Debt snowball vs avalanche: the numbers

Both methods start in the same place: a list of what you owe, and one monthly figure you can put against it. Both pay the minimum on every debt. Both send everything left over to exactly one debt at a time. Both take the payment freed when a debt clears and add it to the next one, so the amount attacking the pile never shrinks. That rolling payment is what the word snowball describes, and the avalanche rolls it in exactly the same way.

The methods disagree about one thing only, which debt goes first.

• Debt avalanche. Sort by interest rate, highest first. Balances are ignored.
• Debt snowball. Sort by balance, smallest first. Rates are ignored.

When the smallest balance also carries the highest rate both methods point at the same debt, and with only two debts that settles it. With three or more it settles only the first move: the second-smallest balance and the second-highest rate need not be the same debt, so two lists that agree at the top can still part company below it. The question is sharpest when a small balance at a low rate sits in front of a large balance at a high rate, which is the pair worked through on this page:

The budget is $500 a month, held steady until both cards are clear, with nothing new charged to either. Take the $138 of interest out of that and $362 comes off the balances in month one, whichever order you pick. The avalanche starts on the rewards card. The snowball starts on the credit union card. Everything below comes out of that single difference.

Interest is charged on each balance at that balance's own rate, so what a month costs depends on where the money is sitting and not only on how much of it there is. Write the interest charged in month $t$ as:

$$I_t = \sum_i b_{i,t} \times \frac{r_i}{12}$$

Here $b_{i,t}$ is each balance and $r_i$ is the annual rate charged on it. With a fixed monthly budget $M$, what you owe in total moves like this:

$$B_{t+1} = B_t + I_t - M$$

$M$ is set by you and $B_t$ is whatever last month left behind, so $I_t$ is the only term the ordering decision can touch. The way to make it smaller is to hold less money at high rates, which means clearing high rates first.

That is the whole argument. Move a dollar of repayment off a 12 percent balance and onto a 24 percent balance and you save the difference between the two rates on that dollar, in every month that is left. Do it with every spare dollar and you have the avalanche. It is not a preference: with the same budget, the same minimum payments and the same compounding, no order clears the same debts for less interest, and none clears them sooner.

Three conditions sit under that result. The rates have to be comparable, which means the same kind of quoted number. A United States card APR is a nominal annual rate, twelve times the monthly periodic rate, and that is the convention every figure on this page uses. In the United Kingdom and the European Union the advertised APR on a card is an effective annual rate instead, with the compounding already inside it, so it is a larger number than the United States convention would give for the same monthly charge and the two cannot be ranked against each other directly. The second condition is that no fee or promotional rate is about to expire. The third is that every minimum is met either way. Break one of those and the exception decides the order, not the rates.

In both runs the waiting card is held exactly still: it receives a payment equal to that month's interest, so its balance neither rises nor falls, and every spare dollar goes to the target. Real card minimums in the United States are usually a small percentage of the balance plus that month's interest, with a floor underneath, so they take a little principal off the waiting card as well. That does not move the two runs the same way. It helps the snowball, whose waiting card is the expensive one and is now being paid down rather than held flat, and it costs the avalanche, which is forced to put money into the cheap card instead of the dear one. On this pair a minimum of one percent of the balance plus interest narrows the gap by roughly a tenth. The order of the two answers does not change; the margin between them gets a little smaller.

Avalanche, rewards card first

Snowball, credit union card first

Stage 2 opens on an odd number in both tables because the last payment of stage 1 is a short one, and what is left of it rolls onto the other card in that same month.

The honest summary is that the avalanche saves $296.37 and both runs finish in month 19. That is 23 percent of the avalanche's interest bill, 3 percent of everything handed over, and about two and a half months of what the rewards card charges in interest at the start. Which of those framings is the fair one is a question about you rather than about the arithmetic.

The gap is not a fixed property of the two methods. It is set by how far apart the rates are, how much money the snowball parks in front of the expensive debt, and how long it parks it there. Hold the two balances and the $500 budget from above, keep the large card at 24 percent, and move only the small card's rate:

The top row is the check on the whole idea: when both debts charge the same rate, the two methods cost exactly the same, because the order of identical rates cannot change $I_t$. Everything below it is the price of the delay.

Balance size moves it as hard as the rate does. Shrink the smaller card to a sixth of the balance used here and the snowball's extra cost falls to about 5 percent, because the expensive card waits only a month or two. Raise it to two and a half times that balance and the extra passes 40 percent.

Two things it barely moves. Finish dates stay close: across every row above the two orders end within a month of each other, so the difference shows up as money rather than as time. And the budget matters more than the order does. Lifting the monthly payment by 40 percent cuts the avalanche's interest bill by about 31 percent in this same pair, more than the entire distance between the two methods.

The case for the snowball was never that it is cheaper. It is that a plan you finish beats a plan you abandon, and that closing an account is the clearest evidence of progress a repayment plan can produce.

There is evidence behind that, and it is worth being exact about what kind. Consumer research on real repayment records has found that the number of accounts a person closes, rather than the amount of money repaid, predicts whether they clear the whole debt. That is an association in observed behaviour, not a demonstration that choosing the snowball causes anyone to finish: people who close accounts early may differ from people who do not in ways the records cannot show. Separate experimental work, where the repayment order was assigned rather than chosen, found that concentrating on one account instead of spreading payments across several raised the sense of progress and the willingness to keep going, which is closer to a causal claim but sits in a laboratory rather than in a household budget. The findings are not unanimous and the size of the effect is argued over. None of them says the snowball costs less. What they say is that persistence is not something to assume.

Set the numbers against that. Under the snowball the credit union card is gone in month 5. Under the avalanche the same card is still open in month 18 and clears in month 19, and the first thing to close is the rewards card in month 15. That card closes fourteen months earlier under the snowball, but the two runs differ in the number of open accounts for only ten of the nineteen months, because from month 16 the avalanche is down to one account as well. So the snowball is buying ten months of one fewer open account, at $296.37.

Most of what the research points at is available either way. Concentrating everything spare on one debt is common to both methods, and so is watching the target balance drop faster every month as freed payments roll in. What only the snowball delivers is the account closing early.

The two ideas can also be mixed, and the tables above price the mixture. Sorting by rate while letting a genuinely small balance jump the queue is cheap when clearing it takes a month or two: shrinking the smaller card to a sixth of the balance used here left the snowball only about 5 percent dearer. Where the rates sit within a point or two of each other the arithmetic barely separates the orders at this size of debt, though the same one or two points on balances ten times larger, cleared with a budget ten times larger, produce a bill ten times larger. What the arithmetic cannot settle is how much an early closed account is worth to the person making the payments, and that is the part of this decision that is not arithmetic at all.

The choice between the two orders is the last decision in this sequence, not the first.

• Every minimum, every month. A missed payment in the United States can trigger a late fee and a penalty rate, and once it is 30 days late it can be reported to the credit bureaus, where a delinquency can sit on the file for years and weigh on credit scoring the whole time. Any one of those can cost more than the whole distance between the two methods.
• The rate itself, before the order. In $I_t$ the rate is the multiplier and the ordering only decides which balance meets it. A promotional balance transfer rate or a consolidation loan changes $r_i$ directly, which is a larger lever than the sequence. Whether it helps turns on the transfer fee, the length of the promotional window, the rate waiting at the end of it and, for a consolidation loan, the term: a lower rate stretched over enough extra months can still cost more in total than the debts it replaced. Those sit in the offer terms rather than in the arithmetic here.
• Deadlines beat rates. A deferred interest promotion, common on United States store cards, waives accrued interest only if the balance clears inside the window and bills all of it at once if the window closes first. That date decides the order on its own.
• Debts with consequences other than interest. Secured borrowing where an asset can be repossessed, tax debt, and anything close to collections are ranked by what happens if they go unpaid, not by rate.
• The size of the payment. More money against the debt beats a better order for that money almost every time, which is what the credit card payoff calculator above is for.

Only once those are settled does the ordering question this page is about become the live one, and on cost the arithmetic points one way. The loan payment calculator covers any debt in the list that already has a fixed term.