Mortgages
APR calculator: what a mortgage really costs
The nominal rate says how the payment is computed. The APR says what the offer costs, because it carries the compulsory charges too: it is the only figure by which two proposals can be compared. Work it out here, and see which line is pushing it up.
The rate you negotiate is not the rate you pay
The nominal rate is a rule for computing: it says how the payment follows from the amount and the term, and nothing else. It knows nothing of the arrangement fee withheld at drawdown, the valuation paid to the surveyor, the tax that goes to the state, the two euros on every payment or the policy the lender insists on. All of them are paid in order to get that credit on those terms, and so all of them are part of its price.
The APR puts the picture together on a principle that is easy to state and impossible to solve by hand: it is the rate at which the sum you actually received is worth, today, exactly as much as every payment you will make. There is no closed form for it. It is found by search, which is why a calculator here earns its place rather than being a convenience.
The useful number, though, is not only the APR: it is knowing which line is pushing it. A three-hundred-euro valuation on a thirty-year loan barely moves it, while two euros on each of three hundred and sixty payments moves it a good deal more. The chart separates the contributions precisely because a negotiation happens one line at a time.
Common mistakes
- Comparing two offers on the nominal rate. It is the figure quoted first and the one that says least.
- Forgetting the recurring charges. Two euros a payment looks like nothing and over thirty years is worth more than a valuation.
- Entering the insurance as an upfront cost when it is an annual premium: where it falls in time changes the answer.
- Believing a lower APR always means a lower payment. They are different things: the APR measures cost, the payment measures what you can carry.
Frequently asked questions
Why is the APR higher than the nominal rate?
Because the nominal rate is only the rate the payment is computed from, while the APR measures the whole cost: arrangement fee, valuation, tax, the charge on each payment and any compulsory insurance. Some of those are withheld at the start, so you receive less than you are charged for, and the effective rate rises.
Can two loans at the same nominal rate cost differently?
Yes, and often they do. That is why publishing the APR is a legal requirement: comparing two offers on their nominal rate is like comparing two cars on the list price while ignoring delivery and the compulsory extras.
What goes into the APR and what stays out?
Everything compulsory in order to obtain the credit on those terms goes in. Optional and contingent charges stay out — late-payment penalties, the cost of settling early — because they depend on future behaviour rather than on the contract itself.
Why do upfront costs weigh more on a short loan?
Because a cost paid once is spread over the term: across five years it bites far harder than across thirty. The chart on this page shows each line's weight, and changing the term moves it.
Is the APR here the one in the contract?
It is computed on the same principle — the rate that makes the sum received equal in present value to the payments made — but the result depends on the lines you enter. If the lender counts a charge you left out, their APR will be higher.
How this calculation works
The APR is the rate at which the net present value of the operation is zero. With A the sum actually received — the amount borrowed less the costs withheld at the start — and P_k the payment in period k, the periodic rate i solves A = Σ P_k / (1 + i)^k. The equation has no closed form and is solved by bisection: the present value falls as the rate rises, so exactly one root lies in the useful interval and halving always converges on it. The annual figure follows by compounding: APR = ((1 + i)^p − 1) · 100, with p the number of payments in a year. Annual premiums are placed in the period they actually fall due rather than spread across the payments, because position in time changes present value.
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