# When will my loan payoff be done?

Computes how many months a monthly payment takes to pay off a loan balance, and the interest saved by paying extra, or the payment that pays it off in a chosen number of months.

- Page: https://www.acalculator.org/finance/loan-payoff-calculator
- JSON spec: https://www.acalculator.org/finance/loan-payoff-calculator.json
- Version: bf97b4d913b8

## Default answer

Example with the default inputs (Loan balance today $12,000.00, Interest rate (APR) 8%, What do you know? My payment, Monthly payment $350.00, Extra each month $100.00, Next payment month September 29, 2026) on the example date Tuesday, September 29, 2026: Paying $450.00 a month clears $12,000.00 at 8% in 2 years, 6 months, with $1,257.12 of interest.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| balance | Loan balance today | The amount you still owe on the loan today. |
| rate | Interest rate (APR) | The yearly interest rate. The monthly rate is this divided by 12. |
| goal | What do you know? | Pick "My payment" to find when the loan is paid off, or "A payoff time" to find the payment. |
| payment | Monthly payment | The amount you pay each month now. |
| extra | Extra each month | An extra amount paid with every payment. It goes straight to the balance. |
| months | Pay it off in (months) | The number of monthly payments you want the loan paid off in. |
| start | Next payment month | The month of your next payment. It dates the schedule and the payoff month. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| months | Months to pay it off | The number of monthly payments until the balance is 0, extra included. |
| level | Monthly payment | The amount paid each month: your payment plus any extra, or the payment that clears the loan in time. |
| time | Time to pay it off | The number of payments in years and months. |
| payoff | Last payment | The month of the last payment, when a month is given. |
| interest | Total interest | All the interest paid until the loan is paid off. |
| paid | Total of payments | The balance plus all the interest. |
| saved | Interest saved by paying extra | The interest the extra amount saves, compared with paying only the monthly payment. |
| sooner | Months saved by paying extra | How many fewer payments the extra amount takes, compared with paying only the monthly payment. |

## Method

Each month, interest = balance × r (r = APR ÷ 12) and the payment minus the interest lowers the balance; the months to pay off are −ln(1 − B·r ÷ P) ÷ ln(1 + r) rounded up, and the payment for n months is B × r ÷ (1 − (1 + r)^−n).

## Assumptions

- The rate is fixed and interest is charged monthly at APR ÷ 12 on the balance.
- The balance is what you owe today; the first payment is at the end of the first month.
- Extra payments go straight to the balance. The last payment is whatever is left.
- No new charges are added to the balance.
- Values are not rounded to the cent between months; only the display is rounded.

## Worked examples

1. balance = $15,000.00, rate = 8%, goal = payment, payment = $350.00, extra = $100.00 gives months = 38, interest = $2,020.42, saved = $703.45, sooner = 13. Source: hand calculation in content.mdx; Python 3 in docs/progress/WP-31/python/loan_payoff.py.
2. balance = $15,000.00, rate = 8%, goal = months, months = 36 gives level = $470.05, interest = $1,921.64, time = {"years":3,"months":0}. Source: hand calculation in content.mdx: 15,000 × r ÷ (1 − (1 + r)^−36), r = 0.08 ÷ 12.
3. balance = $2,400.00, rate = 0%, goal = payment, payment = $100.00, start = 2026-11-01 gives months = 24, interest = $0.00, payoff = 2028-10-01. Source: hand calculation in content.mdx: 2,400 ÷ 100.

## FAQ

### How do I work out when my loan will be paid off?

Each month the lender adds interest (the balance times the yearly rate ÷ 12) and your payment pays that interest first; the rest lowers the balance. The number of months is −ln(1 − B × r ÷ P) ÷ ln(1 + r), rounded up, where B is the balance, r the monthly rate, and P the monthly payment. $15,000 at 8% with $450 a month takes 38 payments.

### How much does paying extra save?

Every extra dollar lowers the balance right away, so each later month charges less interest. On $15,000 at 8%, paying $450 instead of $350 a month ends the loan 13 months sooner and saves $703.45 of interest.

### What payment do I need to be debt-free by a certain date?

Choose "A payoff time" and enter the number of months. The page uses the loan payment formula B × r ÷ (1 − (1 + r)^−n). To clear $15,000 at 8% in 36 months you need $470.05 a month.

### Why does the page say my payment never pays off the loan?

If the payment is not more than the first month's interest, the balance never goes down. Raise the payment above the balance × APR ÷ 12. The page also stops at 50 years.

### Where do I find my balance and rate?

Your latest loan statement or your lender's website shows the principal balance and the interest rate. Use the principal balance, not a payoff quote, which can include interest up to a future date.

### Is it better to pay off a loan early or save the money?

Paying extra earns you, in effect, the loan's interest rate with no risk. That is often a good deal for a high-rate loan. Keep an emergency fund first, and check that your loan has no prepayment penalty.

## Sources

- Consumer Financial Protection Bureau, Can I prepay my loan at any time without penalty? https://www.consumerfinance.gov/ask-cfpb/can-i-prepay-my-loan-at-any-time-without-penalty-en-843/
- Consumer Financial Protection Bureau, What is amortization and how could it affect my auto loan? https://www.consumerfinance.gov/ask-cfpb/what-is-amortization-and-how-could-it-affect-my-auto-loan-en-771/
- Number of payments and loan payment formulas: S. A. Broverman, Mathematics of Investment and Credit, chapter 3.