Skip to content

El Cerebro

Mortgage and housing

Mortgage payment

The monthly payment on a loan and the path the outstanding capital travels over its whole life.

What it does

It calculates the constant payment on a loan under the French amortisation system from the amount, the annual interest rate and the term in years. It also builds the amortisation schedule month by month, with the part of each payment that goes to interest and the part that goes to capital, and summarises it in the total interest and the total paid.

Key concepts

  • French amortisation system: the payment is the same throughout the life of the loan. Each month the interest on the outstanding balance is paid, and everything left over from the payment goes to reducing that balance.
  • Monthly interest: the annual interest rate divided by twelve. It is the conversion that produces the most errors when calculating a payment by hand: an annual 3 % is twelve payments of 0,25 %, not twelve of 3 %.
  • Amortisation: the part of the payment that goes to capital. At the start of the loan it is a small fraction of the payment and at the end it is almost all of it, because interest is calculated on an ever smaller balance.
  • Total interest: the sum of the payments minus the amount borrowed. It does not include fees, insurance or expenses; to compare offers the TAE is used, which does include them.
  • Term: the number of years. Lengthening it lowers the payment and raises the total paid, because the credit is repaid over more time.

Frequently asked questions

How is the payment calculated?

With the formula of the French system: payment = amount · m / (1 − (1+m)^−N), where m is the monthly interest rate and N the number of payments in months. With 200.000 € at 3 % over 30 years, the payment comes out at around 843,21 €.

Why doesn't the payment change even though the balance falls?

Because the payment is constant by definition in this system. What changes is its composition: at the start almost all of it is interest. Each month the interest on the outstanding balance is paid, and the difference up to the fixed payment is what amortises capital.

What happens when the term is lengthened?

The monthly payment falls, because there are more payments to repay the same amount. The total paid rises, because the outstanding balance stays around longer and keeps generating interest. The calculator's detail shows both figures, so that the comparison does not depend on the payment alone.

What happens with an interest rate of zero per cent?

The closed formula turns into a division by zero, and its limit is the amount split into equal parts: 60.000 € over ten years gives 500 € a month. It is not a degenerate case, it is a loan with no interest cost.

What is shown on the chart?

Two curves per year: the outstanding capital, which falls to zero in the last month, and the accumulated interest, which rises. The distance between the two widens slowly at first, and that shape explains why the first years of a mortgage are paid almost entirely in interest.

Is there any opening cost, insurance or valuation?

No. The account only knows the amount, the interest rate and the term, which is what determines the payment. The other items of the credit are not calculated here, so the total paid is that of the payments and not that of the complete operation.

What limits do the fields accept?

The amount runs from 0 to 2.000.000 €, the annual interest rate from 0 % to 25 % and the term from 1 to 35 years. An empty field does not equal zero: the calculator distinguishes between not having filled in the amount and having typed a 0, which would be two very different loans.

Related calculators

A note to Cerebro

What would you improve?

A member of the team reads it. Tell us what brought you here and what was missing.

The tone of your visit
Between 10 and 2000 characters.0 / 2000

Only if you want an answer.