BYTETOOLS

Loan Interest Rate Calculator

Work out the interest rate on a loan from the amount borrowed, the monthly payment and the term. Solves the annuity equation numerically for the true rate.

6.000%
Annual interest rate
0.5000%
Monthly rate
$3,199.60
Total interest
$23,199.60
Total repaid

Details

Number of payments
60
Effective annual rate (compounded)
6.168%
Interest as a share of the amount borrowed
16.0%

The annual rate shown is the monthly rate multiplied by 12, the nominal convention lenders quote. The effective annual rate compounds that monthly rate and is always a little higher.

This is the rate implied by the payment alone. It excludes fees, so it is the note rate rather than the APR — use the APR calculator if points or origination fees are involved. Estimates only, not financial advice.

What is the Loan Interest Rate Calculator?

The ByteTools Loan Interest Rate Calculator runs a normal loan calculator backwards. Instead of giving you a payment from a rate, it takes the amount you borrowed, the payment you make and the number of payments, and finds the interest rate that fits.

  • Solves the annuity equation for the rate by bisection plus Newton refinement
  • Term entered in months or years, whichever you have to hand
  • Reports nominal annual rate, monthly rate and effective annual rate
  • Shows total repaid and total interest for the solved rate
  • Detects impossible combinations instead of showing a wrong answer
  • Local, offline and private

How to use the Loan Interest Rate Calculator

  1. 1

    Enter the loan amount you received.

  2. 2

    Enter the regular payment amount.

  3. 3

    Enter the term, and choose whether it is in months or years.

  4. 4

    Read the solved annual interest rate, the monthly rate and total interest.

  5. 5

    Check the effective annual rate for the compounded equivalent.

About the Loan Interest Rate Calculator

The ByteTools Loan Interest Rate Calculator runs a normal loan calculator backwards. Instead of giving you a payment from a rate, it takes the amount you borrowed, the payment you make and the number of payments, and finds the interest rate that fits. That is useful when a lender quotes a monthly figure without disclosing a rate, or when you want to check a contract.

The annuity equation cannot be rearranged for the rate algebraically, so the tool brackets the answer and narrows it by bisection before refining with Newton's method — converging to well under a hundredth of a percent. It reports both the monthly periodic rate and the annualised nominal rate, plus the effective annual rate with monthly compounding.

It also detects impossible inputs, such as a total of payments that is less than the amount borrowed. All computation happens in your browser and nothing is uploaded. Estimates only, not financial advice.

Frequently asked questions

Can you calculate an interest rate from the payment?

Yes, but only numerically. The formula payment = L × i ÷ (1 − (1 + i)^−n) cannot be rearranged to isolate i, so the rate has to be found by iteration. This calculator does that automatically and converges in a few milliseconds.

What is the difference between nominal and effective annual rate?

The nominal rate is simply the monthly rate multiplied by 12. The effective annual rate compounds it — (1 + i)^12 − 1 — so it is slightly higher. A 6% nominal rate with monthly compounding is an effective 6.17%.

Why does my calculated rate differ from the lender's APR?

APR also includes points and fees, so it is normally higher than the pure interest rate this tool derives from your payment. If you want the fee-inclusive figure, use the APR calculator instead.

What if the total of my payments is less than the loan?

Then there is no positive interest rate that fits, and the calculator says so rather than returning a nonsense number. Check that you have entered the payment and the number of payments correctly.

How accurate is the solved rate?

Very. Bisection over 200 iterations narrows the periodic rate far below a millionth of a percent before Newton's method polishes it, so the limiting factor is the precision of the payment you type, not the solver.

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