"Dear Occupant," says a letter I received recently. "Would you like to earn 5 percent interest on money you now keep in a checking account?"

All you have to do is put your money into a savings account, "then write checks as you always have." Each time you write a check, the bank will transfer enough money from your savings account to your checking account to cover your disbursements.

If the balance in your savings account drops under $1,000 in any month, you will have to pay a service charge of $6 for that month. If you keep $1,000 or more in your savings account, the bank will provide the transfer service free - but there will "of course" be a "nominal" charge for check printing.

If this sounds like an attractive offer to you, look at it again. In a time when the United States Treasury pays more than 9 percent interest, high grade bonds pay 10 percent or more, and your thousand dollars is being lent out at 11 percent or more, the bank will pay you only 5 percent for the use of your money. In other words, in order to obtain the bank's "free" zero-balance checking service, you must agree to accept $50 a year for your thousand dollars instead of the $100 or more your could earn elsewhere.

Again we are reminded that there is no such thing as a free lunch. A bank, like any other business, must make a profit on the services it sells. Instead of looking for "something for nothing," the consumer should regard all "free" offers with healthy skepticism.

Go through your last 12 bank statements and count up how much you paid for one year of checking privileges under your present fee schedule. Disregard check printing charges, because those are usually the same under both the old and new plans.

Did your service charges for checks amount to more than $50 last year? If they didn't, the new zero-balance checking account won't save you money, it will cost you money. You will be diverting $1,000 from a potential 10-percent investment to earn 5 percent on a savings account.

A newer plan is not necessarily a better one. Dont't permit yourself to be carried away by the air of excitement in the bank's advertising copy.There may be less to it than meets the eye, dear Occupant.