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What is a loan payment made of

Every payment is split in two: interest on what you still owe, and capital that reduces it. Because the interest is charged on the outstanding balance, the split shifts over the life of the loan. On €150,000 at 3.5% over 25 years, the first payment of €750.94 is €437.50 interest and €313.44 capital: you have paid three quarters of a month’s instalment and reduced the debt by less than a third of it.

The payment stays the same for the whole term but its composition does not: as the debt falls the interest share thins and the capital share grows. That is why overpaying early is worth so much more than overpaying late: a euro put in during the first years removes a euro of debt that would otherwise have accrued interest for two decades.

It is also why the total is so much larger than the amount borrowed. The same loan repays €225,281 in all, €75,281 of it interest: half as much again as the house cost in the first place.

How to calculate a loan payment

The formula is the one for a level payment: payment = C × i ÷ (1 − (1 + i) to the power of minus n), where C is the capital, i is the monthly rate, which is the nominal annual rate divided by 12 and by 100, and n is the number of payments. It does not simplify to "interest divided by the years", because the interest is charged each month on the balance that is left, and that balance changes with every payment.

On €150,000 at 3.5% over 25 years: the monthly rate is 0.0029167, capital times rate is €437.50, and (1 + i) to the power of minus 300 is 0.41739, so €437.50 ÷ 0.58261 gives a payment of €750.94. That €437.50 is also, not by coincidence, the interest portion of the first payment: in month one the balance is still the whole capital.

• Amount borrowed the capital, not the purchase price. On a house, the price minus your deposit.
• Annual rate the nominal rate, as a percentage. Use the APR instead and the instalment will come out slightly too high, because the APR has fees baked in.
• Years the term. Lengthening it lowers the instalment and raises the total paid, every time.
• Read the total the headline is the monthly figure, but the number that should drive the decision is the total interest underneath it.
• The rate-rise line what the instalment becomes with one point more. On a variable rate, that is the figure to check you could still pay.

Nominal rate against APR, and the other words in the contract

• Principal the amount borrowed, before any interest.
• Nominal rate the interest rate alone, used to compute the instalment. In Italy, the TAN.
• APR the rate including compulsory fees and insurance: the figure to compare two offers on. In Italy, the TAEG.
• Amortisation the schedule by which capital is repaid. The constant-instalment method used here is the French schedule, the European default.
• Early repayment paying capital ahead of schedule. It removes future interest, which is why it is worth most in the early years: check whether your contract charges a penalty.

Fixed against variable, and how much the term costs

A longer term is the most tempting lever and the most expensive. Taking the same €150,000 at 3.5% over 30 years instead of 25 drops the monthly payment by about €77, and adds about €17,200 to the total interest, because you are renting the money for five more years. The instalment is what you can afford; the total is what it costs, and they pull in opposite directions.

A variable rate is not simply cheaper. It usually starts lower, and it moves with a reference index, so the instalment you sign is not the instalment you will be paying in year seven. The honest test is the one in the last line of the result: work out the payment a point or two higher and ask whether that is still comfortable. If it is not, the lower starting rate is not a saving but a bet.

And the instalment is not the whole cost of a mortgage. Arrangement fees, a survey, notary and registration costs, and compulsory insurance all sit outside this calculation, which is exactly why the APR exists. Compare offers on the APR; plan your month on the instalment.

When the calculated payment looks wrong

• The payment is far higher than the lender quoted check whether you entered the APR instead of the nominal rate, or months where the field asks for years.
• The total interest looks impossible it usually is not. Over twenty-five years, interest of half the capital again is ordinary.
• “Values have to be greater than zero” an empty amount or term. A zero rate is allowed, that is interest-free credit, but a zero term is not.
• The last payment leaves a few cents rounding. Lenders settle it in the final instalment, which is why the last one is often a few cents different.
• Your bank’s figure differs slightly day-count conventions. Some lenders charge interest on actual days rather than equal twelfths, which moves the instalment by small amounts.