Similar to the lenders for buying a home or car, credit card companies want to do business with customers on solid financial footing. Strengthening your credit will lower your risk to the credit card company, which makes them more willing to lower your rate. So before making contact, pull your credit rating to see where your financial health stands.
If your credit is on the upswing, it's an excellent bargaining chip, so sell that point when you call your card issuer. However, if your credit score needs fixing, you might want to delay your call until the numbers are more solid. Look at where you can achieve quick wins. Pay off a smaller balance or pay a sizable portion of a larger debt. Both will push your credit score upwards.
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Always make it a point to make all payments on time because even a few missteps can hurt your credit rating. If you do have an excellent track record of on-time payments, use it as a point in your favor.