It will take you longer to pay off your debt: Even if you aren't adding to your debt by traveling, you are making a tradeoff. If you put the money you saved for a trip toward your debt instead, you'll pay it off faster—that's just the math of it.
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It's a better decision financially to avoid spending money on travel when you have credit card debt. However, you can consider making an exception for important trips if your debt is manageable.