How do I calculate how many payments are left on a loan?

n = −ln(1 − L × r ÷ P) ÷ ln(1 + r), with L the balance, r the rate per period and P the payment.

Why does the calculator say my loan is never repaid?

Your payment is less than or equal to the interest charged each period, so the balance never goes down.

Why is the answer not a whole number?

The final payment is only part of a normal payment. Round up to count the payments you will actually make.

How much faster does a larger payment pay off the loan?

Enter both payments and compare. Because interest is charged on a smaller balance, a modest increase can cut the term substantially.

Loan Payoff Time (Number of Payments)

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Loan Payoff Time (Number of Payments) Calculator

If you know your balance, your interest rate and how much you can pay each month, this formula tells you how many payments it will take to clear the debt. It is the loan payment formula solved for n: n = −ln(1 − L × r ÷ P) ÷ ln(1 + r). It answers questions such as how long a credit card or car loan will last at a fixed payment, or how much sooner a bigger payment would finish it.

Formula

n = −ln(1 − L × r ÷ P)ln(1 + r)

Where

n: number of payments needed to repay the loan
L: loan balance
P: payment per period
r: interest rate per period

Calculator

Loan balance (L)

Annual interest rate (%)

Payment per period (P)

Payments per year

Result and step-by-step solution

Number of payments

59.29

About 4.94 years at 400.00 per payment; interest paid ≈ 3,715.11.

Rate per period
r = 7% ÷ 12 = 0.00583333
Share of the payment taken by interest at the start
L × rP = 20,000.00 × 0.00583333400.00 = 0.29166667
Apply the formula
n = −ln(1 − 0.29166667)ln(1 + 0.00583333) = −−0.344840490.00581639 = 59.2878
Convert to years
59.2878 ÷ 12 = 4.94 years; 60 payments (the last one smaller)

How to use the formula

The quantity L × r ÷ P is the share of your first payment that goes to interest. If it is 1 or more, the payment does not even cover the interest and the balance never falls; the calculator flags this and shows the minimum payment needed. The closer that share is to 1, the longer the payoff time, which is why small increases in a low payment make such a big difference.

Paying 400 a month on 20,000 at 7% clears the loan in 59.29 payments, just under 5 years, with total interest of about 3,715. The answer is fractional because the last payment is smaller. Compare repayment speeds with the loan payment formula, or check the balance at any point with the remaining balance formula. Excel’s NPER(rate, −payment, balance) gives the same result.

Frequently asked questions

How do I calculate how many payments are left on a loan?: n = −ln(1 − L × r ÷ P) ÷ ln(1 + r), with L the balance, r the rate per period and P the payment.
Why does the calculator say my loan is never repaid?: Your payment is less than or equal to the interest charged each period, so the balance never goes down.
Why is the answer not a whole number?: The final payment is only part of a normal payment. Round up to count the payments you will actually make.
How much faster does a larger payment pay off the loan?: Enter both payments and compare. Because interest is charged on a smaller balance, a modest increase can cut the term substantially.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.