{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"debt-payoff"},"result":{"entity_type":"calculator","id":"debt-payoff","calculator_id":"debt-payoff","canonical_url":"https://tttkmbb.com/finance/debt-payoff","name":"Debt Payoff Calculator","title":"Debt Payoff Calculator – Months to Pay Off a Balance and Total Interest at a Fixed Payment","category":"finance","category_name":"Finance","tool_name":"calculate_debt_payoff","featured_mcp_tool":false,"description":"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.","use_when":"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).","inputs":[{"name":"balance","label":"Current balance","type":"number","required":true,"max":1000000000000,"exclusive_min":0,"description":"Amount owed today.","example":5000},{"name":"annual_rate_percent","label":"APR","type":"number","unit":"%","required":true,"min":0,"max":200,"description":"Annual percentage rate in percent; interest accrues monthly at APR / 12.","example":18},{"name":"monthly_payment","label":"Monthly payment","type":"number","required":true,"max":1000000000000,"exclusive_min":0,"description":"Fixed amount paid at the end of each month. Must exceed the first month's interest (balance × APR / 1200).","example":200}],"outputs":[{"name":"months_to_payoff","label":"Months to pay off","type":"integer","unit":"months","decimals":0,"description":"Number of monthly payments including the smaller final one."},{"name":"payoff_time","label":"Payoff time","type":"string","decimals":4,"description":"months_to_payoff expressed in years and months."},{"name":"months_to_payoff_exact","label":"Months (closed form)","type":"number","unit":"months","decimals":2,"description":"−ln(1 − i·balance/payment) / ln(1 + i), the unrounded annuity solution."},{"name":"total_paid","label":"Total paid","type":"number","decimals":2,"description":"balance + total_interest."},{"name":"total_interest","label":"Total interest","type":"number","decimals":2,"description":"Sum of the monthly interest charges until payoff."},{"name":"final_payment","label":"Final payment","type":"number","decimals":2,"description":"The last, usually smaller, payment that clears the balance."},{"name":"first_month_interest","label":"First month's interest","type":"number","decimals":2,"description":"balance × APR / 1200, the minimum a payment must exceed."}],"input_schema":{"type":"object","properties":{"balance":{"description":"Amount owed today.","type":"number","maximum":1000000000000,"exclusiveMinimum":0,"examples":[5000]},"annual_rate_percent":{"description":"Annual percentage rate in percent; interest accrues monthly at APR / 12. Unit: %.","type":"number","minimum":0,"maximum":200,"examples":[18],"x-unit":"%"},"monthly_payment":{"description":"Fixed amount paid at the end of each month. Must exceed the first month's interest (balance × APR / 1200).","type":"number","maximum":1000000000000,"exclusiveMinimum":0,"examples":[200]}},"additionalProperties":false,"required":["balance","annual_rate_percent","monthly_payment"]},"output_schema":{"type":"object","properties":{"months_to_payoff":{"description":"Number of monthly payments including the smaller final one. Unit: months.","type":"integer","x-unit":"months"},"payoff_time":{"description":"months_to_payoff expressed in years and months.","type":"string"},"months_to_payoff_exact":{"description":"−ln(1 − i·balance/payment) / ln(1 + i), the unrounded annuity solution. Unit: months.","type":"number","x-unit":"months"},"total_paid":{"description":"balance + total_interest.","type":"number"},"total_interest":{"description":"Sum of the monthly interest charges until payoff.","type":"number"},"final_payment":{"description":"The last, usually smaller, payment that clears the balance.","type":"number"},"first_month_interest":{"description":"balance × APR / 1200, the minimum a payment must exceed.","type":"number"}}},"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.","method":"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.","sources":[{"name":"Federal Reserve – Credit Card Repayment Calculator","url":"https://www.federalreserve.gov/creditcardcalculator/","type":"government","retrieved_at":"2026-09-23"},{"name":"CFPB – Credit cards: paying down balances","url":"https://www.consumerfinance.gov/consumer-tools/credit-cards/","type":"government","retrieved_at":"2026-09-23"},{"name":"Wikipedia – Amortization calculator (annuity payment formula)","url":"https://en.wikipedia.org/wiki/Amortization_calculator","type":"reference","retrieved_at":"2026-09-23"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"5,000 at 18 % APR, 200 per month","inputs":{"balance":5000,"annual_rate_percent":18,"monthly_payment":200},"expected":{"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},"url":"https://tttkmbb.com/api/v1/calculate/debt-payoff?balance=5000&annual_rate_percent=18&monthly_payment=200"},{"name":"2,000 at 24 % APR, 50 per month","inputs":{"balance":2000,"annual_rate_percent":24,"monthly_payment":50},"expected":{"months_to_payoff":82,"payoff_time":"6 years 10 months","total_interest":2063.8,"first_month_interest":40},"url":"https://tttkmbb.com/api/v1/calculate/debt-payoff?balance=2000&annual_rate_percent=24&monthly_payment=50"}],"faq":[{"q":"What happens if my payment is too small?","a":"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."},{"q":"How much does paying extra help?","a":"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."}],"tags":["debt payoff","credit card payoff","how long to pay off","months to pay off debt","total interest"],"related":[{"calculator_id":"loan-payment","reason":"Find the payment for a chosen term instead."},{"calculator_id":"mortgage-payment","reason":"Full housing payment for a home loan."},{"calculator_id":"rule-of-72","reason":"How fast an unpaid balance doubles at this APR."}],"links":{"html":"https://tttkmbb.com/finance/debt-payoff","markdown":"https://tttkmbb.com/finance/debt-payoff.md","json":"https://tttkmbb.com/finance/debt-payoff.json","api":"https://tttkmbb.com/api/v1/calculate/debt-payoff","schema":"https://tttkmbb.com/api/v1/calculators/debt-payoff","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:31:32Z","next_actions":[{"tool":"run_calculator","calculator_id":"debt-payoff","reason":"Run Debt Payoff Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/finance/debt-payoff.md"}}