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Your creditors will become increasingly impatient with you, the longer it takes you to pay their bills, and therefore it is usually prudent to pay off the oldest ones first. As for the amount of interest you may be paying, that depends upon two factors, the interest rate (which is not the same for all your bills) and the amount of the bill. But pay the oldest ones first.

If you can pay off bills before they start collecting interest, that is a good thing, but you need to make some choices. Make minimum payments on all credit cards on time. Pay as much more as you can on the ones with the highest interest rate first. That will save you the most money in the long run.

If you have a choice between paying off $100 on a card that has not yet started accruing interest and has a rate of 15% or you can pay $100 on a card that is already at 21%, pay off the 21% card first. If it is the other way around on the interest rate, avoid getting hit with the 21%.

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Q: Is it better to pay off a bill before it accrues interest or to pay off other bills that already are accruing interest?
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