Debt Payoff Calculator (Months)
Solve the months to clear a debt at a fixed monthly payment: n = -ln(1 - r·balance / payment) / ln(1 + r), with r = monthly rate.
Input Data
Results
At a glance:n = -ln(1 - r·balance / payment) / ln(1 + r), r = monthly rate = annual/12. It is the inverse of the annuity PV formula. Example: 10,000 at 12%, pay 500/mo → ≈22.4 months. WARNING: if payment ≤ r·balance (monthly interest), debt never clears (tool returns 0). Simplified model; real terms differ. Education, not advice.
Formula
Monthly rate r = annual rate ÷ 12.
Months n = −ln(1 − r·balance / payment) ÷ ln(1 + r).
If payment ≤ r·balance, the debt never clears (returns 0).
$$r = \\dfrac{\\text{Annual rate}\\%}{12}\\quad(\\text{Monthly rate})$$How to Use
- Enter the debt balance and annual rate.
- Enter the fixed monthly payment.
- View the months to payoff (0 means it cannot be cleared).
FAQ
How is the payoff months computed?
It is the inverse of the annuity present-value formula. Each month, interest = balance x monthly rate; the rest of the payment cuts principal. The closed-form: n = -ln(1 - r·balance / payment) / ln(1 + r). Example: 10,000 at 12% (r=1%), pay 500 → ≈22.4 months, longer than the naive 20 months because interest is paid first.
Why can a too-low payment mean 'never paid off'?
If the payment ≤ monthly interest (r·balance), you never reduce principal — it may even grow (negative amortization). Mathematically the term inside ln goes ≥1 and is undefined; the tool returns 0 to flag 'cannot be cleared, raise the payment'. This is the minimum-payment trap.
How do I speed up payoff and save interest?
Pay more each month — extra above interest cuts principal faster, and as principal falls, later interest falls too, accelerating the payoff. Higher payments shorten the term and cut total interest disproportionately. Try several payment levels to plan.
Avalanche or snowball for multiple debts?
Avalanche: pay minimums on all, attack the highest APR first — mathematically least interest, fastest debt-free. Snowball: clear the smallest balance first for psychological wins, possibly paying a bit more interest. Both beat paying only minimums. Keep all minimums current and stop adding high-interest debt.
Why might my result differ from the statement?
This model assumes a fixed annual rate, monthly accrual, on-time full payments and no new spending. Real loans may use daily accrual, flat (flat rate) vs APR, plus fees/penalties, and early-repayment charges. Treat it as a planning estimate; the lender's schedule is final.
Related Tools
References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.