, getting site approvals - at the local level, Altman said.