How loan payments are calculated: annuity, interest and term

What an annuity is and why the payment never changes

payment = amount × r ÷ (1 − (1 + r)⁻ⁿ), r = annual rate ÷ 12 ÷ 100

An annuity is a fixed monthly amount covering both interest and part of the principal, engineered so the debt hits exactly zero after the last payment. Predictability is the whole point — and the main reason banks use this model.

Inside the payment, the ratio shifts: early on, interest is charged on the whole debt and dominates the payment. As the principal falls, interest shrinks and an ever-larger share repays the debt. On long loans you repay surprisingly little principal in the first years.

Worked example: a 50,000 KM loan

At a 6% nominal annual rate over 10 years (120 payments): the monthly rate is 0.5% and the payment comes to about 555 KM. You repay about 66,612 KM in total — so the interest costs you roughly 16,612 KM.

The first payment contains 250 KM of interest (0.5% of 50,000) and only 305 KM of principal. The last one is almost pure principal. The month-by-month schedule is what the amortization table in the calculator shows.

How the term changes total interest

The same loan over 7 years instead of 10: the payment rises from 555 to about 730 KM, but total interest falls from 16,612 to about 11,355 KM — over 5,000 KM saved. A longer term buys a lower monthly burden at the price of a much more expensive loan overall.

A practical rule: pick the shortest term whose payment fits your budget comfortably, and make early repayments when you can — they cut directly into the principal on which future interest accrues.

Why your real payment differs from the calculation

Calculators work with the nominal rate. Banks add processing fees, insurance and other costs — all captured by the effective interest rate (APR/EKS), which they must disclose. Compare offers by the effective rate; use the payment calculation for budgeting.