When it comes to mathematics, certain facts are universally agreed-upon. For example, regardless of your culture or educational system, you must agree that one plus one equals two unless you mistakenly fall for an invalid proof. When dealing with money, why are people inclined to believe that one plus one does not equal two?

If you have a certain amount of money available to pay off a portion of your debt each month, even if that certain amount changes, there is a mathematically correct way of paying off that debt. You can call this approach the Debt Avalanche. It is similar to Dave Ramsey’s popular “debt snowball” method, with one small but important detail: With the Debt Avalanche you will pay off your debt faster and pay less total interest to banks and lenders.

The simple calculation for the Debt Avalanche requires only the interest rates for each debt account. This assumes that all debt accounts have the same tax liability, but if that’s not the case, determine your interest rate after taxes for this calculation.

Step 1. Order your debts from highest interest rate to lowest. You may find credit cards at the top of the list. It’s typical to see interest rates from 10% to 20% or more. Credit cards offered by stores often have the highest interest rates, so you might find these at the very top. Watch out for promotional rates ending, which they may do on the date promised when you enrolled, or earlier. Card issuers also re-evaluate their customers every so often, and will not think twice about raising your rates midstream. Note that if your credit improves, they will not magically lower your rates. While lenders will notify you if they intend to raise your rates, you may have missed the notice.

Your mortgage and home equity loan may be the next debts in line. It’s important for your list to capture every debt for which you make a monthly payment. Student loans may be the last on the list, particularly if you qualify for tax credits. The Debt Avalanche formula won’t work properly if it covers only a portion of your debt, so consider all accounts.

Order your list from the highest interest rate (after tax) to the lowest. You may have noticed we didn’t factor in your account balances in the above formula. That is because your individual account balances are irrelevant. The issue solved by the Debt Avalanche is the best way to pay off your total debt with all available funds.

Step 2. Pay the minimum to all debts every month. If you’re writing down your list, or using a spreadsheet like Excel, add a column next to each debt to list its minimum monthly payment. This is the amount you will pay towards each debt, except for the one account listed at the top of the list.

Another column should list the payment due date if it is relatively static from month to month. For example, my credit card payment is due on the last date of almost every month, so I would write “30.” This would indicate to me the last date of every month. Your payments should always arrive before the due date. In fact, in some cases, you can reduce your total interest paid by paying weeks in advance of your due date.

Step 3. To your debt with the highest interest, send all extra available cash. If you have an emergency fund, this step is simple. Since it’s unlikely that you can earn more in savings than you can “earn” (reclaim) by paying off your debt, all your unused income after paying expenses (necessary and discretionary as you see fit) should be dedicated towards the debt account with the highest interest rate.

Step 4. Repeat every month. You cover all your bases by ensuring every creditor receives the minimum payment, but you hone in on only your debt with the highest interest. Once a debt account has been eliminated — and it may not be the account at the top of the list if other balances are smaller — remove it from the list and re-order if interest rates have changed.

It’s that simple. This is mathematically the best method for paying off your personal debt. No other method will get you out of debt faster and save you as much money.

Despite the facts, many people disagree. The primary reason detractors, or supporters of the “debt snowball” method, may argue is that Dave Ramsey’s method will help you pay off your smaller debt faster, providing you with “early success” and possibly the motivation to continue along the path of debt reduction. The Debt Avalanche will also provide early success, but if you need special motivation to continue your monthly payments, consider this: By choosing the Debt Avalanche method, you will pay off your total debt faster, you will pay less interest, and you are mathematically efficient.

That is motivation enough. Or is it?

Dave Ramsey believes his “debt snowball” method, in which debts are paid off in the order of balance from lowest to highest, has shown better results than any other method thanks to “quick wins.” If he were to ask his followers if they want to carry their debt longer and pay more interest throughout before offering the “debt snowball” method, they would choose the faster, cheaper, better option of the Debt Avalanche.

One of the many reasons people can fall into debt is the difficulty of separating emotional thinking from rational thinking. The Debt Avalanche helps separate these two methods of thinking, as the best financial decisions are almost always the rational decisions. But it helps to pay attention to some of the psychology involved, as well.

The possible motivation due to the “early success” aspect of the debt snowball method is cited by many followers to be its strongest point, encouraging debt reducers to continue down the path. Followers of the mathematically and financially superior Debt Avalanche, if they need this sort of motivation, can achieve the same effect by defining milestones.

Rather than “celebrating” when your first full credit card or other debt account is paid off, take note and reward yourself when you’ve paid off your first $1,000 (or $500 or $10,000, whatever is applicable to you). Setting and achieving these short term goals influences the same area of the brain (the mesolimbic system) as the act of paying off the first credit card and are similar enough to provide the same motivational results.

Quick wins may help to motivate debt reducers to continue along the path, but the real win comes in knowing you’ve made the smarter choice.

Updated on July 8, 2008 with more information about redefining milestones to address the psychological effect of “quick wins.”

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