Mortgages

Variable-rate mortgage calculator

The rate is an index plus a fixed spread, and only the index moves. This shows the instalment today, what it becomes if the index rises, and how many points it can rise before passing the ceiling you set.

What a variable rate is actually choosing

A variable-rate mortgage charges a market index — Euribor in the euro area — plus a fixed spread the lender sets at signing. The spread never changes; the index does, and at each contractual reset the instalment is recomputed on the balance that is left and the instalments that are left. That is why the same move in the index bites far harder in year two than in year twenty: in year two, nearly all of the debt is still there to be repriced.

The question worth asking is not what you pay today but what you could come to pay. A variable rate almost always starts below the fixed one, and that opening difference is the payment for a risk that stays entirely with the borrower. The number you need is the threshold: how many points the index can rise before the instalment passes what the household budget carries. If that margin is under two points, the variable rate is a narrow bet.

The rise is not proportional, and that is the second thing people miss. Doubling the rate does not double the instalment, but nor does it add half: the interest share of each instalment grows faster than linearly, the more so the longer the remaining term. It is why a three-point scenario has to be looked at rather than extrapolated by eye from the one-point one.

Common mistakes

Comparing fixed and variable on the opening instalment alone. The initial difference is the price of the risk: the honest comparison is the fixed instalment against the variable one in the rise you think plausible.
Scaling the rise in proportion. If one point up costs 100, three points do not cost 300 but more, because the relation between rate and instalment is not linear.
Simulating the rise on the original amount instead of the outstanding balance. A rise after ten years lands on a much smaller debt over fewer instalments, and hurts appreciably less.

Frequently asked questions

How is a variable-rate instalment worked out?

With the same formula as a fixed rate, but recomputed at each reset on the outstanding balance and the instalments that remain, using the rate of the moment: index plus spread. The instalment is therefore fixed only until the next reset, not for the whole term.

What is the spread on a mortgage?

The margin the lender adds to the reference index, set at signing and unchanged for the whole term. Two offers on the same index are compared precisely on the spread, because it is the only part the lender decides.

How far can a variable instalment rise?

There is no ceiling unless the contract provides a cap. The practical way to think about it is the threshold: the index level at which the instalment reaches the most you could carry, and how many points of margin you have from here.

Is a variable or a fixed rate better?

Variable starts lower and wins if rates stay put or fall; fixed costs more at the start and buys certainty. The practical test is the margin: if the instalment survives a rise of two or three points without straining the budget, variable is bearable; otherwise the certainty of a fixed rate is worth its price.

How this calculation works

Rate charged: index + spread, floored at zero. Instalment: R = D·i/(1 − (1+i)^−m), where D is the outstanding balance, m the instalments left and i the period rate — the annual rate divided by the number of instalments a year. Balance after k instalments: D = C·(1+i₀)^k − R₀·((1+i₀)^k − 1)/i₀, computed at the opening rate. At each index level the instalment is recomputed on D and m, which is what the lender does at every reset. The curve runs five points below to five points above today's index in quarter-point steps; the threshold is found by linear interpolation between the two curve points straddling the ceiling, because the relation between rate and instalment is not linear and there is no closed form for it.

Mortgage payment

What you will pay each month, and what it costs in total.

Remortgaging

Compare the present mortgage with an offer from elsewhere.

Early repayment

What paying a lump sum off the capital is worth.

Installment comparison

Comparison table: how the instalment changes as you borrow less or shorten the mortgage term.