How is a mortgage payment worked out?
The formula behind every monthly instalment, with one loan worked through step by step.
Mortgage calculator
- Loan€200,000
- Rate4% a year
- Term30 years
Monthly instalment€954.83
From a yearly rate to a monthly one
The rate in your offer is yearly. Each month the lender uses a twelfth of it: 4% a year is 0.3333% a month, or 0.003333 as a decimal.
Each month’s interest
Interest = what you still owe × the monthly rate. On €200,000 at 4%, the first month’s interest is €200,000 × 0.04 ÷ 12 = €666.67.
The rest of the instalment repays the loan, so the next month’s interest is a little lower: €665.71.
The formula for an equal instalment
Instalment = L × r ÷ (1 − (1 + r)−n), where L is the loan, r the monthly rate and n the number of months.
On €200,000 at 4% over 30 years (n = 360), that’s €954.83 a month. In the first month, €666.67 is interest and €288.16 repays the loan.
The total interest
Total interest = instalment × n − L. Here, €954.83 × 360 − €200,000 comes to about €143,740, over 70% of the loan.
The formula for decreasing instalments
Each month you repay the same slice, L ÷ n, plus interest on what’s left. On the same loan, the first is €555.56 + €666.67 = €1,222.23, and each after it about €1.85 less.
Total interest = L × r × (n + 1) ÷ 2: about €120,330, some €23,400 less than with equal instalments.
Questions people ask
I know my instalment. How do I work out the rate?
No formula gives the rate directly. Enter the loan and the term in the mortgage calculator, then change the rate until the instalment matches yours.
Why is my lender’s figure slightly different?
Lenders round each month’s interest to the cent, and some work it out by the day. With a variable rate, the instalment also changes at each review.
What’s the difference between the rate and the APR?
The formula uses the rate, the one interest is charged at. The APR adds fees and required insurance, so it’s the number to compare offers by.
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