Debt Payoff Calculator

The Debt Payoff Calculator computes debt payoff from the relation months = minus log(1 minus (monthly rate x balance) over payment) divided by log(1 plus monthly rate). It takes 3 inputs (current balance in USD, annual interest rate in %, monthly payment in USD) and returns the debt payoff. Because this is a pure mathematical or physical formula rather than a jurisdiction-specific rule, the result never changes over time: the same inputs always produce the same answer, so you can rely on it whether you are checking homework, sizing a design, or sanity-checking another tool. Enter your values in the fields below and the result updates instantly; you can also share a permalink that pre-fills the exact calculation, which is useful for teaching, reports, or collaboration. For example, with current balance = 5000 USD, annual interest rate = 12 %, monthly payment = 200 USD, the debt payoff works out to 28.91181, and the worked example further down the page shows every step so you can follow the arithmetic and reproduce it by hand. The method is the standard form documented by CalculatorHub methodology, and the figure above each result carries the date it was last verified. This tool is general information and is not a substitute for professional engineering, medical, financial, or scientific advice; always check critical results against the primary source and your own judgement.

With Current balance = 5000 USD, Annual interest rate = 12 %, Monthly payment = 200 USD, the result is 28.91181.

Formula: months = minus log(1 minus (monthly rate x balance) over payment) divided by log(1 plus monthly rate). Source: CalculatorHub methodology, as at 2026-06-23.

Debt Payoff28.91181

Applies to: any numeric inputs. Method source: CalculatorHub methodology, checked 2026-06-23.

The formula

months = minus log(1 minus (monthly rate x balance) over payment) divided by log(1 plus monthly rate)

Worked example

With Current balance = 5000 USD, Annual interest rate = 12 %, Monthly payment = 200 USD:

  1. Monthly rate = 12 / 100 / 12 = 0.01
  2. Apply the amortisation payoff formula with balance 5000 and payment 200
  3. Months to pay off = 28.9118097374808
  4. Debt Payoff = 28.91181

This worked example is one of the automated golden-value tests this calculator must pass before it can publish.

What this assumes

  • Inputs are real numbers in the units shown.
  • The result is the exact value of months = minus log(1 minus (monthly rate x balance) over payment) divided by log(1 plus monthly rate); general information, not professional advice.

Frequently asked questions

What formula does this use?

months = minus log(1 minus (monthly rate x balance) over payment) divided by log(1 plus monthly rate), the standard form documented by CalculatorHub methodology.

Does the result ever change over time?

No. This is a pure formula with no external rate, so the same inputs always give the same result.

Official sources and verification

Reviewed by the CalculatorHub team, edited by James Graham, 2026-06-23. See our methodology. General information, not professional advice.