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.
輸入資料
計算結果
重點速覽：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.
計算公式
月利率 r = 年利率 ÷ 12。
還清月數 n = −ln(1 − r × 餘額 ÷ 月供) ÷ ln(1 + r)。
$$r = \dfrac{\text{年利率}\%}{12}\quad(\text{月利率})$$$$n = \dfrac{-\ln\!\left(1 - \dfrac{r \times \text{餘額}}{\text{月供}}\right)}{\ln(1 + r)}$$$$\text{可還清條件}:\; \text{月供} > r \times \text{餘額}$$使用說明
- Enter the debt balance and annual rate.
- Enter the fixed monthly payment.
- View the months to payoff (0 means it cannot be cleared).
以債務餘額 100,000、年利率 12% (月利率 1%) 為例，不同每月還款額下的還清月數。
| 每月還款 | 還清月數 | 備註 |
|---|---|---|
| 2,000 | 約 69.7 個月 | 接近 6 年 |
| 3,000 | 約 40.8 個月 | 約 3 年 5 個月 |
| 5,000 | 約 22.4 個月 | 不足 2 年 |
| 10,000 | 約 10.6 個月 | 不足 1 年 |
理財情境案例
案例一：每月多還 1,000，還債時間大縮短
李先生有一筆 60,000、年利率 18% 的債務 (月利率 1.5%，每月利息 900)。他原打算每月還 2,000。
代入公式：n = −ln(1 − 0.015 × 60,000 ÷ 2,000) ÷ ln(1.015) ≈ 40.2 個月。若每月改還 3,000，n ≈ 24.0 個月。
每月只多還 1,000，還清時間就由約 40 個月縮短至約 24 個月，足足省下約 16 個月的利息 —— 這說明在可負擔範圍內『盡量多還一點』的效益極高。
案例二：月供不足以付息 —— 永遠還不清
陳女士的信用卡結欠 80,000、年利率高達 36% (月利率 3%)，每月產生利息 = 80,000 × 3% = 2,400。她每月只還 2,000。
由於月供 2,000 < 每月利息 2,400，扣息後本金不減反增，計算器回傳「無法還清」—— 這就是負攤還 (negative amortization)。
若她把還款提高到 4,000 (高於利息 2,400)，代入公式約 31 個月即可清還。這個案例警示：高息債務一旦月供追不上利息，就會越滾越大，必須大幅提高還款或尋求債務重組。
常見問題
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 (平息) vs APR, plus fees/penalties, and early-repayment charges. Treat it as a planning estimate; the lender's schedule is final.
相關工具
參考資料
內容審核：香港計算器財經團隊。計算邏輯與公式參考香港金融管理局（HKMA）及投資者及理財教育委員會（IFEC）之個人理財計算指引，結果僅供參考，實際以相關機構公佈為準。