Calculate Loan Term From a Known Payment

This calculator estimates how many monthly payments it takes to repay a loan when you know the loan amount, APR, and payment amount. Enter those figures to get the estimated term in months and years, plus the interest paid over that schedule.

Formula

For a fixed-rate loan with a level monthly payment, the unrounded number of payment periods is:

n = -ln(1 - r × P / M) / ln(1 + r)

The calculator rounds the logarithm-based period count to six decimal places, then rounds up to a whole month: ceil(round(n, 6)). It also checks that the payment covers the interest due in the first month; otherwise, the term cannot be calculated as a payoff schedule.

• P is the starting loan principal, in dollars.
• APR is the annual percentage rate, entered as a percent.
• r is the monthly rate as a decimal: APR / 1200.
• M is the monthly payment, in dollars.
• n is the estimated whole number of monthly payments.

Total interest is estimated as M × n − P, using the entered payment for every month. This simplified total assumes the same payment is made for the full number of months; an actual lender may adjust the final payment to clear the remaining balance.

Worked Example

Using the calculator’s default values—$20,000 principal, 8% APR, and a $405.53 monthly payment:

1. Convert APR to a monthly decimal rate: r = 8 / 1200 = 0.0066667.
2. Substitute the values: n = -ln(1 − 0.0066667 × 20000 / 405.53) / ln(1.0066667).
3. The unrounded result is about 59.98 months. Rounding up gives 60 months, or 5.00 years.
4. Estimated interest using the same payment for all 60 months is $405.53 × 60 − $20,000 = $4,331.80.

The first payment’s interest is about $133.33, so the $405.53 payment exceeds that amount and reduces principal. With cents-rounded payments, the exact final balance may differ slightly from the simplified total-interest estimate.

Assumptions

• The interest rate remains fixed throughout the calculated term.
• Payments are equal, made monthly, and occur at the end of each monthly period.
• Interest compounds monthly at APR divided by 12.
• Fees, taxes, insurance, PMI, escrow, late charges, and extra payments are not included.

How the Calculation Works

Each payment first covers the interest accrued since the prior payment; the remainder reduces principal. As the balance falls, the interest portion generally falls too. The formula reverses the ordinary fixed-payment loan equation: instead of finding the payment from a chosen term, it solves for the number of periods from the payment, principal, and rate.

The calculation produces a fractional period before the result is rounded up. A lender normally does not accept a fraction of a scheduled monthly payment as the final term, so rounding up expresses the result as a whole number of monthly periods. In practice, the last payment may be smaller or larger than the regular payment depending on accrued interest, payment dates, and rounding.

When to Use It and How to Read the Result

Use this estimate when you have a loan balance or proposed principal, a known fixed APR, and a monthly payment amount, and want to understand the approximate payoff duration. The first output is the estimated number of monthly payments. The years output is that month count divided by 12; it is a convenient conversion, not a separate day-by-day payoff date.

For example, a result of 60 months means the modeled schedule spans about five years of monthly payments. The interest output is an arithmetic estimate based on the entered payment repeated for every month. Compare it with the lender’s amortization schedule for the actual amount and timing, especially if the contract specifies a different first payment date or a final adjusted payment.

Common Problems and Limits

The payment must be greater than the first month’s interest, calculated as P × APR / 1200. If it is equal to that interest, the balance does not decline under the model; if it is lower, the balance grows. In either case, there is no finite payoff term using an unchanged payment. The calculator reports that the inputs cannot produce a payoff rather than presenting a misleading duration.

• Entering APR as a decimal: Enter 8 for 8%, not 0.08. The calculator converts the percent to a monthly rate.
• Using the wrong payment frequency: This formula expects a monthly payment. A weekly or biweekly amount must not be entered as though it were monthly.
• Using a changing rate or payment: Variable-rate loans, stepped payments, and irregular payment schedules do not follow this fixed-payment calculation.
• Ignoring fees or added costs: If charges are financed or collected separately, the modeled principal or payment may not match the lender’s figures.
• Rounding differences: Rounding the displayed term to whole months and payments to cents can create a small difference from a lender’s exact payoff quote.

A zero-interest loan is a special case: the logarithmic formula divides by a rate-derived quantity and is not designed for APR of zero. The calculator’s minimum APR is 0.01%. For a genuinely interest-free loan, the basic term is the principal divided by the payment, rounded up to a whole payment period.

Frequently Asked Questions

How do I calculate the loan term from the payment?
Convert APR to a monthly decimal rate, then use n = -ln(1 − rP/M) / ln(1+r) and round up to a whole month. The calculator applies that formula and checks whether the payment exceeds first-month interest.

What if my payment is less than the monthly interest?
The payment will not reduce principal under the fixed-rate model, so there is no finite payoff term. A lender’s account may handle unpaid interest according to the loan terms, which this calculator does not model.

Does the result include the final payment?
It counts whole monthly periods, including the period in which the modeled balance is paid off. The actual final payment can differ from the regular amount because of cents rounding and accrued interest.

Can I use this for a variable-rate loan?
Not for an accurate full-term estimate. The formula assumes one fixed APR and one unchanged monthly payment; a rate or payment change can alter the payoff schedule.

Why does my lender show a different payoff date?
Payment dates, daily interest, fees, rate conventions, rounding, and the final payment amount can all affect the exact date and balance. The calculator uses a simplified monthly model.

This result is an estimate; the lender’s disclosure gives the exact figures.

Related

• Extra Payments on an Auto Loan Calculator
• Extra Payments on a Car Loan: Payoff Calculator
• Extra Superannuation Contributions Calculator

in p | Loan amount | $ | 20000 | 1 | 100000000
in apr | Interest rate (APR) | % | 8 | 0.01 | 100
in pmt | Monthly payment | $ | 405.53 | 0.01 | 100000000
out n | Loan term | months | ceil(round(-ln(1 - (apr / 1200) * p / pmt) / ln(1 + apr / 1200), 6)) + 0 * sqrt(pmt - (apr / 1200) * p) | 0
out yrs | Loan term | years | n / 12 | 2
out int | Total interest | $ | pmt * n - p | 2