The Social Security payroll tax rate is going up on New Year's Day for the 13th time in the past quarter-century as workers pay a price for the 1983 bailout of the retirement program.

The rate increase will boost the tax to 7.51 percent from 7.15 percent. The tax will be levied on the first $45,000 a worker earns next year, up from $43,800 in 1987. But recipients will receive a boost in their monthly benefits.

A worker who paid $2,000 in payroll taxes on $27,972 in wages in 1987 will have to pay $2,100 in payroll taxes on the same amount of earnings in 1988 -- a 5 percent increase. Employers must pay the same.

The bite will be bigger for the self-employed, who paid at a 12.3 percent rate in 1987 and will pay 13.02 percent in 1988.

The self-employed pay the combined employe-employer tax rate, minus a 2 percent credit that will disappear after 1989.

While the 126 million workers covered by the program will have to dig a little deeper in 1988, the system's 38 million beneficiaries will find a 4.2 percent cost-of-living increase in their monthly checks this week.

Those checks will show up in mailboxes -- or be credited directly to beneficiaries' bank accounts -- on Thursday, New Year's Eve, three days early because of the holiday weekend.

The maximum tax on an employe earning $43,800 in 1987 was $3131.70. The tax on that same amount in 1988 will be $3,289.38, or $157.68 more.

An employe earning $45,000 will pay $3,379.50, or $247.80 more than the maximum this year. That amounts to a 7.9 percent increase at the top.

The payroll tax was 1 percent on income up to $3,000 when Social Security started in 1937. It stayed that way until 1950 and has risen every few years since then.

This will be the 20th increase in the tax rate.

The tax pays not only for Social Security retirement benefits, but survivors and disability coverage as well as most of Medicare.

The wage base -- the amount subject to the tax -- also has gone up every year since 1971.

After staying at 7.51 percent through 1989, the rate will climb to 7.65 percent in 1990. No further increases are planned.

Congress voted in 1977 during an earlier pension crisis to raise the tax to 7.65 percent in 1990. Originally, no tax increase was scheduled for 1988, but lawmakers changed that in 1983.

Why 7.51 percent in 1988 and 1989 instead of simply 7.5 percent?

That was the figure the National Commission on Social Security Reform plugged into its formulas in 1983 when it was devising a package of benefit cuts and tax increases as part of its bipartisan plan to bail the system out of a recurrent crisis.

Since then, Social Security's trust funds have experienced robust growth. The old age and disability programs now have $67 billion in reserve and Social Security Administrator Dorcas R. Hardy said they will grow by $38 billion in 1988.

In a program that pays out well over $200 billion a year in benefits, that is still a cushion of only months.

Social Security's long-range plan is to build up a $12 trillion reserve by 2020 -- the equivalent then of more than five years' benefits -- and then draw it down to help pay for the baby boomers' retirement years. The trust funds will be depleted by the middle of the 21st century.

The self-employed, who once were charged bargain rates for Social Security coverage, will pay a full 15.3 percent starting in 1990, when they lose a 2 percent tax credit. But starting in 1990 they will be able to deduct half the tax as a business expense.

The maximum tax on a self-employed worker making $43,000 in 1987 was $5,387.40. The tax on that same amount in 1988 will be $5,702.76. The maximum tax, on earnings of $45,000 or more, will be $5,859 in 1988 -- an increase of $471.60, or 8.8 percent.