PART I: Basic equation expressing the equivalence of loans, on the one hand, and repayments and charges, on the other.
The basic equation, which defines the annual percentage rate of charge (APR), expresses on an annual basis the equality between, on the one hand, the sum of the present values of the uses of the credit and, on the other hand, the sum of the present values of the amounts of repayments and payments of charges, i.e. :
You can view the image in the facsimile of the JO
n º 0151 du 30/06/2016, texte n º 62
https :// www. legifrance. gouv. fr/ jo _ pdf. do? id = JORFTEXT000032797752
-Signification of letters and symbols:
-X is the APR;
-m denotes the serial number of the last use made on the credit;
-k denotes the serial number of a use made on the credit, so 1 ≤ k ≤ m;
-Ck is the amount of the use made on credit number k ;
-tk denotes the time interval, expressed in years and fractions of a year, between the date of the first utilisation made on the credit and the date of each subsequent utilisation made, so t 1 = 0 ;
-m’is the serial number of the last repayment or payment of charges;
-l is the serial number of a repayment or payment of charges;
-Dl is the amount of a repayment or payment of charges;
-sl is the time interval, expressed in years and fractions of years, between the date of the first utilisation made on the credit and the date of each repayment or payment of charges.
PART II-Calculation of the Annual Percentage Rate of Charge (APR) for credit governed by Articles L. 312-1 et seq. and by articles L. 315-1 et seq.
Notes
a) The sums paid on either side at different times are not necessarily equal and are not necessarily paid at equal intervals;
b) The initial date is that of the first loan;
c) The difference between the dates used to calculate the APR, as well as that of the borrowing rate, is expressed in years or fractions of years. A year has 365 days or, in leap years, 366 days, 52 weeks or 12 standardised months. A standard month has 30.416 66 days (i.e. 365/12), whether or not the year is a leap year;
d) The result of the calculation is expressed with an accuracy of at least one decimal place. Where the figure is rounded to a particular decimal place, the following rule shall apply: if the figure to the decimal place following that particular decimal place is greater than or equal to 5, the figure to that particular decimal place shall be increased by 1.
Hypotheses
The annual percentage rate of charge shall be calculated, where applicable, in accordance with the following hypotheses:
1° If a credit agreement gives the consumer a free choice as to how the credit is to be used, the total amount of credit is deemed to be fully and immediately used;
2° If a credit agreement generally gives the consumer a free choice as to how the credit is to be used, but provides among the various methods of use a limit as to the amount and duration, the amount of credit is deemed to be used on the earliest date provided for in the agreement and in accordance with these limits on the method of use;
3° If a credit agreement offers the consumer different options as to how the credit may be used, with different charges or borrowing rates, the total amount of credit is deemed to be used at the highest borrowing rate and with the highest charges in the category of transactions most frequently used in that type of credit agreement;
4° In the case of an overdraft facility, the total amount of credit is deemed to be used in full and for the full duration of the credit agreement. If the duration of the overdraft facility is not known, the annual percentage rate of charge is calculated on the assumption that the duration of the credit is three months;
5° In the case of a credit agreement with no fixed duration, including credit that must be repaid in full within or after a given period but which, once repaid, is available for further use, and other than an overdraft facility or a loan agreement referred to in Articles L. 315-1 and L. 315-2 :
a) The credit is deemed to be granted for a period of one year from the date of initial use, and the final payment made by the consumer clears the balance of the capital, interest and any other charges;
b) The capital is deemed to be repaid by the consumer in equal monthly instalments, with repayment beginning one month after the date of initial use. However, in cases where the capital is to be repaid in full only, in a single instalment, within each payment period, successive uses and repayments of the full capital by the consumer are assumed to be made over the period of one year. Interest and other charges are applied in accordance with these uses and repayments of the capital, on the one hand, and the provisions of the credit agreement, on the other;
5° bis For loan agreements referred to in Articles L. 315-1 and L. 315-2, the credit, for the sole purpose of verifying the provisions relating to usury, is deemed to be granted for a period of ten years from the date of formation of the loan agreement. The final payment settles the balance of the capital, interest and any other charges;
6° In the case of credit agreements other than overdrafts and credit agreements with no fixed term referred to in the assumptions in points 4° and 5°:
a) If the date or amount of a capital repayment to be made by the consumer cannot be established, the repayment shall be deemed to be made on the earliest date provided for in the credit agreement and for the lowest amount provided for in the agreement;
b) If the date of conclusion of the credit agreement is not known, the date of initial use shall be deemed to be the date which corresponds to the shortest interval between that date and the date of the first payment to be made by the consumer;
7° If the date or amount of a payment to be made by the consumer cannot be established on the basis of the credit agreement or the assumptions set out in points 4°, 5° or 6°, the payment is deemed to be made on the dates and conditions required by the creditor and, where these are not known:
a) Interest charges are paid at the same time as capital repayments;
b) Non-interest charges, expressed as a single sum, are paid on the date on which the credit agreement is concluded;
c) Charges other than interest, expressed in the form of multiple payments, are paid at regular intervals, starting from the date of the first repayment of the capital, and if the amount of these payments is not known, the amounts are deemed to be equal;
d) The final payment settles the balance of the capital, the interest and any other charges;
8° If the credit limit has not yet been agreed, the limit is assumed to be €1,500 ;
9° If different borrowing rates and charges are offered for a limited period or for a limited amount, the borrowing rate and charges are deemed to be the highest rate for the entire duration of the credit agreement…;
10° For consumer credit agreements for which a fixed borrowing rate has been agreed as part of the initial period, at the end of which a new borrowing rate is established and is then periodically adjusted in accordance with an agreed indicator, the calculation of the annual percentage rate of charge assumes that, from the end of the fixed borrowing rate period, the borrowing rate is the same as at the time of calculation of the annual percentage rate of charge, in accordance with the value of the agreed indicator at that time.
PART III-Calculation of the Annual Percentage Rate of Charge (APR) for loans governed by Articles L. 313-1 et seq.
Notes
a) The sums paid on either side at different times are not necessarily equal and are not necessarily paid at equal intervals;
b) The initial date is that of the first use of the credit;
c) The difference between the dates used to calculate the APR, as well as that of the borrowing rate, is expressed in years or fractions of years. A year has 365 days or, in leap years, 366 days, 52 weeks or 12 standardised months. A standardised month has 30.416 66 days (i.e. 365/12), whether the year is a leap year or not.
When the difference between the dates used for the calculation cannot be expressed as a whole number of weeks, months or years, it is expressed as a whole number of one of these periods in combination with a number of days. Where days are used:
i) each day is counted, including weekends and public holidays;
ii) the time interval is calculated by standard periods and then by days back to the date of the initial loan;
iii) the duration in days is obtained by excluding the first day and including the last and is expressed in years by dividing the number obtained by the number of days (365 or 366) in the full year going back from the last day to the same day in the previous year;
d) the result of the calculation is expressed to an accuracy of at least one decimal place. Where the figure is rounded to a particular decimal place, the following rule applies: if the figure to the decimal place following that particular decimal place is greater than or equal to 5, the figure to that particular decimal place will be increased by 1;
e) The equation can be rewritten using only one summation and using the concept of flows (A k), which will be positive or negative, i.e. respectively paid or received in periods 1 to n expressed in years, i.e. :
You can see the image in the facsimile in the JO
n º 0151 du 30/06/2016, texte n º 62
https :// www. legifrance. gouv. fr/ jo _ pdf. do ? id = JORFTEXT000032797752
S being the balance of the discounted flows and whose value will be zero if we want to preserve the equivalence of the flows.
Hypotheses
The annual percentage rate is calculated, where applicable, in accordance with the following assumptions:
1° If a credit agreement gives the consumer a free choice as to how to use the credit, the total amount of credit is deemed to be fully and immediately used;
2° If a credit agreement offers the consumer different options as to how to use the credit, with different charges or borrowing rates, the total amount of credit is deemed to be used at the highest borrowing rate and with the highest charges in the category of transactions most frequently used in that type of credit agreement…;
3° If a credit agreement generally allows the consumer a free choice as to how the credit is to be used, but among the various methods of use provides for a limit as to the amount and duration, the amount of credit is deemed to be used at the earliest date provided for in the agreement and in accordance with these limits on the method of use ;
4° If different borrowing rates and charges are offered for a limited period of time or for a limited amount, the highest borrowing rate and charges are deemed to be the borrowing rate and charges for the entire duration of the credit agreement ;
5° For credit agreements where a fixed borrowing rate has been agreed as part of the initial period, at the end of which a new borrowing rate is established and is then periodically adjusted in line with an agreed indicator or internal reference rate, the calculation of the APR assumes that, at the end of the fixed borrowing rate period, the borrowing rate is the same as at the time of the calculation of the APR, depending on the value, at that time, of the agreed indicator or internal reference rate, without being lower, however, than the fixed borrowing rate ;
6° If the credit limit has not yet been agreed, the limit is assumed to be EUR 170,000. In the case of credit agreements, other than sureties or guarantees, the purpose of which is not to acquire or retain a right of ownership over real estate or land, overdrafts, credit cards, this ceiling is assumed to be EUR 1,500;
7° In the case of credit agreements other than overdrafts, bridging or bridging loans, shared-fund credit agreements, sureties or guarantees and open-end loans referred to in the assumptions in points 9°, 10°, 11°, 12° and 13°:
i) if the date or amount of a capital repayment to be made by the consumer cannot be established, the repayment shall be deemed to be made on the earliest date provided for in the credit agreement and for the lowest amount provided for in the agreement;
ii) if the interval between the date of initial use and the date of the first payment to be made by the consumer cannot be established, it shall be deemed to be the shortest interval;
8° If the date or amount of a payment to be made by the consumer cannot be established on the basis of the credit agreement or the assumptions set out in points 7°, 9°, 10°, 11°, 12°, and 13°, the payment is deemed to be made on the dates and under the conditions required by the creditor and, where these are not known;
i) interest charges are paid at the same time as capital repayments;
ii) non-interest charges, expressed as a single sum, are paid on the date on which the credit agreement is concluded;
iii) non-interest charges, expressed as multiple payments, are paid at regular intervals, starting on the date of the first capital repayment, and if the amount of such payments is not known, the amounts are deemed to be equal;
iv) the final payment liquidates the principal balance, interest and any other charges;
9° In the case of an overdraft facility, the total amount of credit is deemed to be used in full and for the full term of the credit agreement. If the duration of the overdraft facility is not known, the APR is calculated on the assumption that the duration of the credit is three months;
10° In the case of bridge or bridging credit, the total amount of credit is deemed to be used in full and for the full duration of the credit agreement. If the duration of the credit agreement is not known, the APR is calculated on the assumption that the duration of the credit is twelve months;
11° In the case of an open-end credit agreement, other than an overdraft facility or a bridge or bridging loan:
i) in the case of credit agreements the purpose of which is to acquire or retain property rights in immovable property, the credit is deemed to be granted for a period of twenty years from the date of initial use, and the final payment made by the consumer liquidates the balance of the capital, interest and any other charges ; in the case of credit agreements the purpose of which is not to acquire or retain property rights in immovable property or where use is made of credit cards, this period is one year;
ii) the capital is assumed to be repaid by the consumer in equal monthly instalments, with repayment beginning one month after the date of initial use. However, in cases where the capital is to be repaid in full only, in a single instalment, within each payment period, successive uses and repayments of the full capital by the consumer are assumed to be made over the period of one year. Interest and other charges are applied in accordance with these uses and repayments of the capital, on the one hand, and the provisions of the credit agreement, on the other.
For the purposes of this point, an open-end credit agreement means a credit agreement with no fixed duration, including credit which must be repaid in full within or after a given period but which, once repaid, is available for further use;
12° In the case of conditional commitments or guarantees, the total amount of credit is deemed to be used in full at once on whichever of the following dates occurs first:
i) the last date of use authorised under the credit agreement likely to involve the conditional commitment or guarantee; or
ii) in the case of a revolving credit agreement, at the end of the initial period prior to renewal of the agreement;
13° In the case of shared-fund credit agreements:
i) payments made by consumers are deemed to occur on the last date(s) authorised under the credit agreement;
ii) the percentage increase in the value of the immovable property securing the shared-fund credit agreement, as well as the rate of any inflation index referred to in the agreement, are assumed to be equal to the higher of the prevailing central bank target inflation rate and the level of inflation in the Member State where the immovable property is located at the time the credit agreement is concluded or 0% if these percentages are negative.