Many people believe that carrying a balance will help them build credit or up their chances of getting approved for a credit card. People think that if they pay interest then the bank is making money off them (that part is true!) So if the banks are making money, then their pockets are like a gold rush for the banks, causing all of them to come running and approve him for credit cards . Therefore, even if these people can afford to pay more than the minimum payment due on their credit card bill, they will still go ahead and pay only the minimum amount due, thinking (falsely) that this is helping them build credit.
A Myth on Fire
Credit models look mostly at 5 factors. These 5 factors are how credit scores are calculated (you can read about them here). Carrying a balance is absolutely not one of the 5 factors. What is one of them is credit utilization. Credit utilization accounts for 30% of the FICO scoring model. Carrying a balance from month to month may strongly effect your credit utilization, which may ultimately have a strong negative effect on your credit score.
So by carrying a balance on your credit cards, not only will it not help you build credit, but it actually may help you lower your credit score. And with a low credit score, you can pay the bank as much interest as you wish; you will still be a second class customer.
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