Irish Calculators
Loans & mortgages

Loan Interest Rate from Payments Calculator

Solve the non-negative interest rate implied by a conventional monthly payment stream. The result does not include unentered fees or establish a regulated APR or APRC.

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Your numbers

€
Use the principal owed before the next interest period.
Your figures stay on this device.

How the calculation works

When principal, regular payments and term are known, the missing interest rate can be inferred from their cash-flow relationship. The result distinguishes the monthly rate, its nominal annual multiple and its compounded annual equivalent.

Solve principal = payment × PV annuity factor + balloon/(1+i)^n for the unique non-negative monthly rate. Nominal annual rate = 12i; effective annual rate = (1+i)^12 − 1.

  1. Set up the present-value equation

    The principal must equal the discounted value of all regular payments plus the discounted final balloon. All amounts use one currency and equal monthly intervals.

  2. Find a non-negative monthly rate

    The solver searches for the rate that balances that equation. Payments insufficient to repay principal even at zero interest are rejected; negative implied rates are outside this tool’s scope.

  3. Convert the solved rate

    The nominal annual rate is twelve times the monthly rate. The effective annual rate compounds that monthly rate over twelve periods, so it is normally higher when interest is positive.

Worked example: Interest-free loan implied by payments

Sample inputs demonstrate the method. They are not a forecast or product offer.

The example advances €1,200 and receives twelve monthly payments of €100 with no balloon. Those payments sum exactly to principal, so zero interest balances the equation. Both the monthly rate and nominal annual rate are zero.

Loan balance (€)
1200
Equal monthly payment
100
Remaining term (months)
12
Final additional balloon
0

Expected result

Implied nominal annual rate
0%
Monthly rate
0%
Worked example: One percent monthly with final balloon

Sample inputs demonstrate the method. They are not a forecast or product offer.

Loan balance (€)
1000
Equal monthly payment
510
Remaining term (months)
1
Final additional balloon
500

Expected result

Implied nominal annual rate
12%
Implied effective annual rate
12.68%
Monthly rate
1%

Understanding your result

The inferred rate explains the specific cash flows you entered. It does not establish that a lender quoted, approved or legally calculated that rate.

If the result seems inconsistent with a statement, check payment timing, additional fees and whether the final amount includes or excludes the last regular instalment.

Questions you might have

Why is this different from APR?

APR may include fees and statutory timing conventions. This result infers the rate from the entered regular loan cash flows only.

Choosing the right inputs

Loan balance
Use the single amount advanced at the start of the modelled loan. Fees are not added automatically and this calculation is not a fee-inclusive APR.
Equal monthly payment
Enter one equal payment made at each month-end. Use the same payment throughout; an irregular schedule does not fit this rate solver.
Final additional balloon
Enter any residual paid in addition to the final regular payment. Use zero for a loan that amortizes completely through the monthly instalments.

Common mistakes to avoid

  • Do not describe the result as regulatory APR; fee and timing rules are not applied.
  • A payment holiday or changing rate cannot be represented by one average payment without changing the problem.

Assumptions to check

  • Only conventional non-negative payment streams and non-negative rates are supported.

Sources and method

Read our calculation and testing approach.