The overheated hotel meeting room was crowded with investors listening to a representative of Multicapital Services Inc., a Zug, Switzerland-based financial consulting company, extol the virtues of Swiss bank accounts. Eventually, the audience's questions turned to secrecy and the Internal Revenue Service, and an elderly woman near the front raised her hand.

"I think the box you check on your tax return to show you have foreign accounts is underneath the place where you sign your name. So, if you don't check it, you're not really breaking the law, because you've already signed your name," she said.The instructor of the seminar, which was held as part of The Ruff Times 1988 National Convention in Orlando last month, did not respond; but, of course, the woman was wrong.

Intrigue and misinformation surround the existence of offshore bank accounts. Their popularity has been fed recently by the news that such notable citizens as Lt. Col. Oliver North and Wall Street trader Dennis Levine allegedly stashed millions in such accounts.

Middle-class taxpayers are showing increasing interest in Swiss bank accounts. Some are attracted by the roguish history of the numbered Swiss bank account, and many more are attracted by the Swiss government's stiff banking secrecy laws. In other words, they want to evade their federal income taxes.

Opening a Swiss bank account is as easy as slipping a check into an envelope and mailing it overseas to the Swiss bank of your choice. But before you take pen in hand, consider: For honest taxpayers, the romance of having a Swiss account doesn't make up for the fact that Swiss banks charge high fees and pay little or no interest.

And for the average would-be tax evader, Swiss accounts are not a foolproof means of ducking tax responsibilities. The federal government can track individuals' foreign investments in many ways, and the United States and Switzerland frequently exchange financial information when criminal activity is suspected.

"There are problems for the small investor when it comes to Swiss bank accounts," said Mark Skousen, editor of the financial newsletter "Forecasts and Strategies," from his office in Winter Park, Fla.

Swiss deposit accounts typically come in two flavors: plain-vanilla savings accounts, and custodial accounts, which are equivalent to U.S. brokerage accounts. Either may be identified by a number rather than a name, but the fabled numbered Swiss accounts are not entirely anonymous. The identity of the depositors in a numbered account is always known to the top three or four officers of the bank or branch where the deposit was made.

Generally, though, Swiss accounts are run the same way as American accounts: The banks issue regular statements, take deposits and issue withdrawals, usually paying some interest. And the Swiss banks charge fees.

"One thing about Swiss bank accounts," Skousen said, "they charge for everything. If you have them look up your account, they'll charge you. The monthly statements, they charge you for. All that reduces the return."

Fees and minimum deposits vary greatly among Swiss banks and from one kind of account to another. Exact fees, minimums and interest rates are difficult to pin down from this side of the Atlantic Ocean, but consider, by way of example:

-For a custodial account, at most banks you'll pay the equivalent of a full-service broker's fee, which usually ranges from 2 percent to 8 percent of the value of each transaction.

-Swiss Bank Corp., with headquarters in Basle, Switzerland, doesn't charge a flat fee for the statements it issues on a custodial account but starts charging an annual handling fee of up to $21 when the number of transactions exceeds about 15 a year.

-Foreign Commerce Bank, with headquarters in Zurich, Switzerland, charges $5 for its quarterly statement. Some banks issue the statements monthly, some quarterly.

The biggest drawback to a Swiss account from an American investor's standpoint is the low interest it pays: 3 percent or less. If your deposit is denominated in any currency other than Swiss francs, most Swiss banks pay you no interest at all.

On that meager interest, the Swiss government withholds a tax of 30 percent. Foreign depositors, such as Americans, must file a Swiss tax form to have 5/6 of the tax returned, then must file another form with the IRS to get a U.S. tax credit for the 1/6 of the Swiss tax they did not receive.

For example, a depositor sends $200,000 to a Swiss bank. If the account earns 3 percent interest annually, in a year the depositor would have earned $6,000, and the Swiss government would have withheld $1,800 of those earnings. The depositor would have to file with the Swiss government to reclaim $1,500, then file for a tax credit with the IRS for the remaining $300.

Needless to say, money withdrawn from the overseas account, bank statements and other information must be mailed back to the United States, and that takes time. And Swiss banks charge a fee for the postage.

But for some people, one of a Swiss account's most attractive qualities is the fact that it is far away, supposedly hidden from the IRS' prying computers. Having an account overseas, however, does not exempt any U.S. taxpayer from reporting its existence and its earnings to the IRS.

The place for reporting income from foreign accounts or trusts is on Schedule B, which you must fill out if you had any foreign interest or dividend income. Taxpayers must pay taxes on those earnings as they do on domestically earned interest. If you fail to do so you face a penalty of up to $100,000 and five years in jail, plus legal and court costs.