Debt Snowball Calculator Formula

Understand the math behind the debt snowball calculator. Each variable explained with a worked example.

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Formulas Used

Months to Pay Off

months_to_payoff = monthly_rate > 0 ? (monthly_payment > total_debt * monthly_rate ? ceil(-log(1 - total_debt * monthly_rate / monthly_payment) / log(1 + monthly_rate)) : 999) : ceil(total_debt / monthly_payment)

Total Interest Paid

total_interest = monthly_rate > 0 ? (monthly_payment > total_debt * monthly_rate ? monthly_payment * ceil(-log(1 - total_debt * monthly_rate / monthly_payment) / log(1 + monthly_rate)) - total_debt : total_debt * 10) : 0

First Debt Paid Off (Approx)

first_win_months = monthly_rate > 0 ? round(ceil(-log(1 - total_debt * monthly_rate / monthly_payment) / log(1 + monthly_rate)) / num_debts * 0.3) : round(total_debt / monthly_payment / num_debts * 0.3)

Variables

VariableDescriptionDefault
total_debtTotal Debt Balance(USD)30000
avg_rateWeighted Average Interest Rate(%)15
monthly_paymentTotal Monthly Payment(USD)800
num_debtsNumber of Separate Debts5
monthly_rateDerived value= avg_rate / 12 / 100calculated

How It Works

Debt Snowball Method

Popularized by Dave Ramsey, the snowball method pays off debts from smallest balance to largest.

How It Works

1. List debts from smallest to largest balance 2. Make minimum payments on everything 3. Throw all extra money at the smallest debt 4. When the smallest is gone, roll that payment into the next 5. The payment amount "snowballs" as each debt is eliminated

Why It Works Psychologically

Quick wins provide motivation. Seeing debts disappear early keeps you committed to the plan.

Worked Example

$30,000 total debt across 5 accounts at 15% average, paying $800/month.

total_debt = 30000avg_rate = 15monthly_payment = 800num_debts = 5
  1. 01Monthly rate = 15% / 12 = 1.25%
  2. 02Months to payoff = -ln(1 - $30,000 x 0.0125 / $800) / ln(1.0125) = 49 months
  3. 03Total paid = $800 x 49 = $39,200
  4. 04Total interest = $39,200 - $30,000 = $9,200
  5. 05First small debt paid off in approximately 3 months

Ready to run the numbers?

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