According to a draft of the Reagan administration's latest tax-simplification plan, it will include a 20 percent minimum tax on individuals and corporations.

The draft document, obtained from congressional sources yesterday, says the minimum tax is necessary in part because so many loopholes have been restored in the new version of the tax plan that some corporations and individuals could still pay little or no taxes without the minimum.

The document also shows that the new administration plan would curtail deductions for interest paid on second-home mortgages and consumer loans even more than in the Treasury Department's original plan proposed last November.

In the first Treasury plan, taxpayers would have been allowed to deduct all interest paid on the mortgage of a principal residence, but only a limited amount of other interest payments, up to $5,000 plus an amount equal to the income the taxpayer received on investments, would be deductible. The new Treasury plan limits deductible interest for second homes and consumer loans to $2,000 more than the amount of the taxpayer's investment income.

However, the new plan retains a loophole for interest paid on a second home that is rented by others most of the year.

The documents obtained yesterday were copies of chapters in the new proposal, but the tax plan is still subject to alteration before President Reagan announces it on May 28. Treasury Department officials refused to confirm or deny that this draft represented the latest version.

The November tax plan called for repeal of the existing minimum tax on individuals and companies on the grounds that a simplified tax code that wiped out nearly all tax loopholes would make a minimum levy unnecessary.

The new draft acknowledges that because many loopholes have now been restored, a minimum tax is more attractive. "Since the administration proposals contain incentive provisions that depart from the measurement of economic income, some high-income individuals . . . and corporations will be able to eliminate their tax liabilities or substantially reduce their effective tax rates by heavy utilization of such provisions," it says.

"Consequently, a minimum tax designed to limit the number of high-income, low-tax returns should be retained."

Both the corporate and individual minimum taxes would be "alternative" taxes: taxpayers would calculate their taxes using the regular method and the minimum-tax method, then pay whichever is greater.

The House is expected to vote next week on a minimum-tax amendment to the congressional budget resolution. Congressional Democrats are sharply divided over whether to use a minimum tax to raise revenue, use it to offset lower rates as part of tax revision or to leave it out of tax overhaul.

Separately, officials of the Department of Housing and Urban Development confirmed that the Treasury Department has backed off several limitations on tax breaks for low-income housing that had been part of the original tax simplification plan.

June Koch, assistant secretary for policy, development and research, said the new plan would not include earlier proposals to limit depreciation deductions for multifamily housing, to limit writeoffs on low-income housing to the actual dollar amount invested and to tax large partnerships in low-income housing projects as corporations.