The Securities and Exchange Commission yesterday accused E. F. Hutton & Co., the second largest publicly owned brokerage firm, of aiding in the manipulation of the stock price of Rapid American Corp.

The commission ordered its allegations to be reviewed in a public hearing.

In addition to the firm, the SEC named Jerome D. Rosentein who manages Hutton's Miami Beach office and Bernard Berger, a former salesman at that office.

The SEC claims Berger came up with a scheme for buying stock at the very end of the trading day for an unnamed customer. The purpose was to artificially inflate the price of the stock, which had the effect of increasing the value of the equity in the customer's account. This, in turn, meant that the customer did not have to put up more capital to meet the margin requirements.

E. F. Hutton President George Ball called the SEC charges "ludicrous" and "totally unfounded." He said the firm "fully intends to litigate the case."

The SEC describes the alleged fraud this way:

In the first half of 1975, the price of Rapid American stock, traded on the New York Stock Exchange, declined. This caused the equity in the customer's margin account also to decline.

The Federal Reserve System says that up to 50 percent of the purchase price of stock can be financed with debt. To do this, however, a customer is required to maintain an equity margin with the brokerage firm equal to at least 25 percent of the market value of the stock purchased.

As the value of Rapid American dropped, the Hutton customer had to put up more equity to cover his margin, the SEC says.

"Berger and the customer had observed that the market price of Rapid American common stock . . . sometimes moved an eighth of a point on limited volume on the final trade of the day," the SEC says.

Between Aug. 3, and Oct. 12, 1976, Berger allegedly bought 100 shares each on 37 different days. These were the last trades on the stock which moved the price up an eighth of a point, the SEC says.

Rapid American was trading at about 5 1/2 at the time.

Since Hutton uses the closing price to value equity in customers' accounts, the SEC says that these final trades had the affect of increasing the value of the customer's holdings in Rapid American.

Without the one-eighth, the SEC suggests the customer would have had to put up more equity in his margin account. The commission says the customer was not named in the action for jurisdictional reasons.

The SEC says Rosenstein failed to supervise Berger. It also claims he destroyed records of the customer's account.

But Ball said: "There is no law saying he had to keep those notes."

The hearing on the case is expected within two months.