Avalanche vs. Snowball: The Real Arithmetic Behind Two Debt Payoff Methods

Two competing pieces of advice show up whenever someone asks how to pay off multiple debts faster: the avalanche method, which targets the highest interest rate first, and the snowball method, which targets the smallest balance first. Both are legitimate strategies and both have been argued over for years, usually in terms of psychology versus math. The psychology argument is easy to state — snowball delivers a quick win that keeps motivation up. The math argument is usually asserted rather than shown. Here it is shown, with one worked example carried through both methods.

The Debts

Suppose a household is carrying three balances:

Debt X: $1,200 balance, 26% APR, $35 minimum monthly payment. Debt Y: $3,000 balance, 12% APR, $70 minimum monthly payment. Debt Z: $900 balance, 9% APR, $40 minimum monthly payment.

Minimum payments total $145 a month. Suppose the household can direct an additional $155 a month beyond the minimums, for a total debt-payoff budget of $300 a month. The two methods only disagree on where that extra $155 goes first — every dollar not sent to the target debt still covers the minimums on the other two.

Where Each Method Points First

Avalanche ranks by interest rate, highest to lowest: Debt X (26%) is attacked first, then Debt Y (12%), then Debt Z (9%).

Snowball ranks by balance, smallest to largest: Debt Z ($900) is attacked first, then Debt X ($1,200), then Debt Y ($3,000).

Notice the two methods disagree on the very first target — avalanche goes after X, snowball goes after Z — which makes this a useful example, since in many real debt loads the smallest balance and the highest rate happen to be the same account, and the methods would agree without telling you much.

Running the Numbers on the First Target

For avalanche, the full extra payment goes to Debt X: $35 minimum plus $155 extra, or $190 a month, while Y and Z receive only their minimums. Using the standard loan amortization relationship — months to payoff n = −ln(1 − r·P / Pmt) / ln(1 + r), where P is the balance, Pmt is the monthly payment, and r is the monthly interest rate — plug in P = $1,200, r = 0.26 / 12 ≈ 0.021667, and Pmt = $190. The term r·P / Pmt works out to (0.021667 × 1,200) / 190 ≈ 0.1368. So 1 minus that is 0.8632, and −ln(0.8632) ≈ 0.1472. Dividing by ln(1.021667) ≈ 0.02143 gives n ≈ 6.87, so Debt X clears in about 7 months. Total paid over that span is roughly 190 × 6.87 ≈ $1,305, meaning about $105 of that was interest on a $1,200 balance — a real cost, but a contained one given the high rate, because the payoff was fast.

For snowball, the full extra payment instead goes to Debt Z: $40 minimum plus $155 extra, or $195 a month. With P = $900, r = 0.09 / 12 = 0.0075, and Pmt = $195: r·P / Pmt = (0.0075 × 900) / 195 ≈ 0.0346. 1 minus that is 0.9654, and −ln(0.9654) ≈ 0.0352. Dividing by ln(1.0075) ≈ 0.00747 gives n ≈ 4.72, so Debt Z clears in about 5 months — roughly two months sooner than avalanche's first payoff — with total interest of only about $19 on the $900 balance, since both the balance and the rate were lower.

What the Comparison Actually Shows

The snowball approach clears its first target in 5 months instead of 7, which is precisely the motivational case for it — a debt fully gone in under half a year is a concrete, visible win. But look at what each method left untouched during that stretch. Under avalanche, the $900 balance at 9% sat accumulating interest at a comparatively low rate while the 26% balance got eliminated first — the expensive debt was neutralized fastest. Under snowball, the $1,200 balance at 26% kept accruing at that high rate for an extra two months while the cheaper $900 balance was paid down first, meaning more total interest accumulates on the expensive debt before it is ever targeted.

This is the general pattern, not specific to these three numbers: avalanche minimizes total interest paid across the full payoff, because it always keeps the most expensive balance shrinking as fast as possible. Snowball can cost somewhat more in aggregate interest over the life of the full payoff, with the gap widening as the mismatch between balance size and interest rate grows larger across the debts involved. In this example, that mismatch was modest — a two-month difference in the first milestone and roughly a $75 to $100 difference in interest during that stretch — but with more debts, larger balances, or a bigger spread between the highest and lowest rate, the gap compounds further with each subsequent debt in the sequence.

Choosing Between Them Honestly

Neither method is wrong. Avalanche is the mathematically cheaper path whenever the numbers are run all the way through, but only if the household actually sticks with a plan that delays the first win. Snowball costs a bit more in total interest but front-loads the sense of progress that keeps some people paying more than the minimum in the first place — and a debt payoff plan that gets abandoned in month four because it felt like nothing was happening costs far more than any interest-rate spread. The honest recommendation is to run both orderings against your own actual balances and rates before choosing, so the decision is made with real numbers instead of a rule of thumb borrowed from someone else's debt load.