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Debt Payoff Calculator

Computes how many months a fixed monthly payment takes to clear a balance charged a given APR with monthly compounding, plus the total interest paid and the size of the final payment.

When to use

You know a credit-card, loan or other balance, its APR and what you can pay each month, and want the payoff date and interest cost.

Do not use when: You know the term and need the required payment (use loan-payment), or the payment is a percentage of the balance that shrinks over time (minimum-payment schedules).

Formula

i = annual_rate_percent / 1200. Each month: interest = balance × i; balance = balance + interest − payment (last payment = remaining balance + interest). Closed form: months = −ln(1 − i × balance / monthly_payment) / ln(1 + i), rounded up.

Month-by-month simulation with interest charged on the remaining balance and the payment applied at month end, matching the standard amortization formula; no fees, rate changes or new charges are assumed.

Inputs

Parameter	Type	Unit	Required	Description
`balance`	number		yes	Amount owed today. Range: > 0, ≤ 1000000000000
`annual_rate_percent`	number	%	yes	Annual percentage rate in percent; interest accrues monthly at APR / 12. Range: ≥ 0, ≤ 200
`monthly_payment`	number		yes	Fixed amount paid at the end of each month. Must exceed the first month's interest (balance × APR / 1200). Range: > 0, ≤ 1000000000000

Outputs

Output	Type	Unit	Description
`months_to_payoff`	integer	months	Number of monthly payments including the smaller final one.
`payoff_time`	string		months_to_payoff expressed in years and months.
`months_to_payoff_exact`	number	months	−ln(1 − i·balance/payment) / ln(1 + i), the unrounded annuity solution.
`total_paid`	number		balance + total_interest.
`total_interest`	number		Sum of the monthly interest charges until payoff.
`final_payment`	number		The last, usually smaller, payment that clears the balance.
`first_month_interest`	number		balance × APR / 1200, the minimum a payment must exceed.

Example

5,000 at 18 % APR, 200 per month: {"balance":5000,"annual_rate_percent":18,"monthly_payment":200} → {"months_to_payoff":32,"payoff_time":"2 years 8 months","months_to_payoff_exact":31.57,"total_paid":6313.96,"total_interest":1313.96,"final_payment":113.96,"first_month_interest":75}

2,000 at 24 % APR, 50 per month: {"balance":2000,"annual_rate_percent":24,"monthly_payment":50} → {"months_to_payoff":82,"payoff_time":"6 years 10 months","total_interest":2063.8,"first_month_interest":40}

GET https://tttkmbb.com/api/v1/calculate/debt-payoff?balance=5000&annual_rate_percent=18&monthly_payment=200

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/debt-payoff (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/debt-payoff · Markdown: https://tttkmbb.com/finance/debt-payoff.md · JSON definition: https://tttkmbb.com/finance/debt-payoff.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="debt-payoff"
OpenAPI operationId: calculate_debt_payoff
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Federal Reserve – Credit Card Repayment Calculator (government)
CFPB – Credit cards: paying down balances (government)
Wikipedia – Amortization calculator (annuity payment formula) (reference)

FAQ

What happens if my payment is too small?

If the payment does not exceed the first month's interest the balance never falls; the calculator returns an error stating the minimum payment and a payment that clears the debt in 5 years.

How much does paying extra help?

Re-run with the higher payment: on 5,000 at 18 %, raising the payment from 200 to 300 cuts the time from 32 to 20 months and the interest from about 1,314 to about 800.

Related calculators

Loan Payment Calculator — Find the payment for a chosen term instead.
Mortgage Payment Calculator — Full housing payment for a home loan.
Rule of 72 Calculator — How fast an unpaid balance doubles at this APR.