Loan Payoff Calculator
Loan Payoff Calculator
How many months until a loan is paid off at the payment you make now — and how much sooner, and how much cheaper, if you pay a little extra each month.
Loan payoff
Balance $5,00,000 at 12%, paying $15,000 plus $5,000 extra
Months to repay a balance
- B
- the outstanding balance
- M
- the monthly payment, including any extra
- r
- the monthly interest rate: annual rate ÷ 1200
- n
- the number of months; it has no answer when M ≤ r × B, because the payment does not cover the interest
Worked example
Balance $5,00,000 at 12%, paying $15,000 plus $5,000 extra
At $15,000 a month: n = −ln(1 − 0.01 × 5,00,000 ÷ 15,000) ÷ ln(1.01) = 40.7 months
At $20,000 a month: n = −ln(1 − 0.25) ÷ ln(1.01) = 28.9 → 29 months
Interest: $1,11,234 at the payment alone, $78,236 with the extra — $32,997 saved
Why a small extra payment goes a long way
Every rupee, dollar or dirham paid above the scheduled amount goes straight to the principal, and principal is what interest is charged on. So an extra payment does two things at once: it cuts the balance today, and it cuts every future month’s interest charge. That compounding in reverse is why the worked example saves a year of payments and about 30% of the interest from an extra payment of a third.
The formula has no answer when the payment does not cover the interest for a month. The balance then grows rather than shrinks, which is the trap of paying only the minimum on a credit card. If the calculator returns nothing, that is the reason. If only the payment alone falls short, the chart shows that balance climbing instead of falling.
The chart puts the two balances side by side, a year at a time. In the worked example the loan is gone within 3 years with the extra $5,000, and within 4 at $15,000 alone; the middle line is the interest paid so far with the extra. Once a loan is cleared, the interest columns use the same exact-fraction totals as the figures under the result.
Two things to check before prepaying a loan. Some lenders charge a prepayment or foreclosure fee, and on floating-rate loans you can often choose whether a prepayment shortens the tenure or lowers the EMI — shortening the tenure saves more interest. To see the instalment on a new loan instead, use the EMI calculator. This is arithmetic on the figures you enter, not financial advice.
Frequently asked questions
How do I work out how long it will take to pay off a loan?
Months = −ln(1 − r × balance ÷ payment) ÷ ln(1 + r), with r the monthly rate. The calculator above does it for you and shows the effect of paying extra.
Is it better to prepay a loan or invest?
Prepaying earns you exactly the loan’s interest rate, risk-free and after tax in most cases. Compare that with the return you realistically expect after tax and risk; for high-rate debt such as credit cards prepaying usually wins.
Why does the calculator show no result?
Because the payment does not cover a month’s interest, so the balance never falls. Increase the payment.
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References
- Brealey RA, Myers SC, Allen F. Principles of Corporate Finance. McGraw-Hill. The present value of an annuity, from which the level-payment loan formula follows.
- Consumer Financial Protection Bureau (CFPB). What is amortization and how could it affect my auto loan? Ask CFPB.