For Individual Clients
Calculation of auto loan interest rates
Attention! Loan interest is calculated at the nominal interest rate. The latter shows the annual interest accrued to the outstanding loan principle. The actual annual percentage rate (APR) shows the cost of the loan in case of due and timely repayments under the agreement.
The amount of interest depends on the annual nominal interest rate and method of loan repayment.
The loan may be repaid by one of the methods below:

Differentiated/repayment of principal in equal portions in which case monthly payments consist of equal principal amounts and varying interest. As a result of reducing the interest, the amount of your monthly payments decreases each month.

Annuity/fixed monthly installments, where the monthly payment throughout the repayment period remains the same and consists of a portion of loan and a portion of interest.

Mixed: the client may choose an individual repayment schedule based on the seasonality of cash flows, provided that the amount of principal repaid each year makes at least 5% of contractual amount in case of loans for purchase/renovation/construction of residential and commercial property and investment loans.
If you choose to repay the loan by the 2^{nd} method, the total amount of payable interest will be higher than in the 1^{st} case.
The 2^{nd} method, however, allows you planning your expenses, because you know the exact amount you’re going to pay each month.
If you repay your loan by differentiated method, the amount of monthly payment shall be calculated according to the following formula:
R = m / n + m * r % / 365 * o, where
R is your monthly payment
m is the loan principal
n is the loan term expressed in months
r is the annual interest rate
օ is the number of days in one month
If you repay your loan by annuity, the amount of monthly payment shall be calculated by the following formula:
R = P x r / (1 – 1/(1 + r) ^{n}), where
R is your monthly payment
P is the loan amount
n is total number of loan repayments throughout the whole loan term (number of months)
r is a monthly interest rate which is equal to 1/12 of the annual interest rate specified in the loan agreement at the moment of loan disbursement
The amount of monthly payments is rounded to one decimal place.
The outstanding loan is calculated according to the following formula:
Pt = R x ((1 – 1/(1 + r) ^{n}) / r, where
Pt is the actual loan outstanding by the end of the term
R is your monthly repayment
t is the number of repayments due by the end of the loan term (number of months)
r is a monthly interest rate which is equal to 1/12 of the annual interest rate specified in the loan agreement at the moment of loan disbursement
Annual percentage rate may be calculated out of the following formula:
where
i is the annual percentage rate (APR)
A is the loan principal (the amount initially provided by the lender to the borrower)
n is the sequence number of loan payment
N is the sequence number of the last payment
Kn is the amount of n^{th} payment under the loan
Dn is the number of days from the day of loan disbursement up to the day of the n^{th} payment
The annual percentage rate “i” may be calculated, if the other data of the equation are available from the loan agreement or another source.
Annual percentage rate is defined on the basis of its constituent conditions, is provisional and may change throughout the validity term of the agreement depending on the early repayment of the loan by the borrower and changes in constituents.
APR calculation example
1. Car loan

Loan principal: AMD 5,000,000

Nominal interest rate: 16% accrued to the outstanding decreasing loan principal

Term: 5 years (1,825 days)

Repayment: equal monthly payments (loan principal and interest)

Other payments to be made by the borrower
Car appraisal fee (lumpsum): AMD 10,000
Notary’s fee: AMD 16,000
Lumpsum fee for a statement from the Police: AMD 5,000
Loan disbursement fee (lumpsum, 0.5% or AMD 50,000, whichever is greater): AMD 50,000
Annual insurance fee: 2.5% of the outstanding loan, where the first payment (5,000,000 * 2.5%=125,000 AMD) should be made prior to the loan disbursement; the 2^{nd} year fee is AMD 107,260; the 3^{rd} year fee is AMD 86,460; the 4^{th} year fee is AMD 62,080 and the 5^{th} year fee is AMD 33,500.
2. Hence N=65, including 1 payment at the moment of provision of the loan, 4 payments of annual insurance fees and 60 payments of the loan and interest.
3. Based on the terms specified in paragraph 1, the loan repayment schedule is as follows:
Sequence of payments: n

Number of days between loan disbursement to each payment: Dn

Other payments

Interest payable

Principal payable

Total amount of each repayment: Kn

1

0

206,000.00



206,000.00

2

30


66,666.67

54923.62

121,590.29

3

61


65,934.35

55655.93

121,590.29

4

92


65,192.27

56398.01

121,590.29

5

120


64,440.30

57149.99

121,590.29

6

151


63,678.30

57911.99

121,590.29

7

181


62,906.14

58684.15

121,590.29

8

212


62,123.68

59466.60

121,590.29

9

242


61,330.80

60259.49

121,590.29

10

273


60,527.34

61062.95

121,590.29

11

304


59,713.16

61877.12

121,590.29

12

334


58,888.14

62702.15

121,590.29

13

365


58,052.11

63538.18

121,590.29

14

366

107,260.00



107,260.00

15

395


57,204.93

64385.35

121,590.29

16

426


56,346.46

65243.83

121,590.29

17

457


55,476.54

66113.74

121,590.29

18

485


54,595.03

66995.26

121,590.29

19

516


53,701.76

67888.53

121,590.29

20

546


52,796.57

68793.71

121,590.29

21

577


51,879.33

69710.96

121,590.29

22

607


50,949.85

70640.44

121,590.29

23

638


50,007.97

71582.31

121,590.29

24

669


49,053.54

72536.74

121,590.29

25

699


48,086.39

73503.90

121,590.29

26

730


47,106.33

74483.95

121,590.29

27

731

86,460.00



86,460.00

28

760


46,113.21

75477.07

121,590.29

29

791


45,106.85

76483.43

121,590.29

30

822


44,087.07

77503.21

121,590.29

31

850


43,053.70

78536.59

121,590.29

32

881


42,006.54

79583.74

121,590.29

33

911


40,945.43

80644.86

121,590.29

34

942


39,870.16

81720.12

121,590.29

35

972


38,780.56

82809.72

121,590.29

36

1003


37,676.43

83913.85

121,590.29

37

1034


36,557.58

85032.71

121,590.29

38

1064


35,423.81

86166.48

121,590.29

39

1095


34,274.92

87315.36

121,590.29

40

1096

62,080.00



62,080.00

41

1125


33,110.72

88479.57

121,590.29

42

1156


31,930.99

89659.29

121,590.29

43

1187


30,735.53

90854.75

121,590.29

44

1215


29,524.14

92066.15

121,590.29

45

1246


28,296.59

93293.70

121,590.29

46

1276


27,052.67

94537.61

121,590.29

47

1307


25,792.17

95798.11

121,590.29

48

1337


24,514.86

97075.42

121,590.29

49

1368


23,220.52

98369.76

121,590.29

50

1399


21,908.93

99681.36

121,590.29

51

1429


20,579.84

101010.44

121,590.29

52

1460


19,233.04

102357.25

121,590.29

53

1461

33,500.00



33,500.00

54

1490


17,868.27

103722.01

121,590.29

55

1521


16,485.31

105104.97

121,590.29

56

1552


15,083.91

106506.37

121,590.29

57

1580


13,663.83

107926.46

121,590.29

58

1611


12,224.81

109365.48

121,590.29

59

1641


10,766.60

110823.68

121,590.29

60

1672


9,288.95

112301.33

121,590.29

61

1702


7,791.60

113798.68

121,590.29

62

1733


6,274.29

115316.00

121,590.29

63

1764


4,736.74

116853.54

121,590.29

64

1794


3,178.69

118411.59

121,590.29

65

1825


1,599.87

119990.41

121,590.29

Total


495,300.00

2,295,417.09

5,000,000.00

7,790,717.09

4. Other payments due at the moment of the loan disbursement (K_{1}) are equal to:
K_{1}=10,000+16,000+5,000+50,000+125,000=206,000
5. With all inputs available it is possible to calculate the APR using the formula defined by the law of the Republic of Armenia "On Consumer Crediting".
5,000,000=


+


+


+


...+


206,000

121,590.29

121,590.29

121,590.29

121,590.29


0
365


30
365


61
365


92
365


1,825
365


(1+i)



(1+i)



(1+i)



(1+i)



(1+i)



, where

5,000,000206,000=


+


+


+...+


121,590.29

121,590.29

121,590.29

121,590.29


30
365


61
365


92
365


1,825
365


(1+i)



(1+i)



(1+i)



(1+i)




whence
i=0.218499*100=21.85%
Thus, actual percentage rate is 21.85 %.
APR Calculation: Representative Example

Loan facility: loan for purchase of a car from secondary market

Principal loan amount: AMD 7,000,000

Annual interest rate: 18.5%

Term: 60 months

Repayment method: differentiated (the loan principal is repaid in equal portions, the interest is accrued to outstanding balance and decreases with each payment)

Loan disbursement lumpsum fee: AMD 50,000

Insurance fee: 2.5% of the outstanding loan principal every year

Car appraisal fee: AMD 10,000

Fee for the Police reference on absence of encumbrance on the vehicle: AMD 3,300

Pledge agreement notarization fee: AMD 24,000

Fee for state registration of security interest: AMD 2,200

Start day: 01/07/2013

First payment day: 01/08/2013
Annual percentage rate: 24.96%
Interest Calculation. Representative Example.
Principal loan amount: AMD 7,000,000
Annual interest rate: 15%
Loan term: 60 months
Monthly payment in case of repayment by annuity will make AMD 166,529.5.
Daily interest will make 7,000,000*15/100/365=2,876.7 AMD.
Updated 10.01.2017, 10:55
