Minimum Payment Trap Calculator Formula

Understand the math behind the minimum payment trap calculator. Each variable explained with a worked example.

Use the Minimum Payment Trap Calculator

Formulas Used

First Minimum Payment

initial_minimum = first_min_payment

Months (Minimum Only)

months_minimum = monthly_rate > 0 ? (first_min_payment > balance * monthly_rate ? ceil(-log(1 - balance * monthly_rate / first_min_payment) / log(1 + monthly_rate)) : 999) : ceil(balance / first_min_payment)

Total Interest (Minimums)

total_interest_min = monthly_rate > 0 ? (first_min_payment > balance * monthly_rate ? first_min_payment * ceil(-log(1 - balance * monthly_rate / first_min_payment) / log(1 + monthly_rate)) - balance : balance * 10) : 0

Months (Double Minimum)

double_payment_months = monthly_rate > 0 ? (2 * first_min_payment > balance * monthly_rate ? ceil(-log(1 - balance * monthly_rate / (2 * first_min_payment)) / log(1 + monthly_rate)) : 999) : ceil(balance / (2 * first_min_payment))

Variables

VariableDescriptionDefault
balanceCredit Card Balance(USD)5000
aprAnnual Percentage Rate(%)22
min_pctMinimum Payment Percentage(%)2
min_floorMinimum Payment Floor(USD)25
monthly_rateDerived value= apr / 12 / 100calculated
first_min_paymentDerived value= max(balance * min_pct / 100, min_floor)calculated

How It Works

The Minimum Payment Trap

Credit card minimum payments are designed to maximize the interest the lender collects. They typically equal 1-3% of the balance or a flat floor (like $25), whichever is greater.

Why Minimums Are Dangerous

At 22% APR with 2% minimums:

  • Most of each payment goes to interest
  • The balance shrinks very slowly
  • A $5,000 balance can take 15+ years to pay off
  • You may pay more in interest than the original balance

    • The Fix

    Doubling your minimum payment can cut payoff time by more than half.

    Worked Example

    $5,000 balance at 22% APR, 2% minimum payment ($25 floor).

    balance = 5000apr = 22min_pct = 2min_floor = 25
    1. 01First minimum = max($5,000 x 2%, $25) = $100
    2. 02Monthly interest = $5,000 x 22%/12 = $92
    3. 03Only $8 goes to principal in month 1!
    4. 04At minimums only: ~199 months (16.6 years)
    5. 05Total interest: ~$14,900 (nearly 3x the balance)
    6. 06Doubling to $200: ~31 months, saving thousands

    Ready to run the numbers?

    Open Minimum Payment Trap Calculator