1987L0102 — EN — 01.03.1990 — 001.001 — 1
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►B COUNCIL DIRECTIVE
of 22 December 1986
for the approximation of the laws, regulations and administrative provisions of the Member States
concerning consumer credit
(87/102/EEC)
(OJ L 42, 12.2.1987, p. 48)
Amended by:
Official Journal
Nopage date
►M1Council Directive 90/88/EEC of 22 February 1990 L 61 14 10.3.1990
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COUNCIL DIRECTIVE
of 22 December 1986
for the approximation of the laws, regulations and administrative
provisions of the Member States concerning consumer credit
(87/102/EEC)
THE COUNCIL OF THE EUROPEAN COMMUNITIES,
Having regard to the Treaty establishing the European Economic
Community, and in particular Article 100 thereof,
Having regard to the proposal from the Commission(1),
Having regard to the opinion of the European Parliament(2),
Having regard to the opinion of the Economic and Social Committee(3),
Whereas wide differences exist in the laws of the Member States in the
field of consumer credit;
Whereas these differences of law can lead to distortions of competition
between grantors of credit in the common market;
Whereas these differences limit the opportunities the consumer has to
obtain credit in other Member States; whereas they affect the volumeand the nature of the credit sought, and also the purchase of goods andservices;
Whereas, as a result, these differences have an influence on the free
movement of goods and services obtainable by consumers on credit andthus directly affect the functioning of the common market;
Whereas, given the increasing volume of credit granted in the
Community to consumers, the establishment of a common market inconsumer credit would benefit alike consumers, grantors of credit,manufacturers, wholesalers and retailers of goods and providers ofservices;
Whereas the programmes of the European Economic Community for a
consumer protection and information policy (
4) provide, inter alia, that
the consumer should be protected against unfair credit terms and that aharmonization of the general conditions governing consumer creditshould be undertaken as a priority;
Whereas differences of law and practice result in unequal consumer
protection in the field of consumer credit from one Member State toanother;
Whereas there has been much change in recent years in the types of
credit available to and used by consumers; whereas new forms ofconsumer credit have emerged and continue to develop;
Whereas the consumer should receive adequate information on the
conditions and cost of credit and on his obligations; whereas thisinformation should include, inter alia , the annual percentage rate of
charge for credit, or, failing that, the total amount that the consumermust pay for credit; whereas, pending a decision on a Communitymethod or methods of calculating the annual percentage rate of charge,Member States should be able to retain existing methods or practices forcalculating this rate, or failing that, should establish provisions forindicating the total cost of the credit to the consumer;
(1) OJ NoC 80, 27. 3. 1979, p. 4 and
OJ NoC 183, 10. 7. 1984, p. 4.
(2) OJ NoC 242, 12. 9. 1983, p. 10.
(3) OJ NoC 113, 7. 5. 1980, p. 22.
(4) OJ NoC 92, 25. 4. 1975, p. 1 and
OJ NoC 133, 3. 6. 1981, p. 1.
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Whereas the terms of credit may be disadvantageous to the consumer;
whereas better protection of consumers can be achieved by adoptingcertain requirements which are toapply toall fo rms o f credit;
Whereas, having regard to the character of certain credit agreements or
types of transaction, these agreements or transactions should be partiallyor entirely excluded from the field of application of this Directive;
Whereas it should be possible for Member States, in consultation with
the Commission, to exempt from the Directive certain forms of credit ofa non-commercial character granted under particular conditions;
Whereas the practices existing in some Member States in respect of
authentic acts drawn up before a notary or judge are such as to renderthe application of certain provisions of this Directive unnecessary in thecase of such acts; whereas it should therefore be possible for MemberStates to exempt such acts from those provisions;
Whereas credit agreements for very large financial amounts tend to
differ from the usual consumer credit agreements; whereas the applica-tion of the provisions of this Directive to agreements for very smallamounts could create unnecessary administrative burdens both forconsumers and grantors of credit; whereas therefore, agreements aboveor below specified financial limits should be excluded from theDirective;
Whereas the provision of information on the cost of credit in advertising
and at the business premises of the creditor or credit broker can make iteasier for the consumer to compare different offers;
Whereas consumer protection is further improved if credit agreements
are made in writing and contain certain minimum particulars concerningthe contractual terms;
Whereas, in the case of credit granted for the acquisition of goods,
Member States should lay down the conditions in which goods may berepossessed, particularly if the consumer has not given his consent;whereas the account between the parties should upon repossession bemade up in such manner as to ensure that the repossession does notentail any unjustified enrichment;
Whereas the consumer should be allowed to discharge his obligations
before the due date; whereas the consumer should then be entitled to anequitable reduction in the total cost of the credit;
Whereas the assignment of the creditor’s rights arising under a credit
agreement should not be allowed to weaken the position of theconsumer;
Whereas those Member States which permit consumers to use bills of
exchange, promissory notes or cheques in connection with credit agree-ments should ensure that the consumer is suitably protected when sousing such instruments;
Whereas, as regards goods or services which the consumer has
contracted to acquire on credit, the consumer should, at least in thecircumstances defined below, have rights vis-à-visthe grantor of credit
which are in addition to his normal contractual rights against him andagainst the supplier of the goods or services; whereas the circumstancesreferred to above are those where the grantor of credit and the supplierof goods or services have a preexisting agreement whereunder credit ismade available exclusively by that grantor of credit to customers of thatsupplier for the purpose of enabling the consumer to acquire goods orservices from the latter;
Whereas the ECU is as defined in Council Regulation (EEC) No 3180/
78 (
1), as last amended by Regulation (EEC) No 2626/84 (2); whereas
Member States should to a limited extent be at liberty to round off theamounts in national currency resulting from the conversion of amounts
(1) OJ NoL 379, 30. 12. 1978, p. 1.
(2) OJ NoL 247, 16. 9. 1984, p. 1.
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of this Directive expressed in ECU; whereas the amounts in thisDirective should be periodically re-examined in the light of economicand monetary trends in the Community, and, if need be, revised;
Whereas suitable measures should be adopted by Member States for
authorizing persons offering credit or offering to arrange credit agree-ments or for inspecting or monitoring the activities of persons grantingcredit or arranging for credit to be granted or for enabling consumers tocomplain about credit agreements or credit conditions;
Whereas credit agreements should not derogate, to the detriment of the
consumer, from the provisions adopted in implementation of thisDirective or corresponding to its provisions; whereas those provisionsshould not be circumvented as a result of the way in which agreementsare formulated;
Whereas, since this Directive provides for a certain degree of approx-
imation of the laws, regulations and administrative provisions of theMember States concerning consumer credit and for a certain level ofconsumer protection, Member States should not be prevented fromretaining or adopting more stringent measures to protect the consumer,with due regard for their obligations under the Treaty;
Whereas, not later than 1 January 1995, the Commission should present
to the Council a report concerning the operation of this Directive,
HAS ADOPTED THIS DIRECTIVE:
Article 1
1. This Directive applies tocredit agreements.2. For the purpose of this Directive:
(a) ‘consumer'means a natural person who, in transactions covered by
this Directive, is acting for purposes which can be regarded asoutside his trade or profession;
(b) ‘creditor'means a natural or legal person who grants credit in the
course of his trade, business or profession, or a group of suchpersons;
(c) ‘credit agreement'means an agreement whereby a creditor grants or
promises to grant to a consumer a credit in the form of a deferredpayment, a loan or other similar financial accommodation.
Agreements for the provision on a continuing basis of a service or a
utility, where the consumer has the right to pay for them, for theduration of their provision, by means of instalments, are not deemedto be credit agreements for the purpose of this Directive;
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(d) ‘total cost of the credit to the consumer' means all the costs,
including interest and other charges, which the consumer has to payfor the credit;
(e) ‘annual percentage rate of charge'means the total cost of the credit
to the consumer, expressed as an annual percentage of the amountof the credit granted and calculated in accordance with Article 1a.
Article 1a
1. (a) The annual percentage rate of charge, which shall be that equiva-
lent, on an annual basis, to the present value of all commitments(loans, repayments and charges), future or existing, agreed bythe creditor and the borrower, shall be calculated in accordancewith the mathematical formula set out in Annex II.
(b) Four examples of the method of calculation are given in Annex
III, by way of illustration.
2. For the purpose of calculating the annual percentage rate of
charge, the ‘total cost of the credit to the consumer'as defined in Article
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1 (2) (d) shall be determined, with the exception of the followingcharges:
(i) charges payable by the borrower for non-compliance with any of
his commitments laid down in the credit agreement;
(ii) charges other than the purchase price which, in purchases of goods
or services, the consumer is obliged to pay whether the transactionis paid in cash or by credit;
(iii) charges for the transfer of funds and charges for keeping an
account intended to receive payments towards the reimbursementof the credit the payment of interest and other charges exceptwhere the consumer doesn ot have reasonable freedom of choice inthe matter and where such charges are abnormally high; this provi-sion shall not, however, apply to charges for collection of suchreimbursements or payments, whether made in cash or otherwise;
(iv) membership subscriptions to associations or groups and arising
from agreements separate from the credit agreement, even thoughsuch subscriptions have an effect on the credit terms;
(v) charges for insurance or guarantees; included are, however, those
designed toensure payment tothe credito r, in the event o f thedeath, invalidity, illness or unemployment of the consumer, of asum equal to or less than the total amount of the credit togehterwith relevant interest and other charges which have to be imposedby the creditor as a condition for credit being granted.
3. (a) Where credit transactions referred to in this Directive are subject
to the provisions of national laws in force on 1 March 1990which impose maximum limits on the annual percentage rate ofcharge for such transactions and, where such provisions permitstandard costs other than those described in paragraph 2 (i) to (v)not to be included in those maximum limits, Member Statesmay, solely in respect of such transactions, not include theaforementioned costs when calculating the annual percentagerate of charge, as stipulated in this Directive, provided that thereis a requirement, in the cases mentioned in Article 3 and in thecredit agreement, that the consumer be informed of the amountand inclusion thereof in the payments to be made.
(b) Member States may no longer apply point (a) from the date of
entry into force of the single mathematical formula for calcu-lating the annual percentage rate of charge in the Community,pursuant to the provisions of paragraph 5 (c).
4. (a) The annual percentage rate of charge shall be calculated at the
time the credit contract is concluded, without prejudice to theprovisions of Article 3 concerning advertisements and specialoffers.
(b) The calculation shall be made on the assumption that the credit
contract is valid for the period agreed and that the creditor andthe consumer fulfil their obligations under the terms and by thedates agreed.
5. (a) As a transitional measure, notwithstanding the provisions of
paragraph 1 (a), Member States which, prior to 1 March 1990,applied legal provisions whereby a mathematical formuladifferent from that given in Annex II could be used for calcu-lating the annual percentage rate of charge, may continueapplying that formula within their territory for a period of threeyears starting from 1 January 1993.
Member States shall take the appropriate measures to ensure that
only one mathematical formula for calculating the annualpercentage rate of charge is used within their territory.
(b) Six months before the expiry of the time limit laid down in point
(a) the Commission shall submit to the Council a report, accom-panied by a proposal, which will make it possible in the light ofexperience, to apply a single Community mathematical formulafor calculating the annual percentage rate of charge.
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(c) The Council shall, acting by a qualified majority on the basis of
the proposal from the Commission, take a decision before 1January 1996.
6. In the case of credit contracts containing clauses allowing vari-
ations in the rate of interest and the amount or level of other chargescontained in the annual percentage rate of charge but unquantifiable atthe time when it is calculated, the annual percentage rate of charge shallbe calculated on the assumption that interest and other charges remainfixed and will apply until the end of the credit contract.
7. Where necessary, the following assumptions may be made in
calculating the annual percentage rate of charge:
— if the contract does not specify a credit limit, the amount of credit
granted shall be equal tothe amo unt fixed by the relevant MemberState, without exceeding a figure equivalent to ECU 2 000;
— if there is no fixed timetable for repayment, and one cannot be
deduced from the terms of the agreement and the means forrepaying the credit granted, the duration of the credit shall bedeemed tobe o ne year;
— unless otherwise specified, where the contract provides for more
than one repayment date, the credit will be made available and therepayments made at the earliest time provided for in the agreement.
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Article 2
1. This Directive shall not apply to:
(a) credit agreements or agreements promising to grant credit:
— intended primarily for the purpose of acquiring or retaining
property rights in land or in an existing or projected building,
— intended for the purpose of renovating or improving a building
as such;
(b) hiring agreements except where these provide that the title will pass
ultimately tothe hirer;
(c) credit granted or made available without payment of interest or any
other charge;
(d) credit agreements under which nointerest is charged pro vided the
consumer agrees to repay the credit in a single payment;
(e) credit in the form of advances on a current account granted by a
credit institution or financial institution other than on credit cardaccounts.
Nevertheless, the provisions of Article 6 shall apply to such credits;
(f) credit agreements involving amounts less than 200 ECU or more
than 20 000 ECU;
(g) credit agreements under which the consumer is required to repay
the credit:
— either, within a period not exceeding three months,
— or, by a maximum number of four payments within a period not
exceeding 12 months.
2. A Member State may, in consultation with the Commission,
exempt from the application of this Directive certain types of creditwhich fulfil the following conditions:
— they are granted at rates of charge below those prevailing in the
market, and
— they are not offered to the public generally.
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3. The provisions of Article 1a and of Articles 4 to 12 shall not applyto credit agreements or agreements promising to grant credit, secured bymortgage on immovable property, insofar as these are not alreadyexcluded from the Directive under paragraph 1 (a).
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4. Member States may exempt from the provisions of Articles 6 to12 credit agreements in the form of an authentic act signed before anotary or judge.
Article 3
Without prejudice to Council Directive 84/450/EEC of 10 September
1984 relating to the approximation of the laws, regulations and adminis-trative provisions of the Member States concerning misleading advert-ising (
1), and tothe rules and principles applicable tounfair advertising,
any advertisement, or any offer which is displayed at business premises,in which a person offers credit or offers to arrange a credit agreementand in which a rate of interest or any figures relating to the cost of thecredit are indicated, shall alsoinclude a statement o f the annualpercentage rate of charge, by means of a representative example if noother means is practicable.
Article 4
1. Credit agreements shall be made in writing. The consumer shall
receive a copy of the written agreement.
2. The written agreement shall include:
(a) a statement of the annual percentage rate of charge;
(b) a statement of the conditions under which the annual percentage
rate of charge may be amended.
In cases where it is not possible to state the annual percentage rate
of charge, the consumer shall be provided with adequate informa-tion in the written agreement. This information shall at least includethe information provided for in the second indent of Article 6 (1);
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(c) a statement of the amount, number and frequency or dates of the
payments which the consumer must make to repay the credit, aswell as of the payments for interest and other charges; the totalamount of these payments should also be indicated where possible;
(d) a statement of the cost items referred to in Article 1a (2) with the
exception of expenditure related to the breach of contractual obliga-tions which were not included in the calculation of the annualpercentage rate of charge but which have to be paid by theconsumer in given circumstances, together with a statement indenti-fying such circumstances. Where the exact amount of those items isknown, that sum is to be indicated; if that is not the case, either amethod of calculation or as accurate an estimate as possibe is to beprovided where possible.
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3. The written agreement shall further include the other essential
terms of the contract.
By way of illustration, the Annex to this Directive contains a list of
terms which Member States may require tobe included in the writtenagreement as being essential.
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Article 6
1. Notwithstanding the exclusion provided for in Article 2 (1) (e),
where there is an agreement between a credit institution or financialinstitution and a consumer for the granting of credit in the form of anadvance on a current account, other than on credit card accounts, theconsumer shall be informed at the time or before the agreement isconcluded:
(1) OJ NoL 250, 19. 9. 1984, p. 17.
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— of the credit limit, if any,
— of the annual rate of interest and the charges applicable from the
time the agreement is concluded and the conditions under whichthese may be amended,
— of the procedure for terminating the agreement.
This information shall be confirmed in writing.2. Furthermore, during the period of the agreement, the consumer
shall be informed of any change in the annual rate of interest or in therelevant charges at the time it occurs. Such information may be given ina statement of account or in any other manner acceptable to MemberStates.
3. In Member States where tacitly accepted overdrafts are permis-
sible, the Member States concerned shall ensure that the consumer isinformed of the annual rate of interest and the charges applicable, andof any amendment thereof, where the overdraft extends beyond a periodof three months.
Article 7
In the case of credit granted for the acquisition of goods, Member States
shall lay down the conditions under which goods may be repossessed, inparticular if the consumer has not given his consent. They shall furtherensure that where the creditor recovers possession of the goods theacco unt between the parties shall be made up soas toensure that therepossession does not entail any unjustified enrichment.
Article 8
The consumer shall be entitled to discharge his obligations under a
credit agreement before the time fixed by the agreement. In this event,in accordance with the rules laid down by the Member States, theconsumer shall be entitled to an equitable reduction in the total cost ofthe credit.
Article 9
Where the creditor’s rights under a credit agreement are assigned to a
third person, the consumer shall be entitled to plead against that thirdperson any defence which was available to him against the originalcreditor, including set-off where the latter is permitted in the MemberState concerned.
Article 10
The Member States which, in connection with credit agreements, permit
the consumer:
(a) to make payment by means of bills of exchange including prom-
issory notes;
(b) to give security by means of bills of exchange including promissory
notes and cheques,
shall ensure that the consumer is suitably protected when using these
instruments in those ways.
Article 11
1. Member States shall ensure that the existence of a credit agree-
ment shall not in any way affect the rights of the consumer against thesupplier of goods or services purchased by means of such an agreementin cases where the goods or services are not supplied or are otherwisenot in conformity with the contract for their supply.
2. Where:
(a) in order to buy goods or obtain services the consumer enters into a
credit agreement with a person other than the supplier of them;
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and
(b) the grantor of the credit and the supplier of the goods or services
have a pre-existing agreement whereunder credit is made availableexclusively by that grantor of credit to customers of that supplierfor the acquisition of goods or services from that supplier; and
(c) the consumer referred to in subparagraph (a) obtains his credit
pursuant tothat pre-existing agreement; and
(d) the goods or services covered by the credit agreement are not
supplied, or are supplied only in part, or are not in conformity withthe contract for supply of them; and
(e) the consumer has pursued his remedies against the supplier but has
failed to obtain the satisfaction to which he is entitled,
the consumer shall have the right to pursue remedies against the grantor
of credit. Member States shall determine to what extent and under whatconditions these remedies shall be exercisable.
3. Paragraph 2 shall not apply where the individual transaction in
question is for an amount less than the equivalent of 200 ECU.
Article 12
1. Member States shall:
(a) ensure that persons offering credit or offering to arrange credit
agreements shall obtain official authorization to do so, either specif-ically or as suppliers of goods and services; or
(b) ensure that persons granting credit or arranging for credit to be
granted shall be subject to inspection or monitoring of their activi-ties by an institution or official body; or
(c) promote the establishment of appropriate bodies to receive
complaints concerning credit agreements or credit conditions and toprovide relevant information or advice to consumers regardingthem.
2. Member States may provide that the authorization referred to in
paragraph 1 (a) shall not be required where persons offering to concludeor arrange credit agreements satisfy the definition in Article 1 of thefirst Council Directive of 12 December 1977 on the coordination oflaws, regulations and administrative provisions relating to the taking upand pursuit of the business of credit institutions(
1) and are authorized in
accordance with the provisions of that Directive.
Where persons granting credit or arranging for credit to be granted have
been authorized both specifically, under the provisions of paragraph 1(a) and also under the provisions of the aforementioned Directive, butthe latter authorization is subsequently withdrawn, the competentauthority responsible for issuing the specific authorization to grantcredit under paragraph 1 (a) shall be informed and shall decide whetherthe persons concerned may continue to grant credit, or arrange for creditto be granted, or whether the specific authorization granted under para-graph 1 (a) should be withdrawn.
Article 13
1. For the purposes of this Directive, the ECU shall be that defined
by Regulation (EEC) No 3180/78, as amended by Regulation (EEC) No2626/84. The equivalent in national currency shall initially be calculatedat the rate obtaining on the date of adoption of this Directive.
Member States may round off the amounts in national currency
resulting from the conversion of the amounts in ECU provided suchrounding off does not exceed 10 ECU.
2. Every five years, and for the first time in 1995, the Council, acting
on a proposal from the Commission, shall examine and, if need be,
(1) OJ NoL 322, 17. 12. 1977, p. 30.
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revise the amounts in this Directive, in the light of economic andmonetary trends in the Community.
Article 14
1. Member States shall ensure that credit agreements shall not
derogate, to the detriment of the consumer, from the provisions ofnational law implementing or corresponding to this Directive.
2. Member States shall further ensure that the provisions which they
adopt in implementation of this directive are not circumvented as aresult of the way in which agreements are formulated, in particular bythe device of distributing the amount of credit over several agreements.
Article 15
This Directive shall not preclude Member States from retaining or
adopting more stringent provisions to protect consumers consistent withtheir obligations under the Treaty.
Article 16
1. Member States shall bring intofo rce the measures necessary to
comply with this Directive not later than 1 January 1990 and shallforthwith inform the Commission thereof.
2. Member States shall communicate to the Commission the texts of
the main provisions of national law which they adopt in the fieldcovered by this Directive.
Article 17
Not later than 1 January 1995 the Commission shall present a report to
the Council concerning the operation of this Directive.
Article 18
This Directive is addressed tothe Member States.
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►M1 ANNEX I ◄
LIST OF TERMS REFERRED TO IN ARTICLE 4 (3)
1.Credit agreements for financing the supply of particular goods or
services:
(i) a description of the goods or services covered by the agreement;
(ii) the cash price and the price payable under the credit agreement;
(iii) the amount of the deposit, if any, the number and amount of instal-
ments and the dates on which they fall due, or the method of ascer-taining any of the same if unknown at the time the agreement isconcluded;
(iv) an indication that the consumer will be entitled, as provided in Article
8, toa reductio n if he repays early;
(v) who owns the goods (if ownership does not pass immediately to the
consumer) and the terms on which the consumer becomes the owner ofthem;
(vi) a description of the security required, if any;
(vii) the cooling-off period, if any;
(viii) an indication of the insurance (s) required, if any, and, when the choice
of insurer is not left to the consumer, an indication of the cost thereof;
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(ix) the obligation on the consumer to save a certain amount of money
which must be placed in a special account.
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2.Credit agreements operated by credit cards:
(i) the amount of the credit limit, if any;
(ii) the terms of repayment or the means of determining them;
(iii) the cooling-off period, if any.
3.Credit agreements operated by running account which are not otherwise
covered by the Directive:
(i) the amount of the credit limit, if any, or the method of determining it;
(ii) the terms of use and repayment;
(iii) the cooling-off period, if any.
4.Other credit agreements covered by the Directive:
(i) the amount of the credit limit, if any;
(ii) an indication of the security required, if any;
(iii) the terms of repayment;
(iv) the cooling-off period, if any;
(v) an indication that the consumer will be entitled, as provided in Article 8,
toa reductio n if he repays early.
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ANNEX II
THE BASIC EQUATION EXPRESSING THE EQUIVALENCE OF
LOANS ON THE ONE HAND, AND REPAYMENTS AND CHARGES ON
THE OTHER:
Meaning of letters and symbols:
K is the number of a loanK/prime1 is the number of a repayment or a payment of charges
A
K is the amount of loan number K
A/prime1K/prime1 is the amount of repayment number K /prime1
represents a sum
m is the number of the last loan
m/prime1 is the number of the last repayment or payment of charges
tK is the interval, expressed in years and fractions of a year,
between the date of loan No 1 and those of subsequent loansN os2t o m
t
K/prime1 is the interval expressed in years and fractions of a year
between the date of loan No 1 and those of repayments orpayments of charges Nos 1 to m /prime1
i is the percentage rate that can be calculated (either by algebra,
by successive approximations, or by a computer programme)where the other terms in the equation are known from thecontract or otherwise.
Remarks
(a) The amounts paid by both parties at different times shall not necessarily be
equal and shall not necessarily be paid at equal intervals.
(b) The starting date shall be that of the first loan.
(c) Intervals between dates used in the calculations shall be expressed in years
or in fractions of a year.
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ANNEX III
EXAMPLES OF CALCULATIONS
First example
Sum loaned S = ECU 1 000.It is repaid in a single payment of ECU 1 200 made 18 months, i. e. 1,5 years,
after the date of the loan.
The equation becomes 1 000 =1 200
( 1+i )1,5
or ( 1+i )1,5= 1,2
1 + i = 1,129243 …i = 0,129243 …
This amount will be rounded down to 12,9 % or 12,92 % depending on whether
the State or habitual practice allows the percentage to be rounded off to the firstor second decimal.
Second example
The sum agreed i s S = ECU 1 000 but the creditor retains ECU 50 for enquiry
and administrative expenses, sothat the lo an is in fact ECU 950; the repaymentof ECU 1 200, as in the first example, is made 18 months after the date of theloan.
The equation becomes 950 =1 200
( 1+i )1,5
or ( 1+i )1,5=1 200
950= 1,263157 …
1 + i = 1,16851 …
i = 0,16851 … rounded off to
16,9 % or 16,85%.
Third example
The sum lent is ECU 1 000, repayable in two amounts each of ECU 600, paid
after one and two years respectively.
The equation becomes 1 000 =600
1+i+600
( 1+i )2;
it is solved by algebra and produce s i = 0,1306623, rounded off to 13,1 % or
13,07 %.
Fourth example
The sum lent is ECU 1 000 and the amounts to be paid by the borrower are:
After three months (0,25 years) ECU 272
After six months (0,50 years) ECU 272After twelve months (1 year) ECU 544
Total
ECU 1 088
The equation becomes:
1 000 =272
( 1+i )0,25+272
( 1+i )0,50+544
1+i
This equation allows i to be calculated by successive approximations, which can
be programmed on a ocket computer.
The result is:i = 0,1321 rounded off 13,2 or 13,21 %.