Consumer debt / payoff sequencing

Debt snowball vs avalanche

Run the same monthly budget against two payoff orders — smallest balance first, or highest rate first — and see exactly what the motivational strategy costs in interest and months.

CheapestAvalancheExtra / month$300.00Blended rate13.95%

Snowball interest

$7,343

52 months to debt-free

Avalanche interest

$6,601

51 months to debt-free

Avalanche saves

$742.81

Interest advantage of highest-rate-first

Months difference

1 mo

How much sooner the cheaper strategy finishes

Debt inventory and payoff order

Each balance with its rate, minimum payment, and the month it clears under each strategy.

$30,500 total

Debt inventory and payoff order
Debt	Balance	Rate	Min payment	Snowball clears	Avalanche clears
Card A	$4,200	18.90%	$150.15	Month 13	Month 30
Card B	$8,600	22.90%	$336.12	Month 39	Month 23
Car loan	$11,400	6.90%	$293.55	Month 52	Month 51
Personal loan	$6,300	11.20%	$184.80	Month 26	Month 39

Minimum payments include accrued interest plus the greater of $25 or 2% of the balance — a common revolving-credit model.

Total balance under each strategy

The two payoff orders converge only at the very end — the interest gap accumulates quietly.

Interest paid by debt

Where the interest actually accrues under each order.

Canonical equations

The exact relationships implemented by this engine.

min = B·r/12 + max(25, 0.02·B) · interest plus a revolving-credit principal floor

B ← B + B·r/12 − min · interest is charged before the payment lands

argmin Bᵢ · smallest balance first, for momentum

argmax rᵢ · highest rate first, for minimum interest

Show model notation and computationOpen the symbolic form, the variable definitions, and the step-by-step derivation when you need the detail.

A clear path from inputs to results.

Two payoff orders, one budget. Snowball clears the smallest balance first for momentum; avalanche clears the highest rate first for minimum interest. This engine runs both month by month on the same money and reports the exact cost of choosing the motivational strategy.

Step-by-step methodWorked exampleAssumptions explained

How to use

Enter the balance and rate for each of your four debts.

Set the extra amount you can put toward debt each month.

Read the payoff order each strategy produces — they are listed explicitly.

Compare total interest and months to debt-free.

Watch the balance curves: they separate slowly, then converge only at the end.

Choose avalanche if the interest gap matters; choose snowball if early wins keep you paying.

The formula

B_i \leftarrow B_i\left(1 + \frac{r_i}{12}\right) - \min_i, \qquad \text{pool} = \text{extra} + \sum_{\text{cleared}} \min_i, \qquad \text{snowball}: \arg\min B_i, \quad \text{avalanche}: \arg\max r_i

Reference: Consumer debt-rollover simulation with minimum-payment conventions for revolving credit (Broverman, Mathematics of Investment and Credit).

Worked example

Four debts, $300 extra per month (default inputs)

Inputs

Card A $4,200 at 18.9%; Card B $8,600 at 22.9%.
Car loan $11,400 at 6.9%; personal loan $6,300 at 11.2%.
Extra payment $300 per month; minimums are the greater of $25 or 2% of the balance.

Calculation path

1
Snowball order: Card A ($4,200) → personal loan ($6,300) → Card B ($8,600) → car loan ($11,400).
2
Avalanche order: Card B (22.9%) → Card A (18.9%) → personal loan (11.2%) → car loan (6.9%).
3
Each month, every live debt accrues interest and receives its minimum; the pool of extra money plus freed minimums attacks the target.
4
Avalanche pays less total interest because the most expensive balance disappears first.
5
The gap is real but usually modest — a few hundred dollars on a $30,500 debt stack.

Result

Both strategies clear the same $30,500; avalanche costs less interest and finishes sooner, snowball delivers the first cleared balance earlier.

Interpreting the result

The arithmetic always favours avalanche. The case for snowball is behavioural: clearing a whole account early produces a visible win, and people who quit a payoff plan pay far more interest than the theoretical gap. The honest framing is that snowball buys motivation at a measurable price — this engine tells you what that price is.

Assumptions & limitations

Minimum payments are modelled at the greater of $25 or 2% of the balance, which approximates revolving-credit terms.

Rates are fixed. A promotional 0% period that expires needs a separate scenario.

No new borrowing is added during the payoff period.

The extra payment is constant; a rising payment would shorten both strategies.

Payments are applied monthly in a fixed order: minimums first, then the pool to the target.

Frequently asked questions

Which is mathematically better?

Avalanche, always. Paying the highest rate first minimises the interest paid for any given total budget. There is no set of rates and balances where snowball wins on interest.

How much does snowball actually cost?

It depends on how different the rates are. When all debts carry similar rates, the gap is negligible. When one card is at 29% and another at 5%, avalanche wins decisively.

What if I can only afford the minimums?

Then both strategies are identical — the pool is zero, so no target receives extra money. The plan only starts working when there is surplus to direct.

Then why does anyone use snowball?

Because debt payoff is a behaviour problem more than a maths problem. Clearing an account completely gives a psychological reward that keeps people in the plan. A slightly higher interest cost is worth it if the alternative is abandoning the plan.

Should I include my mortgage?

Usually not. A mortgage is secured, long-term and low-rate; rolling it into a consumer debt payoff plan distorts both the timeline and the risk. Pay off revolving debt first.

Does consolidating beat both?

Only if the consolidation rate is below the weighted average of your current rates and you do not run the cards back up. A consolidation loan that leaves the cards open often ends with both balances.