Debt Snowballs Explained

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If you read or listen to any financial advisors, particularly Dave Ramsey, you've likely run across the term 'debt snowball'.
What exactly is a debt snowball, and should you be using one? The concept behind it is simple: given all the debts you need to pay off, you start by paying the minimum on everything and then putting all of your extra money towards the smallest one.
Once that's paid off, you take everything you were putting towards the smallest bill and add it to what you're paying on the new smallest bill, and so on.
As each bill gets paid off, you're making larger and larger payments towards one of the new bills so they get paid off faster and faster.
The main advantage of this is psychological: if all the bills have the same interest rates, you're going to get them paid off at the same time no matter what order you do it in (with the caveat that if you're making new charges, you want to have a card with no balance to do that so you aren't paying any interest if you pay it off at the end of the month); otherwise, you'd want to pay down the card with the highest interest rate first.
From a strictly mathematical standpoint, then, the debt snowball doesn't particularly make much sense.
From a psychological standpoint, though, it can be very encouraging to see debts disappearing, making fewer payments each month, and taking bigger and bigger chunks out of the remaining debt.
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