The one reason in getting rid of the smaller debtf first is as fairy76 said above. When you have alot of different debts and feeling overwhelmed; getting rid of a few smaller debts eases the load. You have got to consider the time, envelopes, postage, and general keeping track of more debt. It gives you a feeling that you can do it and getting somewhere. Some people need the visuals to motivate them. Another factor is that the monthly payment on even one of the smaller debts could be a high one and you could get rid of it faster as to use the money on the next debts.
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