Debt payoff calculator: avalanche vs snowball

How the formula works

There is no closed form here — the calculator runs your debts forward a month at a time, twice, from the same inputs. Each month every open debt accrues interest at its monthly rate

and receives its minimum payment, which keeps every account current. Everything you can pay beyond the minimums is concentrated on one target debt. Your total outlay never falls: when a debt is cleared, its minimum is not pocketed but rolls into the attack on the next target, so each month you pay

where \(x\) is the extra and the \(m_k\) are all the original minimums — the payments freed by finished debts simply change address. The two methods differ in exactly one line of the simulation: which debt is the target. The avalanche attacks the highest APR outstanding; the snowball attacks the smallest current balance outstanding. Everything else — the interest accrual, the minimums, the rolling — is identical.

That one line is why the avalanche can never pay more interest than the snowball. Every flexible dollar retires balance that would otherwise accrue at some rate \(i_k\) each month from now on; sending it to the highest rate cancels the most future interest per dollar, every month. The snowball spends the same dollars in a different order, so its interest total is mathematically greater than or equal to the avalanche's. The difference is often smaller than people expect, though: the minimums do most of the work regardless of order, and the flexible money only decides the sequence of a payoff whose total monthly firepower is fixed.

What each input means

Balance (each debt)

What you owe on that account today. A row with a balance of 0 is ignored — enter one, two, three or four debts. The model assumes no new borrowing on any of them.

APR (each debt)

The interest rate on that account, converted to a monthly rate of APR/12. This is what the avalanche sorts by: the rate is the price per dollar per month of leaving that balance alone.

Minimum payment (each debt)

The required monthly payment, held constant for the whole payoff. Real card minimums shrink as the balance falls; holding them constant means the model retires debt slightly faster than a strict minimum-only reality would.

Extra each month

What you can pay beyond the sum of the minimums. This is the money the two methods argue about — it all lands on the target debt, and it grows as cleared debts hand over their minimums.

A worked example

The worksheet's defaults: a $4,500 credit card at 22% (minimum $90), a $9,000 car loan at 7% ($250), a $12,000 student loan at 5.5% ($150) and a $2,000 personal loan at 11% ($60) — $27,500 owed in all — plus $200 extra a month. Total outlay: $750 a month, comfortably above the $208 of interest the four balances accrue in the first month, so the debt actually falls.

• The avalanche sorts by APR and clears the debts in the order credit card → personal loan → car loan → student loan — the credit card first, gone in month 19. Debt-free in 42 months (3.5 years) with $3,832 of interest.
• The snowball sorts by balance and clears them in the order personal loan → credit card → car loan → student loan — the personal loan first, gone in month 9. Debt-free in 43 months (3.6 years) with $4,117 of interest.
• The difference: $286 of extra interest on the snowball route, over roughly 3.6 years. Real money — and small next to the $27,500 being repaid.

Which is the honest conclusion of the whole comparison: the method that matters is the one you finish. If crossing the personal loan off the list in month 9 keeps you paying $750 a month for 3.6 years, the snowball's $286 is cheap. The order of attack is worth far less than the attack itself.

Assumptions and limits

• Every APR is fixed for the whole payoff, and no new borrowing lands on any account. A promotional rate expiring, or fresh charges on a card, change the arithmetic.
• Minimum payments are held constant at today's amount. Real card minimums shrink with the balance, so against a strict minimum-only reality this flatters the timeline slightly — and understates what minimums alone would cost.
• Every payment lands on schedule. Late fees and penalty APRs are not modeled.
• If the minimums plus the extra do not cover the first month's interest, the balance grows forever and the calculator says never. Payoffs longer than 100 years are treated the same way.
• This is arithmetic, not advice — it prices the two orders of attack and nothing else about your situation.

Questions people ask

Which method saves more money?

The avalanche, always — by construction it can never pay more interest than the snowball, because every flexible dollar goes to the balance charging the most per dollar per month. On the worksheet's default four debts the gap is $286 of interest over roughly 3.6 years. Run your own numbers: the wider the spread between your highest and lowest APRs, and the bigger the balance at the top rate, the more the avalanche is worth.

Which should I actually pick?

The one you will finish. The snowball's quick wins — a whole account closed in a few months — are exactly what keeps many people paying the extra month after month, and abandoning the plan halfway costs far more than any ordering ever saves. If you are motivated by the math, take the avalanche and keep the savings; if you are motivated by crossing debts off a list, the snowball's premium is usually a cheap price for actually getting there.

What about consolidation or a balance transfer?

They change the inputs rather than the method: a consolidation loan replaces several APRs with one (hopefully lower) rate, and a 0% balance-transfer card parks a balance rent-free for 12–21 months in exchange for a 3–5% fee. Both can genuinely shrink the interest bill — compare the fee and the new rate against what this calculator shows for your current debts. The trap is consolidating, feeling lighter, and borrowing the freed-up cards back up. The debt moved; it did not leave.

Should I stop investing to pay debt down faster?

Not all of it. An employer 401(k) match is an instant return no debt payoff can beat — take the full match before throwing extra at any balance. Beyond that, compare rates: extra payments on a 22% card are a guaranteed 22% return, better than any market's expected return, while a 5.5% student loan loses that comparison for many investors. High-rate debt first, the match always, the low-rate middle ground a judgment call.

What happens when a debt is paid off?

Its minimum payment does not disappear — it rolls into the attack on the next target, which is the engine of both methods. In the default scenario the total outlay stays $750 a month from first month to last; as each account closes, its minimum changes address and the target debt takes ever-bigger hits. That is why the payoff accelerates toward the end instead of dragging.