Debt Payoff & Snowball/Avalanche Formula

Finance Formula • Published on July 30, 2026 • Last updated July 30, 2026

Mathematical Equation

$$B_{t} = (B_{t-1} + B_{t-1} \cdot i) - (P_{\text{min}} + P_{\text{extra}} + P_{\text{rollover}})$$

Variable Definitions

B_t

Remaining debt principal balance at month t

i

Monthly interest rate (Annual APR / 12 / 100)

P_min

Mandatory monthly minimum payment for the debt

P_extra

Extra monthly payment pool allocated to priority target debt

P_rollover

Reallocated payments from previously cleared debts (Cascade)

Detailed Explanation

In-Depth Guide

Key Concept

The Debt Payoff Formula models the multi-debt elimination process using an amortization cascade. In every month t, interest accrues on outstanding loan balances.

Mandatory minimum payments are made across all debts, while all extra funds and rolled-over payments from paid-off debts are funneled toward a single priority target debt. The priority order is determined by either the Debt Avalanche (highest APR first) or Debt Snowball (smallest balance first) method.

How to Calculate: Step-by-Step

1. List all active debts with current balance ($B$), annual APR, and minimum monthly payment ($P_{\text{min}}$). 2. Order debts based on strategy: Debt Avalanche (descending APR) or Debt Snowball (ascending balance). 3. Calculate monthly interest for each active debt ($B \times i$). 4. Apply mandatory minimum payments to all debts. 5. Allocate the combined Extra Payment Pool ($P_{\text{extra}} + P_{\text{rollover}}$) to the top-ranked active debt. 6. When a debt reaches $0, add its minimum payment to $P_{\text{rollover}}$ for subsequent months.

Worked Calculation Example

Consider 2 debts with a $500/month extra payment pool under Debt Avalanche: - Debt A: $5,000 balance at 24% APR (Min $150) - Debt B: $15,000 balance at 10% APR (Min $350) Month 1: - Debt A Interest = $5,000 \times (0.24/12) = $100 - Debt A Payment = $150 (Min) + $500 (Extra) = $650 - Debt A New Balance = ($5,000 + $100) - $650 = $4,450 - Debt B Interest = $15,000 \times (0.10/12) = $125 - Debt B Payment = $350 (Min) - Debt B New Balance = ($15,000 + $125) - $350 = $14,775 Once Debt A is fully paid off, its $150 minimum rolls into the extra pool ($500 + $150 = $650/month) to accelerate clearing Debt B.

Common Use Cases

  • Multi-debt acceleration simulation
  • Comparing Debt Avalanche vs Debt Snowball interest savings
  • Evaluating debt rollover cascade benefits
  • Personal loan and credit card consolidation

Frequently Asked Questions

Debt Avalanche targets the debt with the highest APR first to minimize total interest paid. Debt Snowball targets the smallest balance first to build fast psychological wins.

When a debt is cleared, continuing to spend the same total monthly budget by redirecting that cleared payment to the next debt creates a snowballing cascade effect that eliminates debt years earlier.

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