Overpayment on your credit card does not improve your credit rating or increase your card's limit. If you make an overpayment, the card company will apply the negative balance toward your next statement, but you can also request a refund.
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It's a good idea to pay off your credit card balance in full whenever you're able. Carrying a monthly credit card balance can cost you in interest and increase your credit utilization rate, which is one factor used to calculate your credit scores.
If you only make the minimum payment, you will also likely incur interest charges that you could otherwise avoid by paying your statement balance in full.