Every fixed-rate mortgage payment comes from one formula. This piece walks through it with real numbers, using the same maths as the mortgage calculator on this site: a €200,000 loan over 25 years at a fixed 3.8%.
A mortgage is repaid in equal monthly payments. Each payment covers that month's interest first, and whatever is left pays down the loan.
The formula
The monthly payment is P × r ÷ (1 − (1 + r)^−n). P is the amount you borrow, r is the monthly rate (the yearly rate divided by 12), and n is the number of monthly payments.
P = 200,000
r = 0.038 / 12 = 0.0031667
n = 25 × 12 = 300
payment = 200,000 × 0.0031667 ÷ (1 − 1.0031667^−300)
= 633.333 ÷ 0.612678
= €1,033.71Where each payment goes
In the first month, interest is €200,000 × 0.0031667 = €633.33. The rest of the €1,033.71, €400.38, reduces the loan.
Because the balance shrinks, the next month's interest is a little lower and a little more goes to the loan. By the last payment, interest is €3.26 and €1,030.45 pays off what's left.
Over the first year, €7,515 goes to interest and €4,889 to the loan. In year 25 it's €252 and €12,153. The balance only drops below half the loan in year 16. In total you pay €310,114: the €200,000 you borrowed plus €110,114 of interest.
Why the length matters
The same loan over 20 years costs €1,190.99 a month and €85,837 in interest. Over 30 years it's €931.91 a month and €135,489 in interest. A lower monthly payment means paying for longer, so more interest in total.
What this leaves out
- Fees, insurance and taxes on the loan, which add to the real cost.
- Variable rates. The payment is recalculated when the rate changes; the calculator's variable scenarios show how.
- Paying extra early. It cuts the total interest, because it lowers the balance that interest is charged on.
What's next
Try your own numbers in the mortgage calculator. A future piece compares fixed and variable rates.
General information only, not financial advice.