Short-term interest rates have fallen sharply in recent weeks, but consumers with $10,000 to invest for six months still can earn substantially more than the 5 1/4 percent banks pay on passbook accounts, or the 5 1/2 percent savings and loan association pay on their passbooks.

Savers can buy a $10,000 money market certificate at their local bank and S&L, where the rate changes each Thursday depending upon the results of the Treasury Department's weekly auction of bills. Or, with some extra effort, the investor can buy a bill directly through either the Treasury or the local bank or branch of the Federal Reserve.

It is more complicated to buy a bill than to visit your local banker. But the interest on a Treasury bill is not taxed by state and local governments and the interest return, because of some quirks in the way federal government computes interest rates, is generally a little higher.

Every Monday, the Treasury Department sells at auction billions of dollars worth of securities it calls bills. A bill, in federal financial parlance, is a security the government promises to pay off within a year or less.The government uses the money it raises to pay its debts.

On Monday, the Treasury sells three-month bills for six-month bills. Last Monday, for example, the agency sold $4.3 billion each of three-month and six-month bills.

The smallest denomination bills the Treasury will issue are for $10,000, and they can be purchased in multiples of $5,000 above that, according to Richard Gregg, assistant commissioner of finance in the Treasury's Bureau of Public Debt.

The Treasury sells the bills at a discount. That means the investor pays less than $10,000 for the bill, which at maturity is worth $10,000. The difference between what the investor pays and the $10,000 he gets back at the end of three or six months is the interest. Last Monday, the average investor paid $9,388.50 for a six-month bill. The $611.50 difference between purchase price and the $10,000 the bill is worth when it matures is the interest.

The so-called discount rate is computed as if the purchaser paid the full $10,000 and received an interest payment of $611.50 after six months. Last Monday the average discount rate was 12.096 percent on the six-month bill (it was 12.758 percent for the three-month security).

At that rate, the banks and savings and loan associations are permitted to tack on another 1/4 percentage point to their rates on six-month money market certificates and pay 12.346 percent to investors who keep $10,000 on deposit for that period.

But the investor who bought a bill did not invest $10,000, as the discount rate calculation assumes.Instead the investor put down $9,388.50. The Treasury mails the $611.50 back to the bill purchaser shortly after the auction. As a result, the real rate of interest the investor receives is 13.06 percent, what the Treasury calls the coupon equivalent, or investment, rate. It is higher than both the discount rate and the rate financial institutions can pay.

Most of those who buy Treasury bills are large investors -- insurance companies, pension funds or government securities dealers. They enter what are called "competitive bids," offering to buy a fixed amount of the Treasury securities at a specific price. The Treasury usually takes the highest bid, then the next highest bid and so on until, in last week's case, it has sold $4.3 billion worth of six-month bills and $4.3 billion in three-month securities.

But the Treasury also permits investors to submit a noncompetitive offer to buy (called a tender offer) under which the investors agree to take the bill at whatever the Treasury computes to be the average price in the auction.

The least expensive way to buy a Treasury bill is through the Treasury Department itself or through the local Federal Reserve Bank. To buy a Treasury bill, the offer to buy must be in the hands of either the Fed or the Treasury by 1:30 p.m. the day of the auction. The bills are issued the following Thursday.

The Treasury's Gregg said the Fed and the Treasury prefer it if an investor applies to buy a bill using the standard government form. those forms can be obtained at the local branch of the Federal Reserve -- in the Washington area there is a Federal Reserve branch in Baltimore and a full-fledged Federal Reserve Bank in Richmond -- or at the main office of the Treasury Department itself at 15th Street and Pennsylvania Avenue NW.

Investors also can get the forms by writing: Bureau of Public Debt, Department F, Washington, D.C. 20226 or call (202) 287-4113.

Once the investor has the form in hand, he or she must obtain a certified chekc or a cashier's check for $10,000 (or $15,000 or whatever $5,000 increment above the $10,000 minimum the investor wishes to purchase).

Shortly after the auction the Treasury will send the investor a notification that the agency has opened a bill account in his or her name and will send a check for the difference between the average sales price and, say $10,000. Since 1977 the Treasury has not sent a physical "Treasury bill" to customers, but merely the notice that the purchaser has a bill account for say, $10,000, that comes due at whatever date the bill matures.

When the investor fills out the form, he or she has the option of instructing the Treasury to reinvest the bill at maturity. If the investor does not tell the Treasury to do so, the Treasury will send a notice after about 1 1/2 months for three-month bills and three months for six-month bills, asking the investor whether the Treasury should reinvest the proceeds in another bill (financiers call that rolling it over) or send the investor a check for $10,000.

Investors do not have to deal directly with the government. Most banks or brokerage houses, for a fee, will buy a Treasury bill for their customers. Riggs National Bank, for example, charges $30, while Dean Witter Reynolds charges $25 per transaction plus 25 cents per thousand. A purchase of a $10,000 bill at Dean Witter would cost $27.50.

If the investor needs the money before the bill matures, he or she can go to a bank or a broker and arrange to sell the bill for whatever price is current. If interest rates have risen since the bill was purchased, the investor can expect to lose some money on the sale. If rates have fallen, however, the investor may make some money. But in any event, when the investor sells the bill before maturity, he or she probably will have to pay a fee to the bank or broker.