Employers across the country adjusted how much money to withhold from paychecks in accordance with new schedules formulated to match lower-income brackets as a tax cut went into effect Tuesday.

The $330 billion tax package (search) was signed into law in May. Aside from seeing a little extra in their paychecks due to income tax reductions, millions of Americans will also receive a $400 check for each child, to arrive later this month -- and investors will see Washington take a smaller bite out of capital gains and dividend income.

While the income tax cut was made retroactive to the beginning of 2003, employees will not receive a refund check, but will apply for the normal income tax return for the higher rate charged in the first half of the year.

"This year's tax cut unfortunately will come in bits and pieces, and [employees] won't see the full magnitude of it for some time," said Scott Hodge, executive director of the Tax Foundation (search).

The new law extends the 10 percent income tax rate from $6,000 to $7,000 of taxable income or from $12,000 to $14,000 for married couples. The other brackets are now at 15, 25, 28, 33 and 35 percent.

When broken down, the cuts play out differently for families depending on income and number of dependents. For instance, a married couple with two children and an annual income of $40,000 will see $1,133 per year. That same couple will see $2,021 per year if they make $75,000; $3,158 per year if they earn $200,000.

However, that same couple with no children will get back $333 per year for a $40,000 income; $1,604 per year for a $75,000 salary; and $3,280 per year for a $200,000 salary. The dollar amount is lower in the first two income categories where the couple doesn't qualify for the $400-per-child tax credit.

Single individuals with no children who generally sign up for fewer exemptions will receive $126 per year for a $40,000 income; $826 per year for a $75,000 salary; and $2,766 per year for a $200,000 salary.

The income tax cuts are the first break taxpayers will see.

"This is the first stage, in which we will see the small changes that will impact your paycheck," said Hodge.

The next stage -- the child tax credit (search) given for each child under age 17 living at home -- will start arriving in 25 million homes in the last week of July. All the checks should be delivered by mid-August.

The wealthy will receive the biggest dollar return for the income tax cut. But as a percentage of income tax liability, low- and middle-income taxpayers fare better. The tax cut returns 96 percent of the taxes a family of four earning $40,000 would have paid this year. It gives back 28 percent of the taxes the same family earning $75,000 would have paid. It gives back 9 percent to families earning $200,000.

"The top 1 percent of taxpayers earns about 20 percent of the income in America, but pays 40 percent of all the income taxes. And so when they get a 10 percent tax cut, it's a pretty large dollar amount, but after all, they paid an awful lot to begin with," Hodge said.

Employees can find out how the Bush tax cut affects them personally by calculating its value at www.paycheckcity.com. The site sells tax-calculating software and also provides calculators for personal accounting.

Fox News' Major Garrett contributed to this report.