The federal Urban Mass Transportation Adminstration (UMTA) proposed a new financial arrangement yesterday that would see 73 miles of Metro's planned 101-mile subway system brought to operation under a three-year funding schedule.

The federal plan is a major proposed revision to a three-year schedule the Metro board had offered. The federal plan virtually eliminates preliminary subway work in the Maryland suburbs and concentrates on bringing into operation segments in Virginia and the District of Columbia that can be completed readily.

The Metro board plan was designed, like all Metro plans, to have something for everybody. It would bring Metro's operating mileage to 64, but would include property acquisition, design and structural work on all the uncompleted lines in all Metro's participating jurisdictions.

Thirty-one miles of Metro are now in operation; 60 milas are funded. There is identifiable money for canceled interstate highway projects in the metropolitan area to build about $6 billion worth of subway.

The problem is that Metro is now projected to cost about $7 billion, probably more, and the federal government has said it will not guarantee federal appropriations beyond the interstate money until other elements of Metro's complex financial puzzle are worked out.

The big argument - and it has been raging for two years - is what should be built within that $6 billion. The problem for the Metro board has been how to keep happy each of the eight local jurisdictions that contribute to Metro's operating and construction costs.

Metro board members are planning to meet and discuss the new federal proposal next week. Metro General Manager Richard S. Page declined to comment on the federal proposal until after the meeting.

The federal letter, signed by acting UMTA administrator Gary D. Gayton, also proposed a schedule of local and federal participation in retiring a $1 billion debt Metro incurred when it sold bonds to raise money for construction.

Total interest on the debt, over a 40-year period, is estimated at $3 billion. The federal government, which guaranteed the bonds, already has agreed in principle to pay two-thirds of the interest and the Metro board has agreed in principle to pay one-third. At present, Metro is paying 15 percent and the federal government is paying 85 percent of the annual debt service.

Transportation Secretary Brock Adams agreed earlier that the federal government would provide a period of grace so that local government could adjust their budgets to finance the one-third local annual payment. Gayton proposed yesterday that the grace period end after payment due July 1, 1980.

It had always been agreed that the interest tables would be juggled so that, in the end, total debt service over the years would be two-thirds federal, one-third local. Gayton's letter, while offering short-term federal help, also proposes that the localities pay interest on the advance.

More federal-local negotiating sessions on these mind-boggling problems are planned soon.