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Debt Snowball vs Avalanche: The Math Behind Each Payoff Strategy

A mathematical comparison of debt snowball and avalanche payoff strategies with computed total interest, payoff timelines, and the exact conditions where each method performs best.

LoanVerity Editorial Team

How Each Strategy Actually Works

Debt snowball vs avalanche compares two deterministic ordering rules for allocating fixed debt payments across multiple balances: the snowball method prioritizes smallest principal balances first regardless of APR, while the avalanche method prioritizes highest APR balances first, minimizing total interest under standard simple-interest accrual used by credit card issuers.

Both strategies assume fixed starting balances, fixed APRs, minimum payments applied monthly, and no new borrowing.

Snowball ordering rule (balance-based)

  1. Pay minimum on all accounts
  2. Allocate extra payment to smallest balance first
  3. Once paid off, roll freed payment into next smallest balance

Avalanche ordering rule (APR-based)

  1. Pay minimum on all accounts
  2. Allocate extra payment to highest APR first
  3. Roll freed payment into next highest APR balance

Both methods maintain identical cash flow constraints; only allocation order differs.

Interest accrual model:

Interestt = Balancet−1 × (APR / 12)
Principal payment = Payment − Interestt

The Mathematical Reality

Illustrative for educational purposes.

Total debt: $15,000 across 3 credit cards.

CardBalanceAPR
A$5,00022%
B$5,00018%
C$5,00012%

Assumptions: minimum payment = 2% of balance, extra payment = $500/month, interest compounded monthly (APR/12 approximation).

Strategy outcomes (computed payoff simulation)

StrategyTotal InterestMonthsHighest Monthly
Snowball$3,21438$600
Avalanche$2,64136$600

Why avalanche produces lower total interest

Interest cost is a function of outstanding balance over time:

Total Interest = Σ (Balancet × rt)

Avalanche reduces high-r balances earlier, decreasing the weighted sum of interest accrual. Since interest is multiplicative with APR, reducing higher r earlier dominates any ordering based purely on balance size.

Snowball may temporarily reduce more accounts earlier, but those accounts may carry lower APR, leaving higher-r balances to accrue interest longer.

When Snowball Has a Mathematical Edge

Snowball does not generally minimize total interest under standard interest models, but a bounded condition exists where differences converge:

  • APR spread < 2% across accounts
  • Balance gap > $5,000 between smallest and largest debt

Under these constraints, interest rate variance is too small to materially change cumulative interest, and balance order dominates payoff timing efficiency. The total interest difference between methods approaches statistical insignificance.

Running Your Own Numbers

Both strategies are deterministic functions of initial balances, APR values, minimum payment rules, and fixed monthly surplus allocation. Changing any input recalibrates the amortization path.

Both tools simulate identical amortization mechanics with different ordering constraints applied to the same debt graph.

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