Nearly 39,000 homeowners or home buyers in the Washington metropolitan area are expected to be eligible for a new below-market-rate mortgage program announced yesterday by Federal National Mortgage Association.

As the nation's largest owner of residential mortages whose average yield now is less than 10 percent, FNMA is offering to refinance many of the mortgages it already owns to enable homeowners to convert paper appreciation into cash or to help buyers obtain attractive financing. Nationally, nearly 2 million homes will be eligible for the FNMA financing plan, beginning March 30.

Fannie Mae, as the Washington corporation is called will benefit by getting old mortgages with low yields out of its $57 billion portfolio of loans. It also will benefit by making new loans that will increase its yield in a market that has been depressed by his mortgage rates for 18 months.

The homeowner whose mortage is owned by FNMA will have the option to literally trade in an existing loan for a new one that can be as much as 90 percent of the home's current market value. The FNMA maximum on a single house loan is $98,500. David Maxwell, new president of FNMA, said the new interest rate will "almost always" be less than the prevailing rate in the market.

Fannie Mae owns FHA VA and conventional (nonfederally insured) mortgages. Homeowners and buyers will deal directly with lenders who are currently collecting their monthly payments to learn whether their loans are now owned by FNMA. Mortgage makers replenish their supply of lendable funds by sellling loans to Fannie Mae, but usually continue to collect the monthly payments for a fee.

Each of FNMA's 2,900 approved lenders across the land will be instructed to quote a special rate for each homeowner on a new loan. The rate will be determined by the unpaid balance, the original interest rate, the amount of the new loan and the payment period -- up to 30 years.

Fannie Mae's Maxwell said the new loan plan will be competitive with the wraparound mortgages and creative financing devised to create new loans for buyers of existing houses while maintaining low-rate original loans.

For example, an owner with a 10 percent mortgage owned by FNMA might have an unpaid balance of $45,000 while the home now is worth $66,700. The owner could refinance and get a new $60,000 mortgage at 11 1/2 percent and thus get $15,000 in cash. The monthly payment on the new loan would be $594, far below the $759 payment on a new 15 percent mortgage or the combined $665 payments on the old loan (395) and a new 18 percent, 10-year second mortgage (270).

In the case of a sale of a home with a Fannie-Mae-owned mortgage, the buyer would benefit by being able to obtain a new loan for 95 percent of market value at a rate that would be below market and also have a lower monthly payment than available by assuming an old loan and taking a second mortgage or a totally new loan at 15 percent.

Details of each loan, it was emphasized, must be worked out with the mortgage servicers along guidlines set down by Fannie Mae. The nation's biggest private mortgage holder also plans to enforce its due-on-sale clause in its conventional mortgage in states where that is permitted by law, such as Maryland, Virginia and the District. All FHA and VA loans are automatically assumable by new byers.

In addition to stimulating new business and getting rid of some of its existing loans that are costly for Fannie Mae to hold in a period of high borrowing rates, the loan program also is expected to stimulate the resale market of houses and also benefit new home sales, because 85 percent of new home buyers have to sell existing houses. h