Borrowing capacity, income and budget · Guide
Calculating the monthly repayment on a mortgage: the formula in six steps, and its blind spots
Calculate the monthly repayment on your mortgage in six steps, then see what the formula omits: insurance, guarantee, fees, APR and usury.
The monthly repayment on an amortising loan with constant instalments is calculated using the constant annuity formula, based on three inputs: the borrowed capital, the interest rate converted to a monthly rate and the number of instalments. The result is an instalment excluding insurance: the insurance premium is added to it, and the guarantee and fees remain outside the formula, whereas they are included in the APR, which is capped by usury regulations.
By Sandy MASCART, mandataire d'intermédiaire en opérations de banque et en services de paiement ORIAS 26000541 sous le mandat de CDV PATRIMOINE & ASSURANCE (ORIAS 14005573)
Key points
- The monthly repayment on an amortising loan depends on three inputs: the capital, the interest rate converted to a monthly rate and the number of instalments.
- The formula yields the instalment excluding insurance: neither the insurance premium, nor the guarantee, nor the fees are included in it.
- The rate used in the calculation is the interest rate. The APR, including fees and mandatory insurance, is the one capped by usury regulations.
- The debt-to-income ratio is measured on the monthly repayment including insurance, not on the one yielded by the formula.
- Never compare two loan offers by their monthly repayment alone: the APR and the total cost, over an equal term, distinguish them.
The monthly instalment of a mortgage is calculated using a formula, that of the constant annuity, and three inputs: the principal, the interest rate, and the term. You must then add what it omits: insurance, guarantee, and fees. See the borrowing capacity, the reverse path in the capacity of a first-time buyer, and the amortisation schedule.
The formula for the monthly instalment
It is derived from the principal, the monthly debit interest rate, and the number of instalments, and it works in both directions. At a zero rate, it is the principal divided by the number of instalments.
M = C × i ÷ (1 − (1 + i)^(−n))
| Letter | What it designates | Where to find it on an offer |
|---|---|---|
C |
The borrowed principal, including financed fees | The loan amount |
i |
The annual debit interest rate, divided by twelve | The debit interest rate, not the APR |
n |
The term in years multiplied by twelve | The term, or the number of instalments |
M |
The instalment excluding insurance, constant | The result |
The interest, heavy at the beginning, diminishes; the share of principal grows. Doubling the term does not halve the monthly instalment (choosing the term).
Six steps on a calculator
- Monthly rate: annual rate ÷ 100 ÷ 12. This is
i. - Instalments: years × 12. This is
n. - Factor:
(1 + i)to the power−n, between zero and one. - Denominator: one minus this factor.
- Monthly instalment:
i÷ denominator ×C. - Check:
M × n − C= total interest, positive.
A few cents of discrepancy with the bank? It may use the equivalent monthly rate. The schedule of the offer prevails. At a zero rate with a deferral, divide by the months that follow it (PTZ and debt, the smoothing).
Check the example in an advertisement
A displayed rate requires a representative example in a fixed format:
L'exemple doit en outre être présenté dans des caractères au moins aussi grands que ceux des informations complémentaires : il ne se relègue pas en note de bas de page.
- En vigueur depuis le
- Source
- Article R. 313-2 du code de la consommation — Légifrance
Recalculate it: a significantly higher instalment includes something else, for example, insurance.
Insurance is added to the instalment
Calculated on the initial capital, it is constant; on the outstanding capital, it decreases.
Le taux annuel effectif de l'assurance (TAEA)
À l'exclusion de tout autre taux, sur les documents remis avant l'offre qui chiffrent l'assurance : un pourcentage du capital présenté comme « le taux de l'assurance » n'y a pas sa place.
- En vigueur depuis le
- Source
- Article L. 313-8 du code de la consommation — Légifrance
- En vigueur depuis le
- Source
- Article L. 313-8 du code de la consommation — Légifrance
The debt-to-income ratio is measured including insurance:
Avec une assurance dont la cotisation décroît, la mensualité la plus lourde est la première : c'est elle qu'il faut confronter à ce plafond, pas une moyenne.
- En vigueur depuis le
- Source
- Décision D-HCSF-2021-7, art. 1er — Légifrance
Compare two contracts: the TAEA.
Guarantee, fees, intermediary: separate, but counted
Paid upfront, they are included in the APRC as soon as they are necessary for the credit.
Financed by the loan, they inflate C.
Le même texte y range les frais de dossier et les coûts d'assurance et de garanties obligatoires, dès lors qu'ils sont nécessaires pour obtenir le crédit. Cela vaut pour tout intermédiaire, Sandy MASCART compris : une rémunération due pour obtenir le prêt figure dans le TAEG de l'offre.
- En vigueur depuis le
- Source
- Article R. 314-4 du code de la consommation — Légifrance
Ils pèsent sur le budget de l'achat sans entrer dans le coût du crédit. Une garantie, elle, y entre : elle est exigée pour obtenir le prêt.
- En vigueur depuis le
- Source
- Article R. 314-5 du code de la consommation — Légifrance
See the guarantees and the ancillary fees.
The APRC does not go into the formula
The APRC is the rate that equalises the amount borrowed and everything you will pay. In the formula, it yields a false instalment.
Calcul actuariel par méthode d'équivalence, intérêts composés
Actuarielle : le TAEG est un résultat, pas une donnée d'entrée. On ne le choisit pas, on le trouve.
- En vigueur depuis le
- Source
- Article R. 314-3 du code de la consommation — Légifrance
The nominal interest rate constructs the instalment; the APRC distinguishes between the loan offers.
The usury threshold
The APR cannot exceed the threshold for its category, which is set each quarter. A manageable instalment can become impossible if the insurance pushes the APR above that limit.
Il s'applique au TAEG de l'offre, assurance et frais compris. C'est une borne légale, pas un taux proposé.
- En vigueur depuis le
- Source
- Légifrance
Même assiette. Changer de durée peut faire changer de catégorie, donc de seuil.
- En vigueur depuis le
- Source
- Légifrance
Application blocked: the usury rate.
When the formula no longer fits
- Variable rate: the instalment or the term changes (the clause).
- New build: first, interim interest.
- Several loans: several instalments.
- Capped term, including any deferral:
Elle borne le nombre d'échéances que l'on peut mettre dans la formule. Un allongement limité existe quand l'entrée dans le logement est décalée, par exemple dans le neuf.
- En vigueur depuis le
- Source
- Décision D-HCSF-2021-7, art. 1er — Légifrance
Three instalments, three uses
| The figure | What it contains | What it is used for |
|---|---|---|
| The one from the formula | Capital and interest | Checking the offer |
| The one leaving the account | Plus insurance | Budget and debt-to-income ratio |
| The total cost | Plus guarantee, fees, intermediary | Comparing, via the APR |
Never compare two offers by their instalment alone.
As a mortgage intermediary working under mandate, I do not set any rate; I present the proposals line by line (documents, fees). An instalment that does not fall due on the correct date can be adjusted by telephone.
Create your file: the offers compared line by line.
Sources
- Article R. 313-2 du code de la consommation — Légifrance
- Article L. 313-4 du code de la consommation — Légifrance
- Article R. 313-1 du code de la consommation — Légifrance
- Légifrance — Article L. 313-25 du code de la consommation
- Article R. 314-4 du code de la consommation — Légifrance
- Article R. 314-5 du code de la consommation — Légifrance
- Article L. 313-8 du code de la consommation — Légifrance
- Légifrance — Article L. 314-6 du code de la consommation
- Décision D-HCSF-2021-7 — Légifrance
Read next
- How much can I borrow? Mortgage capacity in Lyon
- Mortgage amortisation schedule: how to read and check it yourself Amortisation schedule: verify each line with three checks, read the interest, capital and insurance, and see the effect of an early repayment.
- APR: How to read it and compare two loan offers without making a mistake The APR brings together interest, file fees, guarantee, required insurance and intermediary fees. What it contains, what it ignores, how to compare.
- What salary do you need to borrow €200,000 in Lyon? What salary to borrow €200,000: calculating the minimum income, and why disposable income, term and insurance can weigh as heavily as the cap.
- What term should you choose for your mortgage: fifteen years, twenty years, or longer? Paying the least interest without strangling your budget: what each term changes, how far the lender can extend it, and the method for choosing.
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