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If you are like many people, you have cards or lines of credit at rates that range from reasonable to usurious, so your sheet may look like this. Of course you may have more cards than this, but for sake of simplicity, I used three.
Debt Rate Interest
5000 .22 1100
3000 .15 450
2000 .12 240
Tot 10000 1790
Dave suggests paying off the lowest balance, so again to keep the numbers simple, we've paid off the $2000 debt. As you see, you now have a balance of $8,000 and an interest burden of $1550 per year.
Debt Rate Interest
5000 .22 1100
3000 .15 450
0 .12 0
Tot 8000 1550
To my way of thinking, the attack must be on the highest rate debt, and after paying down $2,000 will look as below. This is a difference of $200/yr. For those in debt and struggling to get out, $200 is not a sum to be taken lightly. I would hope this extra $200 brings you better feelings than the card count. I recall when I was in this exact situation, the best rate cards I carried also had the lowest credit lines, so I had many cards with $1500-$2000 limits at a low rate, but you can be sure the 24% cards gave me all the credit I could ever want. The decision is yours.
Debt Rate Interest
3000 .22 660
3000 .15 450
2000 .12 240
Tot 8000 1350