Interest rate from payment calculator

This calculator finds the interest rate from the payment: enter the loan amount, monthly payment and term to see which rate is behind them. A loan of 10,000 repaid in 36 monthly payments of 300 corresponds to a nominal rate of 5.06% and an effective annual rate of 5.18%.

Example: Loan amount or purchase price 10,000 · Monthly payment 300 · Term 36 months · Balloon payment or remaining balance at the end (optional) 0 → Nominal rate p.a.: 5.06%. Source: Directive 2008/48/EC on credit agreements for consumers, Annex I: calculation of the annual percentage rate of charge. Updated: 30 September 2026.

Loan amount or purchase price

Monthly payment

Term

months

Balloon payment or remaining balance at the end (optional)

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Result

Nominal rate p.a.: 5.06%
Effective annual rate: 5.18%
Rate per month: 0.42%
Total of all payments: 10,800.00
Total interest cost: 800.00
Check: 300.00 × 33.3333 = 10,000.00
Year by year: Year Interest Principal repaid Balance at year end
1 433.65 3,166.35 6,833.65
2 269.50 3,330.50 3,503.15
3 96.85 3,503.15 0.00

Year	Interest	Principal repaid	Balance at year end
1	433.65	3,166.35	6,833.65
2	269.50	3,330.50	3,503.15
3	96.85	3,503.15	0.00

How it is calculated

How to calculate the interest rate from the payment

For an installment loan: loan = payment × (1 − (1 + i)⁻ⁿ) ÷ i, with monthly rate i and n monthly payments. This equation cannot be solved for i directly, so the calculator searches step by step until the payments add up to exactly the loan – just like the RATE function in spreadsheets.

10,000 in 36 payments of 300: 5.06% nominal, 5.18% effective, interest cost 800
15,000 in 48 payments of 350: 5.67% nominal, 5.82% effective, interest cost 1,800
20,000 in 48 payments of 250 plus a 9,000 balloon payment: 1.70% nominal

Nominal rate and effective annual rate

The nominal rate is the monthly rate times 12. The effective annual rate reflects that interest is charged on interest month by month: (1 + i)¹² − 1. It is the figure lenders must state under consumer credit rules (in the EU: the APR of Directive 2008/48/EC) – but including all costs.

With a balloon payment

If a larger final payment is due at the end (a balloon payment, common in car financing), enter it as well. Then: loan = payment × annuity factor + balloon × (1 + i)⁻ⁿ.

Installment purchase with no interest?

If the payments add up to exactly the purchase price, the rate is 0%. If they add up to more, the difference is interest and fees – the calculator shows the rate behind it.

Honest limits

The calculator only knows the loan, payment, term and balloon payment. Arrangement fees, payment protection insurance and other costs that are part of the APR in an offer are not included, so the result is usually lower than the APR in the contract. Payments are assumed monthly at the end of each month.

Frequently asked questions

How do I calculate the interest rate from the monthly payment?

Enter the loan amount, monthly payment and term. The calculator solves loan = payment × (1 − (1 + i)^−n) ÷ i for the monthly rate i and shows the nominal and effective rate.

What is the difference between the nominal and the effective rate?

The nominal rate is the annual rate without compounding (monthly rate × 12); the effective annual rate includes monthly compounding and is therefore slightly higher.

Why does the result differ from the APR in a loan offer?

The APR in an offer also contains fees and other costs that this calculator does not know. The contract figure is therefore usually higher.

What is the rate on interest-free financing?

If the payments add up to the purchase price, the rate is 0%. Every markup above it corresponds to interest.

How do I enter a balloon payment?

In the field “Balloon payment or remaining balance at the end”. The term then applies to the regular payments; the balloon payment is paid in addition at the end.

Sources and legal basis

As of: 30 September 2026