CENTRAL BANK OF CYPRUS
MIRMFI/5
EUROSYSTEM
APPENDIX I
CALCULATION OF THE ANNUAL PERCENTAGE RATE OF CHARGE1
PART A:
BASIC EQUATION EXPRESSING THE EQUIVALENCE OF LOANS
ON THE ONE HAND AND REPAYMENT INSTALMENTS AND
CHARGES ON THE OTHER
K m

K 1
K 'm'
Ak
A' k '


tk '
(1  i ) tk
K ' 1 (1  i )
Where:
K
Serial number of a loan.
K'
Serial
number of a repayment instalment or a payment of
charge.
AK
Amount of loan number K.
A'K'
Amount of repayment instalment or payment of charge number
K'.
Σ
Symbol of the sum.
m
Serial number of the last loan.
m´
Serial number of the last repayment instalment or payment of
charge.
tk
The interval, expressed in years and fractions of a year,
between the date of granting of loan no. 1 and the date of
granting of the subsequent loans no. 2 to m.
tk'
The interval, expressed in years and fractions of a year,
between the date of granting of loan no. 1 and the date of
payment of the repayment instalment or charge no. 1 to m´.
i
1
The annual percentage rate of charge that can be calculated
Abstract from the Consumer Credit Law No. 39(I) of 2001, as amended by Laws No. 166(I) of 2001, No. 34(I) of 2002, No.
77(I) of 2002 and No. 33(I) of 2004.
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CENTRAL BANK OF CYPRUS
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(either by algebra, by successive approximations, or by a
computer programme) where the other terms in the equation
are known from the credit agreement 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. The year shall be
considered as having 365 days or 365.25 days or (for the leap
years) 366 days, 52 weeks or 12 equal months. An equal
month shall be considered as having 30.41666 days (namely
365/12).
(d)
The results shall be expressed with an accuracy of at least
one decimal place. When rounding to a particular decimal
place the following rule shall apply:
"If the figure of the decimal place following this particular
decimal place is greater than or equal to 5, the figure of this
particular decimal place shall be increased by one".
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CENTRAL BANK OF CYPRUS
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PART B:
1.
EXAMPLES OF CALCULATIONS
CALCULATION OF THE ANNUAL PERCENTAGE RATE OF CHARGE ON A
CALENDAR BASIS {1 YEAR = 365 DAYS (OR 366 DAYS FOR LEAP
YEARS)}.
First Example
Sum loaned: S = 1000 pounds on 1 January 1994.
The sum is repaid in a single instalment of 1200 pounds on 1 July, 1995, i.e. 1 1/2
years or 546 (=365 +181) days after the date of the loan.
1000 
1200
546
(1i ) 3 6 5
The equation becomes:
or
54 6
(1i ) 36 5
=1, 2
1+i
=1, 1296204
i
=0.1296204
This amount shall be rounded to 13% (or 12, 96% if an accuracy of two decimal
places is preferred).
Second example
The sum loaned is S=1000 pounds, but the creditor retains 50 pounds for
administrative expenses. So that the real loan is 950 pounds. The repayment of
1200 pounds, as in the first example, is again made on 1 July 1995.
950 
1200
546
(1i ) 3 6 5
The equation becomes:
or
546
(1i ) 365
=1, 263157
1+i
=1, 169026
i
=0.169026
This amount shall be rounded to 16, 9%
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CENTRAL BANK OF CYPRUS
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EUROSYSTEM
Third example
The sum loaned is S = 1000 pounds, on 1 January 1994, repayable in two
instalments of 600 pounds paid after one and two years respectively.
1000 
600

(1  i )
The equation becomes:
600
730

(1  i ) 365
600
600

(1  i ) (1  i ) 2
The equation is solved by algebra and produces i = 0, 1306623 rounded to 13, 1%
(or 13, 07% if an accuracy of two decimal places is preferred).
Fourth example
The sum loaned is S = 1000 pounds, on 1 January 1994, and the amounts paid by
the borrower are:
After 3 months (0,25 years/90 days):
272 pounds
After 6 months (0,5 years/181 days):
272 pounds
After 12 months ( 1 year/365 days):
544 pounds
TOTAL
1088 pounds
1000 
The equation becomes:
272
(1  i)
90
365

272
(1  i)
181
365

544
(1  i )
365
365
The equation allows i to be calculated by successive approximations, which can be
programmed on a pocket calculator.
The result is i = 0, 13226 rounded to 13, 2% (or 13, 23% if an accuracy of two
decimal places is preferred.
2.
CALCULATION OF THE ANNUAL PERCENTAGE RATE OF CHARGE ON
THE BASIS OF A STANDARD YEAR (1 YEAR = 365 DAYS OR 365, 25
DAYS, 52 WEEKS OR 12 EQUAL MONTHS)
First Example
Sum loaned: S = 1000 pounds
This sum is repaid in a single instalment of 1200 pounds in 1,5 years (i.e. 1,5 x 365
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= 547,5 days, 1,5 x 365,25 = 547, 875 days, 1,5 x 366 = 549 days, 1,5x12 = 18
months or 1,5 x 52 = 78 weeks) after the date of the loan.
1200
1000 
(1  i )
The equation becomes:

547.5
365
1200
(1  i)
547.875
365.25

1200
(1  i )
18
12

1200
(1  i)
78
52
or
(1  i)1.5
= 1, 2
1 +i
= 1,129243
i
= 0,129243
This amount shall be rounded to 12, 9% (or 12, 92 if an accuracy of two decimal
places is preferred).
Second Example
The sum loaned is S = 1000 pounds, but the creditor retains 50 pounds for
administrative expenses, so that the real loan is 950 pounds. The repayment of
1200 pounds, as in the first example, is made 1, 5 years after the date of the loan.
950 
The equation becomes:
1200
(1  i )
547.5
365
1200

(1  i )
547.875
365.25

1200
(1  i )
18
12

1200
(1  i )
78
52
or
(1  i)1.5
= 1200/950=1, 263157
1 +i
= 1, 68526
i
= 0,168526
This amount shall be rounded to 16, 9% (or 16, 85% if an accuracy of two decimal
places is preferred).
Third example
The sum loaned is S = 1000 pounds and is repaid in two instalments of 600 pounds
paid after one and two years, respectively:
1000 
The equation becomes:
600
(1  i)
365
365
5

600
(1  i )
730
365

600
(1  i)
365.25
365.25

600
(1  i)
730.5
365.25
CENTRAL BANK OF CYPRUS
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
600
(1  i )
12
12
600

(1  i)

24
12
600
(1  i)
52
52
600

(1  i)
104
52

600
600

(1  i) (1  i) 2
The equation is solved by algebra and produces i = 0, 13066 rounded to 13, 1% (or
13, 07% if an accuracy of two decimal places is preferred).
Fourth example
The sum loaned is S = 1000 pounds and the amounts paid by the borrower are:
After 3 months
(0, 25 years/13 weeks/ 91, 25 days/ 91, 3125 days):
272 pounds
After 6 months
(0,5 years/ 26 weeks/182,5 days /182,625 days): 272 pounds
After 12 months
(1 year/ 52 weeks/ 365 days/ 365, 25 days):
544 pounds
TOTAL
1088 pounds
272

(1  i)
The equation becomes:

272
(1  i )

91.3125
365.25
272
(1  i)

3
12
272
(1  i)

13
52
272

91.25
365
(1  i)
272

(1  i )
272

(1  i)
6
12
(1  i)
26
52
544

(1  i )
365
365
544

(1  i )
365.25
365.25
544

272

182.625
365.25
182.5
365
(1  i)

12
12
544
(1  i)
52
52
272
272
544


(1  i )0.25 (1  i )0.5 (1  i )1
This equation allows i to be calculated by successive approximations, which can be
programmed on a pocket calculator.
The result is i = 0, 13185 rounded to 13, 2% (or 13, 19% if an accuracy of two
decimal places is preferred).
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CENTRAL BANK OF CYPRUS
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PART C:
CRITERIA FOR THE INCLUSION OF PAYABLE CHARGES FOR
PURPOSES OF CALCULATING THE TOTAL COST OF CREDIT AND
THE ANNUAL PERCENTAGE RATE OF CHARGE.
Credit Agreements other than Housing Loan Agreements
1. The total cost of credit to the consumer/customer shall be determined, with the
exception of the following charges:
(a)
Charges payable by the consumer/customer for non-compliance with any
of his commitments laid down in the credit agreement.
(b)
Charges other than the purchase price which, in purchases of goods or
services, the consumer/customer is obliged to pay whether the
transaction is paid in cash or by credit,
(c)
(c) Charges for the transfer of funds and charges for keeping an account
intended to receive payments towards the reimbursement of the credit,
the payment of interest and other charges except where the
consumer/customer does not have reasonable freedom of choice in the
matter and where such charges are abnormally high:
Provided that this paragraph shall not apply to charges for collection of
such reimbursements or payments, whether made in cash or otherwise,
(d)
membership subscriptions to associations or groups arising from
agreements separate from the credit agreement even thought such
subscriptions have an effect on the credit terms,
(e)
charges for insurance or guarantees other than those designed to ensure
payment to the creditor in the event of the death, invalidity, illness or
unemployment of the consumer/customer, of sum equal to or less than
the total amount of the credit, together with relevant interest of the credit,
and other expenses, which are imposed by the creditor as a prerequisite
for the granting of the credit.
2.-(a) The annual percentage rate of charge shall be calculated(i) in the case of a credit agreement,
at the time the agreement is
concluded,
(ii) in the case of an announcement or advertisement relating to the
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offering of credit and mentioning the annual percentage rate of charge,
at the time of publication of such announcement or advertisement, and
(b)
the calculation shall be made on the assumption that the credit
agreement is valid for the period agreed and that the creditor and the
consumer/customer fulfil their obligations under the terms and by the
dates agreed.
3. In the case of credit agreements containing terms allowing the variations in the
rate value of interest and the amount or level of other charges contained in the
annual percentage rate of change but unquantifiable at the time when it is
calculated, the annual percentage rate of charge shall be calculated on the
assumption that interest and other charges remain fixed and shall apply until the
end of the credit agreement. The variability, as mentioned above, shall be
indicated with equal prominence to, and along with, the annual percentage rate
of charge.
4. In the case of credit agreements containing terms allowing variations in the rate
of interest and the amount or level of other charges contained in the annual
percentage rate of charge but quantifiable at the time when it is calculated, the
annual percentage rate of charge shall be calculated to show the rates
applicable, respectively, from specific dates.
5. Where necessary, the following assumptions may be made in calculating the
annual percentage rate of charge.
(a)
If there is no fixed timetable for repayment, and one cannot be deduced
from the terms of the credit agreement and the means for repaying the
credit granted, the duration of the credit shall be deemed to be one year.
(b)
unless otherwise specified, where the credit agreement provides for
more than one repayment date, the credit will be made available "and the
repayments made at the earliest time provided for in the agreement,
(c)
where the amount of credit to be provided is not specified
(i) in the case of a credit agreement concerning a current account, is
shall be assumed to be the maximum amount of the credit, and
(ii) in any other case, it shall be assumed that the amount of credit is
£1000.
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CENTRAL BANK OF CYPRUS
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(d)
where charges are payable at an unspecified date after the ' agreement
is signed, it shall be assumed that they are payable of the beginning at
the agreement.
Mortgage Housing Loans
1. The total cost of credit to the consumer/customer shall be determined with the
exception of the following charges (a)
Charges other than the purchase price which the consumer/customer is
obliged to pay whether the transaction is paid for in cash or by credit
including government duties or taxes on the purchase or acquisition of
the property, and fees payable by the borrower to his own agent for the
carrying out of legal and other procedures associated with the acquisition
of the property,
(b)
charges payable by the borrower for non-compliance with any of his
commitments laid down in the credit agreement,
(c)
charges for insurance on the life of the borrower or for insurance
against property damage which are designed to ensure payment to the
creditor (i) of credit outstanding in the event of the death of the borrower, or
(ii) insurable damage to the property being the subject of the credit
agreement, before termination of the agreement.
2. When necessary, in calculating the annual percentage rate of charge the
following assumptions shall be made:
(a)
That the borrower and the creditor fulfil their obligations arising from the
terms of the credit agreement,
(b)
that in the case of credit agreements providing for fluctuations in the rate
of interest or other charges which are unquantifiable at the time of
calculation the future rates of interest or charges are the current variable
rates which will remain fixed and will apply until the end of the credit
agreement.
(c)
that the borrower is not entitled to any income tax relief or any other
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benefit not granted by the creditor under, or relating to, the transaction.
(d)
that the charges are payable at the beginning of the agreement, where
these are payable at an unspecified date after the agreement is signed.
3. In the case of advertising, the annual percentage rate of charge shall be
calculated on the basis of a typical example, where there is no other way.
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