How to calculate a loan payment

With standard amortization, every payment is the same and is calculated as:

Payment = C × i / (1 − (1 + i)^−n)

• C: amount borrowed.
• i: monthly interest rate, i.e. the nominal annual rate divided by 12 (as a decimal).
• n: number of monthly payments.

A €10,000 loan at a 7% nominal rate over 5 years (60 payments):

1. Monthly rate: 0.07 / 12 ≈ 0.005833.
2. Discount factor: (1 + 0.005833)^−60 ≈ 0.7054.
3. Payment: 10,000 × 0.005833 / (1 − 0.7054) ≈ €198.01.

In total you'll repay €11,880.75, of which €1,880.75 is interest. Because the payment is rounded to the cent, the final payment is adjusted by a few cents.

Each payment first covers the month's interest on the outstanding balance, and the rest repays principal. In the example's first month, interest is 10,000 × 0.005833 ≈ €58.33 and €198.01 − €58.33 = €139.68 of principal is repaid. As the balance falls, the interest share shrinks and the principal share grows: over the first year you pay €645.16 of interest and repay €1,730.96 of principal.

If the same loan is repaid over 7 years (84 payments), the payment drops to €150.93, but total interest rises to €2,677.77: almost €800 more than over 5 years.

The formula uses the nominal interest rate. The APR adds the effect of payment frequency and fees, so it's more useful for comparing offers. Neither necessarily includes linked insurance or other costs: always review the full offer.