How it works
Remaining months = −ln(1−monthly rate × balance/payment)/ln(1+monthly rate), rounded up; zero rate uses balance/payment.
Input definitions
- Outstanding principal
- Enter the value in the labeled unit.
- Fixed monthly payment
- Enter the value in the labeled unit.
- Nominal annual interest (%)
- Enter the value in the labeled unit.
A worked example
- Outstanding principal
- 10000
- Fixed monthly payment
- 500
- Nominal annual interest (%)
- 0
Assumptions & limits
Planning model using the rates, cash flows and periods entered. Examples are illustrative, not market quotes or personalised financial advice. Taxes, inflation and transaction costs are excluded unless explicitly entered.
Sources & review
Maintained by AnsRio. Methods and examples use automated checks; this does not imply independent professional certification.
Method updated 2026-10-18. Content checked against the stated method and examples. Our verification approach.
Common questions
Why might the final payment be smaller?
The formula rounds to a whole number of months. The last payment normally clears the remaining balance rather than matching every earlier payment.
How does Remaining loan term from payment work?
Remaining months = −ln(1−monthly rate × balance/payment)/ln(1+monthly rate), rounded up; zero rate uses balance/payment.
What should I check before using Remaining loan term from payment?
Planning model using the rates, cash flows and periods entered. Examples are illustrative, not market quotes or personalised financial advice. Taxes, inflation and transaction costs are excluded unless explicitly entered.