President and Mrs. Reagan saved $8,681 on their 1987 federal income taxes because of changes in the tax law, and will save $20,113 next year if their income remains roughly the same.

That's the conclusion of Josh Grauer, a senior manager at the accounting firm of Touche Ross, who analyzed the president's 1987 tax return, made public earlier, to see how the Reagans were affected by changes in the tax law.The First Family is benefiting because of provisions in the law that help very wealthy taxpayers. "It's not just the Reagans," said Grauer. "It's everybody else in the same category."

The main change aiding the Reagans is a provision in the new tax law reducing the top tax rate from 50 percent of taxable income to 38.5 percent of taxable income in 1987. That rate will drop to 28 percent for 1988.

The Reagans' income last year was $437,166. Their taxable income was $263,767 after deductions and exemptions. Their tax bill was $86,638.

Like other taxpayers, the Reagans lost the sales tax deduction, which had taken $922 off their taxable income the year before. They also lost $1,440 in personal interest deductions and $6,907 in miscellaneous deductions. Moreover, the increase in the tax rate on capital gains from 20 percent to 28 percent last year cost them $3,696.

But those debits were more than offset by the drop in the top tax rates.

"The big story is the rates," said Grauer. "And the real big story will be next year when the rates drop even further."

Next year, rich people will pay a flat rate of 28 percent on all of their income from the first dollar earned to the last. They will no longer have the benefits of lower taxes on the lower portion of their income, as other taxpayers do, but they still benefit substantially from the drop in the top rate.

The 28 percent flat rate for the super rich has drawn fire from liberals. Jesse Jackson has already said he would repeal it.

In fairness, Grauer noted, that tax reform also benefited the poorest taxpayers, many of whom are dropped from the tax rolls entirely, as well as the wealthiest.

The Reagans paid $7,800 to have their tax return prepared, even though Grauer said the return appeared to be relatively straightforward. They paid another $3,400 for tax advice and $11,000 for audits of their 1985 and 1986 tax returns. Presidential tax returns are audited routinely.

The Reagans' tax return also indicates they avoided losses in the Oct. 19 stock market crash.

They earned only $319 in stock dividends from a blind trust run for the president. Details of the trust, of course, are secret. But the trust showed capital gains of $14,858, indicating any stock the Reagans held was probably sold early in the year. Stock dividends had totalled $2,405 in 1986 and $4,462 in 1985.

At the same time, the Reagans had tax exempt interest income, presumably from municipal bonds, of $91,807. They also had taxable interest income, from banks and the trust, totalling $54,178.