3 different methods of paying off debt with fictional friends John and Jane

 John and Jane are a married couple in their late 30s who graduated at the top of their classes, John from med school, and Jane from law school. They now earn a combined total of $1,400,000 working as a neurosurgeon and corporate counsel. They have a $2,500,000 mortgage; $300,000 left to pay from law school, and $250,000 to pay off from med school. They can allocate up to $23,333.33 every month to pay off their debts, and they want to make some progress on all their debts each month, to avoid a situation where they owe much more than anticipated and are trapped in debt much longer because interest piled up.

               There are three commonly suggested methods for attacking debts like this. First, paying off exactly what the amortization schedule would require of them. These are the terms of  their 3 outstanding debts:

	Amount borrowed	Minimum payment	Interest Rate	Term (in years)
Mortgage on their penthouse	$2,500,000	$11087.03	3.4%	30
Her law school debt	$300,000	$3529.82	7.3%	10
His med school debt	$250,000	$2902.71	7%	10

The first method is to only pay the minimum payment dictated by the amortization schedule, in the third column of the table above. If they do this, they’ll be using only 74.88% of their available debt payoff budget to attack their debts. Everything counted together, they’ll still have some debt for 30 years and pay $4,763,158, counting all their principal and interest.
               The next method is to use their whole budget—so, pay an extra $5860 or so every month—and attack the debt with the smallest balance first. This is called the “snowball” method. It is known that the snowball method is not mathematically optimal, but several online personalities recommend it as psychologically optimal because it allows the debtor to have more frequent victories, thus staving off discouragement and giving the debtor a greater chance of paying off the debt sooner. In order to pay off their debts using this method, they will use their whole budget, and pay the minimums on the 2 debts that don’t have the lowest balance (her law school and their mortgage), and use the rest of their budget to attack, as much as possible, the debt with the lowest balance until it is paid off in full. Then, they’ll readjust by redefining which debt now has the lowest balance (his med school), pay the minimum on the other remaining debt (the mortgage),  and continue until that debt has been paid off in full. Finally, they’ll shift their whole budget to the last remaining debt, paying it off as aggressively as their budget allows, until it is paid in full. They will finish paying off their debts in 165 months as opposed to 360 (saving 16 years and 3 months), and they’ll have saved about $873,500 in interest.
               Finally, the mathematically optimal method is the “avalanche” method. All three of these methods will be summarized below. In this method, they will also use 100% of their available funds to pay off their debt as quickly as possible. But in contrast to the “snowball,” this “avalanche” method organizes the debts by the highest interest rate first and thus is mathematically optimal, even if not psychologically optimal. Economists typically assume that human beings are perfectly rational; a perfectly rational person would always pick this plan over either of the other plans presented above. The plan is, more or less the same, after the reorganization, as the snowball: order the debts, pay the minimum on anything that isn’t deemed the most critical (this time, we order by interest rate), pay out the rest of the budget on the most critical, and repeat until that most critical debt is gone. Then reorder and repeat until all debts are gone. Following this plan will save them about $876,000 and 16 years and 3 months as they pay off their debts. As you can see, the time and money savings are in fact greater, compared to the standard method, doing this than doing the snowball method.
               The snowball method is alluring—and is recommended by plenty of well-meaning people despite not being mathematically optimal, in the sense that it doesn’t take the shortest amount of time and pay the least amount of money—because it almost turns paying off debt into a game, with bosses to defeat and prizes to win at every level. The brain wants that dopamine hit of seeing “$0.00” on their screen when logging into wherever their debt is being serviced, and the rewards it gives itself for accomplishing a smaller goal sooner, so many people do choose to use it.
                Here, we can see the three methods condensed into a single chart for easy comparison.

	Total	Interest	Months	Difference vs. Trad	Time savings in years
Traditional	$4,763,165.00	$1,713,235.00	360	$                0	0
Snowball	$3,889,657.00	$    839,665.00	165	$873,508.00	16.25
Avalanche	$3,887,346.00	$    837,460.00	165	$875,819.00	16.25

Ultimately, the choice of which plan to use is that of the debtor and depends on whether the debtor can afford to throw more than the minimums  at their outstanding debts, and whether they think they’ll need frequent emotional gratification or that they have enough self-discipline to do something slightly more optimal (The degree to which this is more optimal increases as interest rates and balances increase.)