The typical American family of four with $30,120 in income in 1984 will save $84 in federal income taxes in 1985 as a result of the new federal tax "indexing" system that starts next year, and will pay $690 a year less by 1989, the Treasury said yesterday.

Releasing the first detailed projections on the new system, Treasury Secretary Donald T. Regan said, "American taxpayers will save more than $9 billion in taxes in 1985" compared with what they would have paid if tax indexing had not been enacted.

The indexing plan was enacted by Congress in 1981 to prevent taxpayers from being pushed into higher tax brackets merely because their income is rising because of inflation. Under the new law, federal income tax exemptions, tax brackets and standard deductions will be increased each year to keep pace with inflation. A taxpayer whose income increases in pace with inflation will pay about the same proportion of income in federal taxes each year.

Under the old law, where the exemptions, brackets and standard deductions remained constant, such taxpayers paid a higher proportion of annual income in federal taxes each year.

For 1985, the Treasury is increasing the brackets and the standard deductions by 4.08 percent, which was the inflation rate for the base year used for calculations. As a result, the $1,000 personal exemption for each family member will rise to $1,040 for 1985. Regan said the standard deduction or "zero bracket amount" -- on which no taxes are due -- will rise from $2,300 to $2,390 for a single person and from $3,400 to $3,540 for a married couple.

As a result of the bracket changes, taxpayers will not step up to higher tax rate categories quite so fast. For example, in 1984, as a married couple's taxable income rose past $7,600, the tax rate on income between $7,600 and $11,900 rose from 12 percent to 14 percent. In 1985, the 14 percent rate will apply to income from $7,910 to $12,390.

In a series of tables, the Treasury estimated what will happen to various kinds of families if inflation over the next few years is about 4 percent a year and incomes rise as projected by recent administration forecasts:

*A family of four, consisting of one working person, a nonworking spouse and two children, which had $10,000 adjusted gross income in 1984, would pay only $246 federal income taxes for 1985, compared with $283 if there were no indexing. In 1986, it would save $82; in 1987, $127; in 1988, $178, and in 1989, $231.

*A similar family with income of $20,000 in 1984 would save $37 in 1985; $88 in 1986; $147 in 1987; $207 in 1988, and $265 in 1989.

*A family earning $30,120 -- the median income for a four-person family with one wage earner in 1984 -- would save $84 in 1985; $208 in 1986; $362 in 1987; $517 in 1988, and $690 in 1989.

*A family with a $50,000 income in 1984 would save $224 in 1985; $504 in 1986; $781 in 1987; $1,053 in 1988, and $1,364 in 1989.

*A single person with no dependents earning $10,000 in 1984 would save $13 in 1985; $28 in 1986; $45 in 1987; $62 in 1988, and $80 in 1989. For a single person earning $20,000 in 1984, the savings would be $47 in 1985; $105 in 1986; $181 in 1987; $259 in 1988, and $333 in 1989.

*A single person starting at $40,000 in 1984 would save $149 in 1985; $369 in 1986; $606 in 1987; $841 in 1988, and $1,067 in 1989.