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Interest Rate Solver
Find the interest rate behind a known loan amount, monthly payment and term.
Interest rate solver
Monthly rate: —
Annual rate: —
Total paid: — · Total interest: —
—
How to use the Interest Rate Solver
- Enter the loan amount, the payment you have been quoted and the term.
- The solver brackets the rate and bisects until the payment matches.
- Read the monthly and annual rate, plus the total interest.
Features
- Solves the rate from a known payment
- Monthly and annual nominal rate
- Total paid and total interest
- Warns when the payment cannot repay the loan
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Frequently Asked Questions
Common questions about the free online interest rate solver.
It uses bisection on the payment formula, payment = principal x i / (1 - (1 + i) ^ -n),
narrowing the rate until it matches.
The amortisation formula, A = P x i / (1 - (1 + i) ^ -n), where P is the loan, i the monthly
rate and n the payments.
If the payment is smaller than the balance divided by the term, no positive interest rate can
repay the loan, so the solver stops.
It reports the monthly rate and the annual nominal rate, which is simply the monthly rate
multiplied by twelve.
Not exactly. APR adds fees and compounding, so it is usually a little higher than the nominal
rate this solver returns.
The bisection runs 200 iterations, which pins the monthly rate down to far more precision
than any lender would quote.
Yes. Any fixed rate loan with equal payments works, including car loans, mortgages, personal
loans and student loans.
Short terms leave less time for interest to accrue, so the same monthly payment implies a
much higher rate than on a long loan.
No. Feed it only the payment that goes to principal and interest, otherwise the solved rate
will be higher than the true rate.
Last updated: October 10, 2026