Debt Payoff Calculator: time to become debt-free

This calculator determines how long it will take to fully pay off a debt (credit card, personal loan) based on the current balance, interest rate and monthly payment you can make.

Payoff time formula

The number of months required is computed as:

n = −log(1 − r×P/PMT) / log(1+r)

Where P is the current balance, r is the monthly interest rate and PMT is the monthly payment. If PMT ≤ r×P, the debt will never be paid off (payment does not cover interest).

Example 1: credit card

Problem: Balance of $5,000 at 18% annual rate with $200 monthly payment.

1. Data:
   • P = 5,000; r = 0.18/12 = 0.015; PMT = 200.
2. Months:
   • n = −log(1 − 0.015×5000/200) / log(1.015) ≈ 32 months.
3. Total paid:
   • 32 × $200 = $6,400 (interest: $1,400).

Answer: 32 months (2 years and 8 months), total $6,400.

Example 2: accelerated payoff

Problem: Same $5,000 balance at 18% but with $350 monthly payment.

1. Months:
   • n = −log(1 − 0.015×5000/350) / log(1.015) ≈ 16 months.
2. Total paid:
   • 16 × $350 = $5,600 (interest: $600).

Answer: 16 months, total $5,600. Savings of $800 in interest.

Usos comuns

• Planning credit card debt elimination.
• Comparing the impact of different monthly payment amounts.
• Visualizing the real cost of interest over time.
• Deciding between paying debt or investing.
• Setting realistic debt-free goals.
• Evaluating whether debt consolidation is beneficial.

Common mistakes in debt payoff

• Paying only the minimum, which extends debt indefinitely.
• Not considering that the rate may be variable.
• Continuing to accumulate debt while paying existing debt.
• Not prioritizing debts with higher interest rates.

Dica profissional

The "avalanche" method (paying highest interest rate debt first) saves more money than the "snowball" method (paying smallest debt first). However, the psychological motivation of the snowball method should not be underestimated.