# Overall effective rate

The **global effective rate** ( **TEG** ) ^{1} is the translation, in the form of a rate , of the real cost of a mortgage or consumer credit according to the calculation standards applied in France . This rate must be provided obligatorily by the French credit institutions in the credit offer proposed to the borrowers.

The actual cost of a loan is difficult to determine given the very different financial terms that may be included in a credit offer and the complexity of the actuarial calculation . The TEG takes into account all these parameters and allows the borrower to know the real cost of his credit and to be able to compare the offers of the various credit institutions. The calculation of the TEG takes into account the interest rate but also the periodicity of repayment ( *monthly, quarterly,* in fine *, …* ) of the credit, as well as all the expenses and accessories related to this credit and paid by the borrower. (administrative fees , credit insurancemandatory, other commissions ). The TEG is finally and above all the measuring tool prescribed by the Consumer Code to ensure that the cost of credit does not exceed the rate of wear .

## France

**Introductory remark**

- Since 1
^{st}July 2016, the provisions of the Consumer Code have been renumbered. This new codification was made at constant right. For the sake of clarity, it has been chosen, until further notice, to keep the numbering in force prior to this new codification.

### Definition

The TEG is one of two existing effective rates , with the APR.

The TEG, taken broadly, is based on an interest rate , known as the “borrowing rate” or “nominal rate”, plus a set of credit-related costs. The difference between the TEG and the nominal rate of the loan makes it possible to know the actuarial impact ( *the rate supplement* ) of the costs and accessories attached to the granting of the credit. From this point of view, the TEG is one of the elements that contribute to the responsibility of the banker providing credit .

The debtor interest rate can be presented in two different ways: either it is a fixed rate over the life of the credit, or it is a revisable rate, according to the revision rules specified in the loan agreement. In most cases, the monetary index used is either the EURIBOR 1-year rate or the EURIBOR 3-month rate plus a fixed element expressed as a percentage (or *rate points* ). Like Anglo-Saxon countries, the first revision can take place after several years of application of the initial rate. Other indices may be used, but are preferably reserved for professionals or knowledgeable customers.

In the case of a revolving loan and until 2008, the calculation of the TEG was based on the initial loan rate, the only known and certain at the date of signature of the contract. Place agreements, signed by the credit institutions in 2008/2009 at the initiative of the public authorities, agreed that the value of the borrowing rate on the date of the first revision would henceforth be taken into account for the calculation of the TEG. , whether in three months or in 10 years. The rule, specified in the loan agreement, is to take the value of the known benchmark at the beginning of the month of the offer, plus the fixed component, and apply it to the depreciation schedule that follows. the first revision of the rate, while respecting the rules of revision of the deadlines described in the contract.

The transposition in 2016 of the European directive on the TAEG of real estate loans granted to individuals organizes the maintenance of this principle. It states that this method is applicable if the borrowing rate thus revised is higher than the initial rate, in order to avoid that the TEG of an adjustable rate loan may be lower than or equal to the initial loan rate, as observed in some cases since 2009, distorting the two main objectives of the TEG: not to exceed the rate of wear; give a measure in points and hundredths of a rate point of the charges incurred in respect of the credit in addition to the loan rate.

The TEG is calculated at the latest on the date of the signature of the credit agreement, on the basis of known and certain elements at that date ( *see Article L.313-1 of the French Consumer Code* ).

### The TEG includes all costs related to the granting of credit

The main costs attached to a loan are **all costs determined or determinable when the loan contract is signed** , such as, for example:

- the application fees (
*or tuition fees or loan account opening fees*) - insurance contributions (or borrower insurance ) if compulsory subscription to obtain the credit
- commissions paid, for example, to banking intermediaries for obtaining credit
- the costs of setting up a guarantee (
*mortgage,*suretyship*, pledging fees for life insurance contracts or UCITS units*), but not the full amount of the notary’s fees (*distinguishing the “sales expenses”, excluded, and the “loan fees”, included*^{2}) - subscriptions of shares, in cooperative banks, if the opening of the current account is linked to obtaining credit
- loan account management fees (
*to be distinguished from the current account*) opened on the occasion of the conclusion of the loan agreement

and **actually borne by the borrowers** .

Costs related to the execution of the loan contract are excluded ( *for example, the fire insurance premiums included in the Multi-Risk Home insurance premiums that are not lacking to subscribe any responsible occupant. see the judgment of the Court of Cassation of 12 July 2012 – Civ, 11-13.779* ).

It is useful to distinguish between ancillary costs related to services ( *maintenance for example for a car loan* ) to incidental insurance costs.

Some practices aim to develop financing products and solutions that are legally similar to leases, thus avoiding the obligation to produce the TEG contractually. Communication, the rate, often promoted by advertising is usually short ( *12 or 24 months, especially for consumer credit , which does not use the TEG, but the APR* ) or even the if applicable, with a very limited promotional effect over time.

Legislation tends to clarify these processes by imposing advertising on a TEG standard on the one hand and by managing the “announcement effect” by obliging the advertiser to be more rigorous and more precise in terms of information. total cost of the credit transaction, at the price of less readable advertising.

Thus, the customer must be able to understand the characteristics of the offer of credit made to him and financially weigh his risk taking and his commitment.

The overall percentage rate has been set in order to allow borrowers to compare on a single basis the credit proposals made by different credit institutions with different characteristics ^{3} .

Note: TEG is mandatory when submitting a mortgage offer or advertising for a loan; credit agencies communicate with examples of credits with disability death insurance (ADI). The TEGs communicated therefore take into account this ADI insurance, as long as it is mandatory.

### Uses of TEG

Prior to March 21, 2016, the TEG applied to home mortgages.

The APR applies to consumer credit for individuals, from the 1 ^{st} July 2002, as well as housing loans for individuals, since March 21, 2016 ( 1 ^{st} October 2016 in France).

The TEG therefore concerns loans to companies and legal persons under public law, or even other forms of credit to individuals than those to consumption or real estate ( *which remain to be specified* ).

### The “Equivalent” Effective Rate is the APR

Distinct from the TEG, the APR is the effective rate used in France for the main loans to individuals, whether consumer loans or mortgages.

The principle of the APR is laid down by Article L. 314-3 of the Consumer Code , the 1 ^{st} July 2016; its calculation is defined in the Annex Article R.313-1 ^{4} of the Consumer Code :

- it is an annual rate, in arrears, expressed as a percentage and calculated using the equivalence method;
- its accuracy is at least one decimal;
- the unit of period corresponds to the periodicity of the payments.

Examples are given in Decree No. 2002 – 928 of 10 June 2002, made pursuant to Article 1 ^{st} of Decree No. 2002-927 of 10 June 2002 concerning the calculation of the annual percentage rate of consumer credit and amending the Consumer Code.

Like the TEG, it includes all costs related to the credit , with the notable exception of notarial fees – if applicable.

It is legally presented as “APR”: Annual Global Effective Rate (Decree No. 2002-928 of 10 June 2002), described here as the annualized annualized rate of employment .

Note: the translation of this acronym is unfortunate for two reasons: a rate is always, by international convention, an annual data, unless expressly stated otherwise; the letter “A” meant in the European directive of “actuarial” origin, as opposed to “proportional”.

#### Formula for calculating the APR

It is a question of solving the equation below, of unknown the TAEG:

**K**is the amount lent, assumed to be paid in full and at one time;**k**is the order number (*or rank*) of payment of a due date and / or fee; the serial number{\ displaystyle k = 1} refers to the fees paid immediately, at the same time as the payment of the funds, that is at the moment {\ displaystyle t_ {1} = 0} ;**n**is the last payment order number of a due date or fee;- {\ displaystyle F_ {k}} is the amount of a due date and / or fee payable at order number k;
- {\ displaystyle t_ {k}} means the time interval, expressed in years and fractions of years, between the date of payment of funds, the source of the calculation, and the date of each subsequent payment.

In the case of split payments of funds ( *or multiple loans in the same contract* ), for known amounts fixed in advance, on different dates, known and fixed in advance, the calculation formula is as follows:

**i**is the serial number of the split payments of funds (*or the release of loan number i*);**p**is the last order number of the split installments of the funds (*or the release of the last loan*);- {\ displaystyle K_ {i}} is the amount of the loan (or credit) paid to order number i;
- the total amount of the credit granted is equal to {\ displaystyle K = \ sum _ {i = 1} ^ {p} K_ {i}} ;
- {\ displaystyle t ‘_ {i}}means the time interval, expressed in years and fractions of years, between the date of the first payment of funds (
*or the first credit*), the source of the calculation, and the date of each subsequent payment; - in this case of split payments of funds, this is the serial number {\ displaystyle i = 1} which defines the origin {\ displaystyle t ‘_ {1} = 0} the calculation of time intervals;
- sums paid on both sides of equality at different times are not necessarily equal amounts or paid at equal time intervals;
- by definition, we have {\ displaystyle t ‘_ {1} = 0 \ leq t_ {1}} .

#### Examples

The examples below are taken from those in the annex to Decree No. 2002 – 928 of 10 June 2002. The basis of calculation is a standard year, ie: one year = 365 days or 365.25 days or 52 weeks or 12 months standardized. A standard month is 365/12 = 30,416 66 days, a year has 12 normalized months and 365 days, whether the year is leap year or not.

##### Single deadline

Total amount of loan K = 1.000 €, as of 1 ^{st} January 2001. It is paid at once and in full on 1 ^{st} July 2002 in the amount of € 1,200, or 1.5 year later or so 365 + 182.5 = 547.5 days after the starting point of the credit.

The **APR** is the rate **x** which verifies the following equation:

**x**= 0.129 24 rounded to 12.9%, or else 12.92% if a precision of two decimals is preferred.

##### Single expiry and initial costs

Total amount of loan K = 1.000 €, as of 1 ^{st} January 2001. It is paid at once and in full on 1 ^{st} July 2002 in the amount of € 1,200, or 1.5 year later or so 365 + 182.5 = 547.5 days after the starting point of the credit. The application fee is 50 €, paid at the same time as the funds are made available.

The **APR** is the rate **x** which verifies the following equation:

**x**= 0,168,526 rounded to 16,9%, or else to 16,85% if one prefers a precision of two decimal places.

##### Two constant annual deadlines and initial fees

Total amount of loan K = 1.000 €, as of 1 ^{st} January 2001, repayable in two installments of 600 € each on 1 ^{st} January 2002 and 1 ^{st} January 2003, is one year and two years after the provision of funds. The application fee is 20 €, paid at the same time as the funds are available.

The **APR** is the rate **x** which verifies the following equation:

**x**= 0.164334 be rounded up to 14.6%, or else 14.63% if a precision of two decimals is preferred.

##### Three aperiodic deadlines

Total amount of loan K = 1.000 €, as of 1 ^{st} January 2001, repayable in three installments of an amount equal to

272 € after 3 months, ie 1 ^{st} April 2001 (0.25 years and 91.25 days) ;

272 € after 6 months, the 1 ^{st} July 2001 (0.5 years or 182.50 days);

€ 544 after 12 months, the 1 ^{st} January 2002 (one year or 365 days).

Total amount of payments = 1.088 €

The **APR** is the rate **x** which verifies the following equation:

**x**= 0.131855 round to 13.2%, or else 13.19% if a precision of two decimals is preferred.

##### Constant monthly maturities at the beginning of the month

Total amount of loan K = 1.000 € made the 1 ^{st} of January. The monthly periodic standard rate charged by the lender is 0.50%. The repayment schedule provides 36 equal monthly installments of an amount equal to € 30.42, to pay the 1 ^{st} of each month, from the 1 ^{st} of February.

##### Constant monthly maturities at the end of the month

Or a loan of amount K = 1.000 € granted on February 28 ( *end of the month* ). The monthly periodic standard rate charged by the lender is 0.50%. The repayment schedule includes 36 constant monthly payments amounting to € 30.42, to be paid at the end of the month, starting on March 31st.

The **APR** is the rate **x** which verifies the following equation:

The resolution of the equation by successive iterations ( *programmable on free or commercial calculation software* ) gives **x** = 6.2% or 6.16% if a precision of two decimal places is preferred.

##### Constant Maturities plus Initial Costs

Total amount of loan K = 1.000 € made the 1 ^{st} of January. The monthly periodic standard rate charged by the lender is 0.50%. The latter retains a € 10 processing fee on the payment of funds. The repayment schedule provides 36 equal monthly installments of an amount equal to € 30.42, to pay the 1 ^{st} of each month, from the 1 ^{st} of February.

The **APR** is the rate **x** which verifies the following equation:

The resolution of the equation by successive iterations ( *programmable on software of free or commercial calculations* ) gives **x** = 6.9% or 6.88% if one prefers a precision of two decimal places.

##### Constant Maturities and Total Non-Full Duration

Or a loan of amount K = 10.000 € granted on September 15th. The conventional rate charged by the lender is 8.70%, or 0.725% per month ^{[What?]} .

The repayment schedule includes 36 constant monthly payments of an amount equal to € 317.74, to be paid at the end each month, starting on October 31st. Two methods can be used indifferently to determine the **APR**according to the following principle: the differences between two dates can be measured either by relating the exact number of days of this period to 365, or as an entire fraction of the year for the part bounded by identical monthly dates, to which is added or subtracted the number of days remaining reported at 365.

**Method 1** : 46 days ago between September 15th and October 31st.

The **APR** is the rate **x** which verifies the following equation:

*programmable on free or commercial calculation software*) gives

**x**= 9.0471%, rounded to 9.0% or 9.05% if a precision of two decimal places is preferred.

**Method 2** : 15 days ago between the 15th and the 30th of September.

The **APR** is the rate **x** which verifies the following equation:

*programmable on free or commercial calculation software*) gives

**x**= 9.0571%, rounded to 9.1% or 9.06% if a precision of two decimal places is preferred.

**Conclusion** : two methods of calculation are allowed, two different results result. And neither will be declared erroneous (this *is the meaning of the judgment of the court of cassation of 26.11.2014* ).

##### Note Bene relative to the last example

- There is a slight error in the example number 5bis of the decree cited in reference. The spirit is not changed.

It is mentioned a constant maturity of an amount equal to 317.73 €, while the equation of method 1 retains 317.78 €. Notwithstanding this tiny shell, interest accrued as at 31 October, the date of payment of the first maturity, corresponds to 1.5 months normalized, or 108.75 €. The constant repayment term of the credit is therefore equal to € 317.74, solution in **m** of the actuarial equation below, with i = 0.725%:

- If one wishes to keep both examples of the decree, then the following clarifications should be made.

On 46 days, are due € 109.64 of interest to be paid on October 31st. The constant maturity is equal to 317.77 €, solution in **m** of the following equation:

If there are 15 days and then a normalized month of interest, the latter amount to 108.25 €, the constant maturity to 317.73 €, solution in

**m**of the following equation:

Reminder: in each case, it must be ensured that the **APR** thus determined does not exceed the rate of wear and tear of the credit category and the quarter in question.

#### Details

( *applicable both for the calculation of APR and TEG* )

- The difference between the dates used for the calculation is expressed in years or fractions of years. One year has 365 days or, for leap years, 366 days, 52 weeks or 12 normalized months. A normalized month counts 30,416 66 days (ie 365/12 days), whether the year is leap year or not.
- In the event that there is uncertainty about the dates and / or the amounts of split payments of the funds, it is a rule of thumb to consider that 100% of the funds are paid immediately (
*on this point, consult the book by Gérard BIARDEAUD quoted in bibliography*) - The result of the calculation is expressed with an accuracy of at least one decimal place. If the digit of the next decimal is greater than or equal to 5, the digit of the preceding decimal place will be increased by 1.

#### Remarks

- In the case of irregular payments, the period unit is the smallest payment interval of the borrower, but can not be less than one month.
- Article R. 313-1 is the transposition into French law of Directive 98/7 / EC of the European Parliament and of the Council of.

The calculation of the overall effective rate is determined by the resolution of the equation called compound interest ( *according to the periodicity of the payments* ), or so called equivalent and more modern, of the **equality of the discounted flows** entering and leaving, to the like the calculation of an internal rate of return (IRR see Internal rate of return ).

### TEG is a “proportional” rate calculated using the actuarial method

Article R.314-2 of the new Consumer Code distinguishes a credit category for which the calculation must be made differently. These are loans intended to finance businesses, real estate and those granted to legal entities governed by public law.

The calculation must first determine, according to the actuarial method (see Actuarial rate ), the period rate, that is, the rate applicable to the repayment period (for example: the month). The annual rate is then calculated by multiplying the period rate by the ratio between the duration of the year and that of the unit period ( *ie for a monthly deadline, a multiplication by twelve* ), hence the qualifier of “proportional” .

#### Calculation formula

This is to solve the equation below, from unknown period rate **tx _{per}** :

**K**is the amount lent, assumed to be paid in full and at one time;**p**is the maturity date, that is, the number of months (*for a monthly loan*) following the full payment of funds; the rank**p = 0**refers to the fees paid immediately, at the same time as the payment of the funds. This is the rank used when we ignore the exact date of payment of certain fees. The TEG is increased by prudence;**n**is the total initial contractual term of the credit. It is expressed in number of months for a monthly loan;**F**is the amount of maturity due by the borrower at rank_{p}**p**; this amount includes the interest due over the period in question, most often the month, the amortization fraction of the loaned amount**K**, as well as periodic recurring accessories (*usually borrower insurance*) and periodic recurring*insurance*(*annual management fees loan account, for example*).

By definition, we have, for a monthly loan:

^{st}October 2016,

*mutatis mutandis*, we have, for the same loan:

All calculations are carried out with all the precision allowed by the PLC used, the rates ( *period and total number* ) are displayed with an accuracy of at least one decimal place. The use has devoted a display rounded to the first two decimals, like the interest rates of the loans or the returns of the investments communicated to the general public.

#### Lombardy Year

This period rate must itself be related to the duration of the calendar year, ie 365 days (or 366 days). However, credit institutions often practice rate calculations in a fictional year of 360 days, called Lombarde.

Historically, the reason for using the Lombarde year is that the number of divisors of 360 = 2 ^{3} × 3 ^{2} × 5 equals 24, facilitating multiple manual calculations.

However, this is the method of calculating interest on the interbank money market, in particular the EURIBOR rates . This calculation rule is called the EXACT / 360 base, an international interest rate on all rates – IBOR ( *– Interest Banking Offered Rates* ), the prefix indicating the name of the financial center on which the quotations are organized: EURIBOR for the monetary rates in Euro in Frankfurt, GBP LIBOR for the British Pound in London, like the USD LIBOR, the EURO LIBOR, … ( *on these points of market techniques, see inter alia the work of J. M Dalbarade quoted in the bibliography* ).

#### Standardized month

It should not be confused with the calculation “on the basis of the Lombarde year” ( *calculated on the basis of the exact number of days in the month – namely 28, 29, 30 or 31 days – reported 360 days, prohibited constant case law since at least 2005, although commonly used in the interbank money market* ) and the calculation according to the notion of standardized month ( *see the appendix of Article R.313-1 of the Consumer Code* ). In the first case, the stipulation of interest is erroneous, since the rate displayed is implicitly increased (the multiplier coefficient is equal to the quotient 365/360 or 366/360), while in the second case, there is no error, each month having the same duration, one twelfth of the fixed duration of the calendar year, namely 365 days.

A judgment of the Court of Cassation of June 15, 2016 (Civil Chamber, 1, No. 15-16498) indicates that it is necessary to prove by the calculation of the use of the Lombard method in place of that of the normalized month; that it is not enough to mention the mention “360” contained in the credit agreement to pronounce the forfeiture of the conventional stipulation of the interests ( *this judgment breaks the judgment of the court of appeal of Colmar of February 13, 2015* ) .

The calculation of interest on the basis of the normalized month is as follows:

- or
**K**the base for calculating the interest due on a standardized month; - either
**TX**the conventional interest rate, expressed as a percentage;

then the amount **I** of the interest due for a standard month is equal to:

The calculation in normalized months is therefore equivalent to the bond calculation method ( *also called Bond Basis* ) ^{5} , according to which each year is composed of 12 months of 30 days, ie 360 days. This calculation agreement considerably simplified the determination of the amount of the bond coupon accrued between two maturity dates.

This equivalence is recalled in a judgment of the Paris Court of Appeal of March 24, 2017 (RG 15 / 14.551) which states: *[…]; That under Article R313-1 of the Consumer Code, interest is calculated from a year of 365 days and 12 normalized months of 30.41666 days, which leads to the same mathematical result as retaining a year of 360 days and 12 months of 30 days, so that the criticism made of this head is unfounded; *.

According to this device, each month has 30,416 66 standard days, or 30 days of standardized 1.013889 day, including the month of February. For example, between March 15 and April 15, there are 30,416 66 normalized days ( *a normalized month* ) and 31 exact days. Between July 15th and September 15th, there are 60,833 33 standard days ( *ie 2 normalized months* ) and 62 exact days. For a non-leap year, between 28 February and 1 ^{st} March of the same year, there are 3,416 standard 67 days and 1 exact day. If the year is leap year, there are still 3,416 67 normalized days but 2 exact days, because of February 29th.

This method of calculation is called the proportional or legal method, since it is organized by the texts, the other bases of calculations do not respect a strict constant proportionality for the same number of days run, in particular for the calculation of the intermediate interests, those included between the the date of payment of the funds and the next due date, the duration of which is, by definition, less than one month.

The second advantage is to make the calculation of the due date of a loan independent of the date of the starting point of amortization.

Note: a year according to the Social Security is composed of 13 months of 28 days each, or 364 days.

For real estate loans, the Global Effective Rate is therefore, necessarily and until 01/10/2016, proportional to the period rate. The Court of Cassation has also recalled, in a judgment of 27 November 2013.

For information, this judgment broke a judgment of the Court of Appeal of Aix en Provence which had judged that the TEG of any credit should be an actuarial rate equivalent, that is to say a APR.

#### Examples

Below are examples of calculating the TEG of credits based on actual cases. To determine the constituent elements of the TEG in interest rate points from the interest rate of the loan, it is necessary to make the calculations step by step, adding a new element to the precedents, and not in a detailed manner, a term replacing another. . Indeed, because of the hyperbolic form of the discount function, the additional elements converted into rate points accumulate. Taking a measure of the incidence in rate points of each element taken separately, then adding them, invariably leads to a difference with the TEG calculated by integrating all the elements at one time.

##### Example 1

The TEG of a fixed-rate and constant-rate credit, without fees or accessories, is equal, regardless of the terms of repayment of capital ( *constant, progressive or decreasing terms, constant amortization, progressive or decreasing,* in fine *or the card* ) at the nominal loan rate if the periodic rate of interest calculation is proportional to the nominal rate. This intangible result is the direct consequence of the principle of construction of the amortization table of a loan.

**Proof** : either **K** the loan amount, **j** the monthly rate proportional to the credit rate and **n** the duration of the credit in number of months. We note **CRD _{p}** remaining capital after the due payment date of rank

**p**. The rank is between 1 and

**n**. We note that

**CRD**and we make the non restrictive assumption that

_{0}= K**CRD**. Let

_{n}= 0**ECH be**the constant maturity of this credit, paid during

**n**months.

At each rank

**p**we have the following recurrence relations, which give the monthly amount of interest due and due, and the depreciation portion of the capital loaned:

*see telescopic sequence*) of all these equalities makes it possible to simplify the identical terms to the left and to the right of each equality and to make appear the following result:

PS: this result is generalized with maturities that are not necessarily constant and a constant periodic interest rate.

##### Example 2

A real estate loan of € 100,000, at a fixed rate of 3.60%, redeemable in 300 constant installments ( *ie for a period of 25 years* ) in an amount equal to € 506. The tuition fee is € 1,000, the mortgage guarantee fee is € 2,500 and the death insurance premiums are payable in arrears at € 30 per month for 300 months.

The monthly period rate **tx _{per}** solution of the equation below, is equal to 0.374428% and the TEG, to 4.4931%.

The additional elements of the loan rate are as follows:

Tuition

fees : 0.09% Guarantee fee: 0.24%

Death insurance – Disability: 0.56%

( *calculations made with a pocket financial calculator of precision of 9 decimals* )

As of 01/10/2016, the APR = 4.5868% rounded up to 4.59%

##### Example 2a

A real estate loan of € 100,000, at a fixed rate of 3.60%, redeemable in 300 constant installments ( *ie for a period of 25 years* ) in an amount equal to € 506. The tuition fee is € 1,000, the mortgage guarantee fee is € 2,500 and the death insurance premiums are payable in arrears at € 30 per month for 300 months.

As this is a loan to finance the construction of a property, it is preceded by a pre-financing phase lasting 24 months. During this phase, the borrower insurance premiums and the interest on the unblocked funds are paid.

Since the amounts and dates of the unblocked funds are unknown in advance, the standard assumption ( *see BIARDEAUD* ) is that the funds are paid in full and at one time.

The duration of the credit is extended by 24 months during which the borrower is supposed to pay 30 € monthly insurance contribution and 300 € monthly interest.

The monthly period rate **tx _{per}** solution of the equation below, is equal to 0.368944% and the TEG, to 4.4273%.

Additional elements at the loan rate break down as follows:

Tuition

fees : 0.08% Guarantee fee: 0.22%

Insurance Death – Disability: 0.53%

( *calculations performed with commercial calculation software with a precision greater than 15 decimal places* )

As of 01/10/2016, the APR = 4.5183% rounded up to 4.52%

##### Example 2b

A real estate loan of € 100,000, at a fixed rate of 3.60%, redeemable in 300 constant installments ( *ie for a period of 25 years* ) in an amount equal to € 506. The tuition fee is € 1,000, the mortgage guarantee fee is € 2,500 and the death insurance premiums are payable in arrears at € 30 per month for 300 months.

As this is a loan to finance the construction of a property, it is preceded by a pre-financing phase in current account for a period of 24 months. During this phase, the borrower insurance premiums and a portion of the interest due on the unblocked funds are paid. Any interest that is due and unpaid is paid monthly, at each maturity date, to capital and is interest bearing. This is the mode of operation in “current account (which allows in particular payments and withdrawals at any time)” that allows this practice.

This method of financing the construction phase involves agreeing an amount of interest due and unpaid after 24 months. If it is for example agreed that this amount is equal to one year of interest, ie € 3,600, then the amount of capital to be repaid at the end of the construction phase is equal to € 103,600.

Since the amounts and dates of the unblocked funds are unknown in advance, the standard assumption ( *see BIARDEAUD* ) is that the funds are paid in full and at one time.

The duration of the credit is extended by 24 months during which the borrower is expected to pay 30 € monthly insurance contribution and the monthly amount of interest that can go from 100.000 € to 103.600 €. This constant monthly amount is equal to € 155.11.

At the end of the 24 months, the constant maturity of the 300 months of amortization of the debt is equal to € 524.22.

The monthly period rate **tx _{per}** solution of the equation below, is equal to 0.366739% and the TEG, to 4.4009%.

The additional elements at the loan rate are as follows:

Tuition

fees : 0.08% Guarantee fee: 0.21%

Insurance Death – Disability: 0.51%

( *calculations performed with commercial calculation software with a precision greater than 15 decimal places* )

As of 01/10/2016, the APR = 4,4907% rounded up to 4,49%

##### Example 2c

A real estate loan of € 100,000, at a fixed rate of 3.60%, for a period of 25 years, repayable *in fine* . The schedule is composed of 299 installments of an amount equal to 300 €, the last is equal to 100.300 €. The tuition fee is € 1,000, the mortgage guarantee fee is € 2,500 and the death insurance premiums are payable in arrears at € 30 per month for 300 months.

The monthly period rate **tx _{per}** solution of the equation below is equal to 0.348836% and the TEG to 4.1860%.

The additional elements at the loan rate break down as follows:

Tuition

fees : 0.06% Guarantee fee: 0.16%

Insurance Death – Disability: 0.37%

( *calculations carried out with a pocket financial calculator of a precision of 9 decimals* )

As of 01/10/2016, the APR = 4.2673% rounded up to 4.27%

##### Example 3

A real estate loan of € 100,000, at a fixed rate of 3.60%, redeemable in 300 constant installments ( *ie for a period of 25 years* ) in an amount equal to € 506. The tuition fee amounts to € 1,000, payable in 5 times without fees, with the first 5 deadlines; the security deposit is 1.850 €, the monthly insurance premiums Death Disability, payable in arrears, 30 € during the first 180 months, then 18 € during the last 120 months. The brokerage fee is 800 €.

The monthly period rate **tx _{per}** solution of the equation below is equal to 0.370574% and the TEG to 4.4469%.

Additional elements at the loan rate break down as follows:

Fees: 0.09%

Security Deposit: 0.18%

Brokerage Fee: 0.08%

Insurance Death – Disability: 0.50%

( *calculated with commercial calculation software with a precision greater than 15 decimals* )

As of 01/10/2016, the APR = 4.5387% rounded up to 4.54%

##### Example 4

A real estate loan of € 100,000, at a fixed rate of 3.60%, redeemable in 300 constant installments ( *ie for a period of 25 years* ) in an amount equal to € 506. The tuition fee amounts to € 1,000, payable in 5 times without fees, with the first 5 deadlines; the security deposit is € 1,850, of which € 300 security deposit fee payable immediately and € 1,550 bonding fee payable with the last due date; the monthly Invalidity death insurance premiums, payable in arrears, amount to € 30 during the first 180 months, then to € 18 during the last 120 months. The brokerage fee is 800 €.

The monthly period rate **tx _{per}** solution of the equation below equals 0.361931% and the TEG at 4.3432%.

The additional elements at the loan rate break down as follows:

Tuition

fees : 0.09% Security deposit: 0.09%

Brokerage fee: 0.08%

Insurance Death – Disability: 0.48%

( *calculated with commercial calculation software with a precision greater than 15 decimal places* )

As of 01/10/2016, the APR = 4,4307% rounded up to 4,43%

##### Example 5

A real estate loan of € 100,000, at a fixed rate of 3.60%, redeemable in 300 constant installments ( *ie for a period of 25 years* ) in an amount equal to € 506. The fees are 600 €, payable 24 times without fees, a constant amount equal to 25 €, the first 24 deadlines; the guarantee fee is € 2,500, payable upon payment of the funds; the monthly disability insurance premiums, payable in arrears, amount to € 30 during the first 60 months, then to € 60 during the last 240 months. The management fee of the loan account is equal to 40 €, payable in arrears, at each anniversary date of the contract, every twelve months.

The monthly period rate **tx _{per}** solution of the equation below is equal to 0.406914% and the TEG to 4.8830%.

The additional elements of the loan rate are as follows:

Tuition

fees : 0.05% Guarantee fee: 0.24%

Insurance Death – Disability: 0.93%

Loan account management fee: 0.06%

( *Calculations performed with commercial calculation software with a precision greater than 15 decimals* )

As of 01/10/2016, the APR = 4.9937% rounded up to 4.99%

### Determine with certainty the method of calculating interest on the loan

There is an indisputable method for determining whether the credit interest has been calculated according to the so-called “Lombarde” method – in financial terminology, we speak of the calculation base EXACT / 360 – or in those recommended by the texts.

It is sufficient to calculate the TEG of the credit from the schedule communicated by the lender, by integrating into the calculation formula only the non-insurance maturities of the projected depreciation schedule.

Excluding expenses and accessories, the credit TEG is equal to its nominal rate if the interest has been calculated in accordance with the texts in force.

If the interest has been determined according to the so-called “Lombarde” method, which is outlawed by consistent case law, excluding fees, incidentals and insurance, the credit TEG will be shown at the nominal rate weighted by a coefficient equal to the quotient 365/360 = 1.0139.

This result is insensitive to the terms of amortization of the credit.

For example, if the loan rate is equal to 3.60%, in the first case the TEG will equal 3.60%, while in the second case it will show a level equal to 3.65%.

Indeed, in the first case, the constant monthly maturity is equal to € 719.80. In the second case, and assuming a starting point of the amortization set at 06/01/2010 (and therefore a final maturity on 06/01/2025), the constant monthly maturity is € 722.23.

## Regulations

The overall effective rate was introduced by Law No. 66-1010 of 28 December 1966 ^{6} , which defined the notion of usurious loan as a “loan (…) granted to a TEG which exceeds by more than a quarter ( *today third party* ) the average effective rate charged by other credit institutions (…) “. To ensure that the financial conditions attached to a loan ( *interest, costs and accessories* ) do not exceed the threshold of usury at the date of obtaining the loan, the notion of TEG has been constructed to measure actuarially all the costs attached to it.

Since July 2002, for consumer credit , the *annual percentage rate of charge* (APR) has been used ^{7} , the method of calculation of which has been subject to European standardization ^{8} . The appointment of a TEG dedicated to consumer credit , then called APR , is effective in France since 1 ^{st} July 2002, following the Decree No. 2002-927 of 10 June 2002 – Art. 1 Official Journal of 11 June 2002 in force on 1 ^{st} July 2002, taken over by Law No. 2010-737 of 1 ^{st} July 2010, relating to consumer credit ^{9}.

Since 1 October 2016, by transposition of a European directive, the APR replaces the TEG for real estate loans granted to individuals. Its mention in a loan agreement is imperative ^{10} . It includes the associated costs contractually stipulated, namely filing fees, miscellaneous commissions, cost of special guarantees, insurance costs, mortgage-related deed fees, costs directly related to the granting of the loan and known at most. late on the date of signing the loan agreement.

Its normalized method of calculation ( *see Official Journal of 11 June 2002 p.10357 and that of 30 June 2016* ) allows comparisons to be made between similar credits ( *in particular, they must have the same duration and the same repayment terms* ) , while the only nominal rate of interest calculation (so-called “borrowing rate”) does not allow it.

### Penalty in case of erroneous TEG

In the event of an error in the calculation of the TEG by the lender, the maximum judicial sanction is the replacement of the conventional rate by the legal interest rate in France . The latter, published in the JORF, changes every beginning of the year, and at the beginning of each of the two semesters of the year since January 1, 2015. For information, it was equal to 0.04% for the years 2013 and 2014, then it rose to 0.93% for the first half of 2015, to 0.99% for the second half and it is equal to 1.01% (for professionals) for the first half of 2016 ( *see decree of 23 December 2015 on the setting of the legal interest rate – JORF of 27 December 2015* ). It was 0.93% for the second half of 2016 and is equal to 0.90% for the first and second half of 2017 (*cf. decree of December 29, 2016 relating to the fixing of the legal interest rate – JORF of December 30, 2016 and decree of June 26, 2017 – JORF of June 30, 2017* ).

A judgment of the Court of Appeal of Paris ( *dated November 18, 2016* ) specifies that in the matter, only the forfeiture of the stipulation of interests can be retained, in no case the nullity ( *organized by the article 1907 of the Civil Code* ) which deprives the judge of proportionalizing the sanction to the extent of the damage suffered.

The principle is that the borrower is returned to the borrower, according to the terms decided by the judge, the difference between the conventional interest and interest calculated on the basis of an interest rate ( *legal if applicable* ), decided by the judge. It happens most frequently in recent years that the judge, sovereign, decides an amount in Euros and not a reduction in the conventional interest rate to proportion the damage suffered to the error committed.

In the case of a legal rate, the calculation is made on the basis of successive annual or semi-annual legal rates, from the date of implementation of the credit until the last known date. The interest calculated with the legal rate is made on the basis of the exact number of days of the period considered compared to a year of 365 or 366 days ( *so-called “EXACT / EXACT” basis of calculation, such as the interest rate “on the day the day “EONIA* ).

If it is not necessary to demonstrate that the TEG error is prejudicial to the debtor, the credit holder ( *such as, for example, a loss of opportunity to subscribe to better financial terms with a competing bank* ) recent decisions, in particular those of the Paris Court of Human Rights, show that it is necessary to demonstrate with precision that there is indeed an error. But, when the TEG of the credit recalculated on the basis of mandatory elements and omitted intentionally exceeded the usury rate in effect on the date of grant, there is clearly a dolosive punitive maneuver on the part of the bank. to several leaders.

However, the TEG error must have a certain magnitude; a judgment of the Court of Cassation ( *Civ 1, 26 November 2014, appeal No. 13-23.033* ), recalls that a difference, positive or negative, less than the first decimal place is not sufficient to trigger the sanction.

A new judgment of the Court of Cassation ( *Civ 1, October 12, 2016, appeal n ° 15-25034* ) specifies that a difference greater than the first decimal place, by default, does not grieve.

It is written ” *but, having noted that the borrowers argued a lower TEG than that which was stipulated, so that the alleged error did not come to their detriment, the Court of Appeal has, for this reason only rightly, as it has done, that the plea is unfounded […]* “.

In this case, the announced TEG was equal to 6.42%, and that alleged was equal to 6.32%. The judgment of the Court of Appeal of Versailles of May 7, 2015 was therefore not broken.

### Limitation period

It follows from the combined provisions of Articles 1304, 1907 of the Civil Code and L.312-2 of the Consumer Code that in the case of the granting of a credit to a consumer or a non-professional, the point of departure the quinquennial prescription of the nullity action of the stipulation of the conventional interest committed by it because of an error affecting the TEG is the date of the agreement when the examination of its content allows to note the error, or where such is not the case, the date on which it was disclosed to the borrower […] ” ^{11} .

A judgment of the Court of Cassation of 9 December 2015 ( *Civ 1, number 14-29.615* ) states “[…] **that the starting point of the action for nullity of the overall effective rate is the day on which the borrower knew or ought to have known of the error affecting it** , […], the Court of Appeal held supremely that this date was the starting point of the action in nullity of the stipulation of the conventional interest since the borrowers had then known or had the opportunity to take cognizance of the error by them invoked, and they could validly claim the inattention lent to this document to indicate that they had realized the error that 7 years later, upon receipt of a letter from theassociation of help against bank abuse

In this case, it was a credit *ultimately* granted by a bank to individuals on 22 July 2000, the amortization period of which was preceded by a pre-financing phase; that the contract, dated July 22, 2000, mentioned a TEG of 6.362%; at the end of the pre-financing phase, the amortization table published on March 13, 2002 included a TEG equal to 7.02%.

It is by a letter dated May 24, 2009 from the Association d’Aides contre les Abus Bancaires that the borrowers have become aware of an error on the TEG, so that for them, the date of the revelation of the error was May 24, 2009.

By this judgment, the Court of Cassation specifies that if the simple reading of the credit agreement makes it possible to be convinced of an error on the TEG of the loan, the period of 5 years runs from the date of the signature of the contract.

Two other judgments of the Court of Cassation, taken in April 2016, confirm this principle.

That of April 6, 2016 ( *Civ 1, number 15-12.495* ) rejects the appeal *filed* against a judgment of the Court of Appeal of Paris (December 11, *2014* ) in these terms: ” *But expected, on the one hand, that having supremely found that the loan offer, the content of which it reproduced, made it possible to understand the method of calculating the overall percentage rate, thus showing that the borrowers had been able to detect the errors alleged by them, the court of Appeal, without being required to conduct a search that was not requested, has deduced exactly that the starting point of the limitation was the date of acceptance of the offer;*

*Whereas, on the other hand, that the Court of Appeal which found the prescription of the action for annulment of the stipulation of the contractual interests, did not have to answer to a means without influence on the solution of the dispute and, as such, inoperative; *From which it follows that the means can not be accepted … *“*

A second judgment, dated 14 April 2016 ( *Civ 1, number 15-14.760* ) is based on the same principle, confirming a judgment of the Court of Appeal of Nîmes and dismissing the appeal against him.

It reads in particular: ” *But considering that having pointed out that the precision of the offer and the detail of the ancillary charges allowed the borrower to detect by itself that the TEG did not integrate the cost of certain of these charges, which included the commitment fee and, according to the grievance, the handling and accounting fees, the court of appeal legally justified its decision.* ”

## Annexes

### Bibliography

- ( In ) Maria Theresa Calais Auloy, “Consumer Credit Law in Selected Countries: France,” in Royston Miles Goode, (ed.) Consumer Credit , Brill, ( ISBN 9028609288 )
- Octave Jokung-Nguena, Mathematics and Financial Management , De Boeck University, ( ISBN 280414402X ) , “1.4 The global percentage rate (APR)”
- French Banking Federation (ed.),
*The Cost of a Credit*, Series “The Mini Banking Guides” , November 2012 [ read online [ archive ] ] - Jean-Marcel Dalbarade, Mathematics of financial markets , ESKA Editions, 07/2005 3
^{th}edition, “1.3 times the conventions – the basic conventions” - Gérard BIARDEAUD, Practical Guide for THE CONTROL OF REAL ESTATE CREDITS , LITEC,, Number 113 – page 85 »
- Alexandre Duval-Stalla and Constance Monod, a year of TEG’s jurisprudence in the field of mortgage loans, studies and comments BUSINESS 1094 , JCP Legal Week – BUSINESS AND BUSINESS – N ° 6- BANKING AND FINANCIAL LAW STUDY,

### Related Articles

- Credit
- Consumer credit
- Mortgage
- Liability of the credit granting banker
- Interest rate
- Actuarial rate
- Annualized annualized rate

## Notes and references

- ↑ erroneous TEG , ” The mention of the wrong TEG in the loan agreement does not depend on the quality of the borrower and must appear, regardless of it, in all loan agreements. ” [ Archive ] , Rosali (accessed 14 September 2016 )
- ↑ This was again confirmed by a judgment of the Supreme Court – Civil Division 1 – dated 18/10/2016, appeal number 15-19643 – not published in the Bulletin
- ↑ The credit which, at identical nominal rate and repayment method, proposes the lowest TEG is the cheapest credit after taking into account all the elements constituting the credit and made obligatory by the lender (application fees, guarantee (s), insurance …).
- ↑ in the Annex R 314-3 modified since the 1
^{st}July 2016 - ↑ the 2016 study of Alexandre Duval – Stalla and Constance Monod quoted in the bibliography that takes stock of the jurisprudence of the species from September 2014 to December 2015
- ↑ “Mention of the overall effective rate – Study of a measure with questionable efficiency and coherence Part one: Scope of the measure” by Ariane PERIN – DUREAU, lecturer at the University Panthéon – Sorbonne (Paris 1 ) – Banking and Financial Law Review – Bimonthly Review lexisnexis jurisclasseur – September / October 2016
- ↑ For France, see Calais Auloy (1978) , p. 223
- ↑ French Banking Federation – http://www.fbf.fr/fr/la-federation-bancaire-francaise/normes-et-preconisations-professionnelles/bons-usages-fbf/relations-banques-clients/taux-variables-credit -immobilier — glossary [ archive ]Variable rates mortgage: glossary –
- ↑ http://www.legifrance.gouv.fr/affichCodeArticle.do?cidTexte=LEGITEXT000006069565&idArticle=LEGIARTI000006292489&dateTexte=&categorieLien=cid [ archive ]
- ↑ For France, see Calais Auloy (1978) , p. 224
- ↑ cf. study by Alexandre Duval-Stalla and Constance Monod cited in bibliography