How loan amortisation actually works (why early payments are mostly interest)

Look at the first statement of a 25-year mortgage and something odd jumps out. Of a payment of, say, €1,055, perhaps €667 is interest and only €388 actually reduces what you owe. Years later the same €1,055 payment is nearly all principal.

Nothing about the loan changed. That’s just what amortisation is, and the mechanics are worth understanding whether or not you ever check the maths yourself.

This explains how the arithmetic works. It isn’t financial advice, and whether any particular loan suits you depends on a great deal more than its formula.

One payment, two jobs

An amortising loan has a fixed monthly payment doing two jobs at once: covering the interest that accrued that month, and repaying some of the balance. The lender doesn’t choose the split month to month. It falls mechanically out of two rules:

1. Interest each month = current balance × monthly rate.
2. Whatever’s left of the payment reduces the balance.

Early on the balance is large, so rule 1 eats most of the payment. Every month the balance shrinks a little, so next month’s interest is a little smaller, so a little more of the same payment goes to principal. It’s a feedback loop that starts slow and accelerates. That’s the whole phenomenon: no trick, just a large balance generating large interest.

A worked month

Take €200,000 at 4% annual interest over 25 years. The monthly rate is 4% ÷ 12 = 0.3333%. The fixed payment, from the formula below, is €1,055.67.

Month 1: interest is 200,000 × 0.003333 = €666.67. The remaining 1,055.67 − 666.67 = €389.00 reduces the balance to €199,611.

Month 2: interest is 199,611 × 0.003333 = €665.37, which is €1.30 less, so €390.30 goes to principal.

Each month the principal share grows by roughly a third of a percent. It crosses 50/50 around year 10, and in the final year almost the entire payment is principal. Summed across the full term, this loan pays about €116,700 in interest on €200,000 borrowed. That number surprises most people the first time they see a full amortisation table, and the loan calculator shows it month by month.

Where the payment formula comes from

The fixed payment is the unique amount that brings the balance to exactly zero on the final month:

P = L × r / (1 − (1 + r)^−n)

L is the amount borrowed, r the monthly rate, n the number of payments. The derivation is compound interest run forwards: the balance grows by a factor of (1+r) each month and shrinks by one payment, and demanding balance = 0 at month n pins down P.

Two practical notes:

• The rate has to be the per-period rate. Feeding an annual rate into a monthly formula is the classic error, and it produces payments about twelve times too high.
• When r is 0, the formula divides zero by zero, so a correct calculator special-cases it to L ÷ n. A surprising number of online calculators return NaN for a 0% loan.

Why sensitivity to the rate is so extreme

Interest recurs on the whole outstanding balance for the entire term, which is why small rate changes move the totals so dramatically. The same €200,000 over 25 years:

Rate	Monthly payment	Total interest
3%	€948	€84,500
4%	€1,056	€116,700
5%	€1,169	€150,800

One percentage point, 4% to 5%, adds €34,000.

It’s also why early overpayments have such an outsized effect on the arithmetic. Money paid in year 2 removes balance that would otherwise have been generating interest for 23 more years. Whether overpaying is the right use of that money is a separate question involving what else it could earn and any early repayment fees. The calculator shows you the mechanics; the decision is yours.

Term does something different from rate

Stretching the term lowers the payment and raises the total. €200,000 at 4% costs €116,700 in interest over 25 years and €153,500 over 30.

The longer term doesn’t make the loan cost more per month, quite the opposite. It makes each euro of balance exist for longer, generating interest the whole time. Payment affordability and total cost pull in opposite directions, and the amortisation table is the honest way to see both at once.

A parsing footnote from building the calculator here. European-format inputs like 250.000, meaning a quarter of a million, were being read by an earlier version as 250. A thousandfold error. The tool now derives the number format from the selected country, but wherever you compute this, check that the loan amount it understood matches the one you meant before trusting anything downstream of it.