Montgomery County Executive Charles W. Gilchrist, counting on higher property tax assessments, said yesterday that he will propose an 8.7 percent increase in the county's 1986 operating budget that will add funding for programs for the elderly and handicapped and day care, and meet the school superintendent's request for services.

The operating budget that Gilchrist will recommend Friday to the County Council would cost homeowners between $40 and $145 depending on where they live, according to estimates released earlier by the county executive. Gilchrist released no total figure for his budget proposal yesterday, but increasing the current $883.2 million budget by 8.7 percent would result in a total budget of about $960 million. Last year Gilchrist recommended a 6 percent increase over the 1984 budget.

Under the proposal, according to Gilchrist, the tax rate -- now $2.06 per $100 of assessed value -- would likely drop. But tax bills in the county's three assessment districts would, on an average, increase about 5.5 percent because of rising valuations. That percentage is the rate of inflation for the Washington metropolitan area during the last year, he added, and an amount that Gilchrist said would generate the money that the fast-growing county needs to meet an "era of change."

"If we are to be masters of our fate in an era of change," Gilchrist said when announcing the preliminary outlines of his budget at a press luncheon, "we will have to respond to the challenges confronting us."

Specific challenges that Gilchrist said should receive more county money would be child day care -- new programs that he said could cost the county nearly $1 million -- schools, transportation systems, mental health programs and homes for the mentally retarded.

Gilchrist, who submitted a request last year to abolish 100 jobs in the county, said the county would likely need more employes next year. But he did not give any numbers.

Gilchrist had few specific budget figures yesterday, although he said he was ready to allot $435.8 million to the Board of Education. That figure is $3.1 million less than the board asked for but identical to the figure requested by Superintendent Wilmer S. Cody earlier this year.

The county executive pointed to expected cuts in federal funding as one of the reasons for increasing his budget. "We do not know the extent to which the Congress will implement President Reagan's budget cuts nor can we predict how many cuts will apply to county government or others who provide services to our people . . . but I believe that the county must maintain its resources," Gilchrist said.

The final budget must be approved by the County Council by May 15.

Since Gilchrist's budget proposal exceeds the inflation rate, according to a 1978 charter amendment it must be approved by five council members, instead of a simple majority of four. Last year's budget forced the council to follow that rule for the first time.

In explaining his plans for increased services, Gilchrist cited budget and census figures collected during the last eight years:

* Money from real and personal property taxes have increased from $6.8 million to $13.8 million.

* Unemployment has dropped from 3.4 percent to 2.7 percent while the work force has increased from 575,000 to 620,000.

* The number of passenger vehicles registered in the county has risen from 376,000 to 419,000, he said.

At the same time, he said, the percentage of the population 65 years and older living in Montgomery has increased from 6 percent to 9 percent, and the number of minorities has increased from 5 percent to 15 percent. The growth in the work force is a sign that more women are working, he said, and as a result, 65,000 children in Montgomery have mothers who work outside the home.

Gilchrist said he believed the county could meet the needs of the changing family structure by providing more after-school activities for children, establishing a clearinghouse for day care where workers can be trained and helping enforce child-support obligations.

Gilchrist said he would continue to work for more state money for roads and the county should expand its Ride-On system and Share-A-Ride programs. Social services such as the county's mental health program, group homes for the mentally retarded and day care for the elderly also needed more funds, he said.