There are two primary ways that people pay down debt. Attacking the debt with the smallest balance or attacking the debt with the highest interest rate.
Before I explain these I want to give a general thought process or framework for debt. I believe you should have a healthy dislike for debt. While I don't think a reasonable mortgage or student loans (if pursuing some sort of forgiveness) are unhealthy, most other forms of debt - credit card, auto loan, etc. should be avoided.
Two primary debt payoff strategies:
Snowball - This strategy is more about human psychology and involves attacking the debt with the smallest balance owed first. For example, if you have a $10K credit card with a 25% interest rate and a $4K car loan with a 5% interest rate under this strategy you would pay off the car loan first and then move to the credit card. You would then take your regular excess plus the amount you were paying on the car loan to then attack the credit card. This strategy allows the number of loans to disappear more quickly but may result in paying more in interest than the next method.
Avalanche - This is my personal preference and the one the math generally supports. In this strategy you attack the debt with the highest rate and then second highest rate and so on. Under this strategy you would pay off the credit card first and then the auto loan (assuming the above numbers).
I have also heard of people intentionally attacking the debt with the lowest interest rate first. I think this may be because of a false understanding of how debt works and is generally not recommended. This doesn't mean you won't pay off debt with low rates or even a 0% rate but you are just not specifically prioritizing debt because it has a low rate.
In reality, you will likely use some combination of Snowball and Avalanche when paying down debt. For example, let's assume the following $300K mortgage at 6%, $15K credit card at 25%, $10K auto loan at 5%, and $1K medical loan at 2%. You may choose to just knock out the medical loan since the balance is so small (snowball method) and then move to the credit card because of the high rate (avalanche method) and then move to the auto loan since the balance is so much less than the mortgage and the rates are close (snowball method).
Regardless of what method you choose, having a plan for paying off and staying out of debt (particularly consumer debt) is paramount and can free up margin to spend on the other uses of money.
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