Borrow €300,000 at 4.5% for 30 years and you'll pay back about €547,000. Where did the extra quarter million go, and why does your balance barely move in the first years even though you pay every single month? The answer is one formula — and once you understand it, every mortgage decision (15 vs 30 years, extra payments, refinancing) becomes simple arithmetic.
The formula behind every mortgage
Nearly all mortgages are fully amortizing: you pay the same fixed amount every month, and by the final payment the loan is exactly zero. That fixed payment comes from:
M = P × [ r(1 + r)ⁿ ] / [ (1 + r)ⁿ − 1 ]
P — the principal (amount borrowed)
r — the monthly interest rate (annual rate ÷ 12)
n — the total number of payments (years × 12)
For €300,000 at 4.5% over 30 years: r = 0.045 ÷ 12 = 0.00375 and n = 360, which works out to about €1,520 per month. You don't need to crunch that by hand — the mortgage calculator does it instantly and shows the full cost breakdown.
Why your early payments are mostly interest
Here's the part that surprises everyone. The payment is fixed, but its composition changes every month:
Each month, interest is charged on the remaining balance: balance × 0.00375.
Whatever is left of your payment reduces the principal.
Month one on our example loan: interest is 300,000 × 0.00375 = €1,125, so only €395 of your €1,520 actually pays down the debt. Ten years in, you've paid roughly €182,000 — and still owe around €240,000. Because the balance shrinks slowly at first, interest dominates early and principal dominates late. That's amortization: not a trick, just compound interest running in reverse. (If you want the forward version working for you instead, read our compound interest guide.)
15 years vs 30 years: the real price of time
Same €300,000 at 4.5%:
30 years: ~€1,520/month → ~€247,000 total interest
15 years: ~€2,295/month → ~€113,000 total interest
The shorter loan costs about 50% more per month but saves roughly €134,000 in interest. Neither answer is universally right — the 30-year payment leaves room to breathe and invest, the 15-year builds equity fast. Run both through the loan calculator and compare against your real budget, which means your net income — see where your paycheck actually goes if you're estimating from gross.
The cheapest trick in personal finance: extra payments
Anything you pay above the required amount goes 100% to principal — and every euro of principal you kill today stops generating interest for decades. On our example loan, a single extra payment per year (≈€127/month more) shortens the loan by roughly 4 years and saves over €30,000 in interest.
Three rules to get it right:
Confirm your lender applies extra payments to principal, not to "future payments".
Check for early-repayment penalties (common on fixed-rate loans in some countries).
Compare alternatives: if your mortgage costs 4.5% but you carry credit card debt at 20%, the card wins every time — the credit card payoff calculator makes that painfully clear.
What the payment doesn't include
The formula covers principal and interest only. Your real monthly housing cost adds property taxes, home insurance, possibly mortgage insurance (typically required below 20% down payment), and maintenance — a common rule of thumb is 1% of the home's value per year. Budget on the full number, not the loan payment.
The bottom line
A mortgage isn't mysterious: one formula sets the payment, and the balance decides how much of each payment is interest. Before you sign anything, spend two minutes with the mortgage calculator — check the total interest line, not just the monthly payment, and test what one extra payment a year would do. It's the difference between choosing a loan and being chosen by one.