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First it was plain old Visa and MasterCard-with high rates.

Then came the challengers: Sears, AT&T and a bunch of others from outside the banking industry.

In Round 3, you saw General Motors offer “credits” toward the price of a car, depending on how much you used GM’s card.

Round 4 initially promises to be the best of all. Here’s why:

Banks are waving, cold hard cash to get you to use their plastic instead of a competitor’s. Car buying? Airline miles? Store merchandise? Forget those card-user gimmicks. As the Beatles sang, “Give me money, that’s what I want.”

Isn’t that what everybody wants?

Five institutions have just introduced money-back plans, or something like them. Each offer has its own twists, however, and that makes shopping the deals difficult.

Figuring out which card is best for you depends largely on how much you charge each month, but may also hinge on what kind of balance you carry.

To make card-shopping easier, let’s assume that you charge $500 every month. We’ll see what you’d earn in a year’s time if you paid off the balance in full and then what would happen if you carried a balance of $2,000. We’ll take the cards in no particular order:

– Chase Manhattan USA in Delaware (800-282-4273) rebates 1 percent of monthly purchases, or $60 a year in this case. If you carried the $2,000 balance and were charged the recent rate of 16.40 percent, you’d also get a rebate on the interest and earn $32.80 annually for a total of $92.80.

– Cincinnati-based GE Capital Consumer Card Co. (800-544-5232) would pay $60 annually based on purchases and mail you quarterly coupons good toward discounts at participating stores. The card issuer doesn’t have any rewards based on the card balance.

– Mellon Bank Delaware (800-753-7011) has a rather unusual plan. Keep its card for 20 years and the bank will refund 100 percent of your interest at that time. Over a shorter period of time, you’ll get a smaller percentage. Using the criteria listed above and Mellon’s 17.90 percent rate, the rebate on one year’s worth of interest would be $35.80 if you waited just the minimum two years to earn a 10 percent rebate. Pay off the balance in full and you earn zip.

– Fidelity Trust Co. (800-323-5353), best known for mutual funds, rebates 1 percent of purchases, or $60 assuming $500 charged each month. You could do a little better if you opened an interest-bearing savings account at its Salt Lake City bank and had your rebate deposited there. But at current rates, that would add no more than $2 to the total. No deal is based on the card balance.

– Colonial Bank USA, Delaware (800-513-8989), credits one point for every $1 charged toward U.S. savings bonds. You’d rack up 6,000 points in a year, enough to get two $50 bonds. However, they couldn’t be redeemed at face value for as long as 18 years. In six months, they’d be worth $25 plus a little interest. Carrying a balance wouldn’t make a difference.

So, what’s the best deal if you pay off the balance in full? Chase, GE Capital and Fidelity all will give you $60 in cash. Neither Chase nor GE has an annual fee, but Fidelity charges $2 a month if you don’t carry a balance of at least $500; that’s as much as $24 over a year’s time, plus interest charges.

In all fairness to Fidelity, what it really wants you to do is sign up for yet a third option in which you transfer at least $20 a month to its savings account. That’s something currently available only from Fidelity.

Colonial Bank USA charges an $18 annual fee, which reduces your net benefit and knocks the card out of the competition. You could give GE the edge over Chase because of the shopping coupons.

If you carry a balance, Chase wins because it has two rebates, one on purchases and the other on interest paid. The way to get ahead, though, is to carry a massive balance such as $10,000. In that case, Chase would write a check for $224 and Mellon for $179.

To complicate matters, AT&T Universal (800-786-3131), which is tied to the long-distance phone company, has entered the race with a non-cash package. For every $1 in month-ending balance, you get one point. With $2,000 monthly, that’s 25,000 points annually, including a 1,000-point bonus for enrolling.

The points would earn you a discount of at least $50 off the rental of a Hertz car. You could also get five hours of free AT&T long-distance calls; at 20 cents a minute, that would be worth $60. If you always paid your balance in full, you’d get no points.

AT&T credits could be worth more than the cash from Mellon or Chase, but the Georgia-based bank charges a $20 annual fee, which also brings the net benefit to $40 or less, depending on how you redeem your points.

However, if you carried that gigantic $10,000 balance, AT&T Universal would issue you a $1,200 credit toward a new Honda.

Which card would you select? If cash is more useful than AT&T credits, then the Chase card would be best.

These examples assume you make fairly good use of your cards. If you find that you charge only one or two items each month and that you always pay off the balance, then these latest card deals offer you very little.