Top Banner

of 42

50518497-simp1

Apr 04, 2018

Download

Documents

laokoontas
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
  • 7/30/2019 50518497-simp1

    1/42

  • 7/30/2019 50518497-simp1

    2/42

  • 7/30/2019 50518497-simp1

    3/42

    , .

    , , , ,

    , ...... ...,, 1.1. 1.1.2.. (...).

  • 7/30/2019 50518497-simp1

    4/42

  • 7/30/2019 50518497-simp1

    5/42

    1. ........................................................................... 8

    2. ...................................................................................................... 11

    2.1. ............................................................................................................ 11

    2.2. ........................................................................................... 12

    2.3. ........................................................................ 17

    2.3.1. .................................................................................. 18

    2.3.2. . ............................................................................................ 192.3.3. ........................................................................... 19

    2.3.4. ..................................................................................... 19

    2.4. .................................................................................. 21

    2.5. ................................................................................ 25

    2.6. ............................................................. 27

    3. ................................................................................................. 33

    3.1. ............................................................................................................ 33

    3.2. .............................................................................................. 34

    3.3. ............................................................... 373.4. ....................................................... 42

    4. ................................................................................................................. 45

    4.1. ............................................................................................................ 45

    4.2. ........................................................................................................................... 46

    4.3. ................................................................................................. 47

    4.4. .............................................................................................. 54

    4.5. ............................................................................................................ 59

    5. .................................................................................................................................. 63

    5.1. ............................................................................................................ 635.2. .............................................................................................................. 64

    5.3. ............................................................................................ 66

    5.4. ...................................................................................................... 67

    5.4.1. () ..................................................... 67

    5.4.2. ....................................................... 69

    5.4.3. ............................. 71

    5.4.4.

    ( ).............................................................................................. 73

    5.4.5. ...... 76

    5.4.6. ........................................................................... 77

  • 7/30/2019 50518497-simp1

    6/42

    6

    5.5. ..................................................................................................... 78

    5.5.1. ....................................................... 79

    5.6. ....................................................................................................... 80

    6. ................................................................................................................... 87

    6.1. / ............................................................................................ 87

    6.2 ...........................................................................................88

    6.3. ........................................................................................ 89

    6.4 .. ...................................................... 91

    6.5 ............................................................................. 92

    6.6 ......................................................................................................................... 92

    6.6.1 ....................................................................................................... 92

    6.6.2 ....................................................................................................... 93

    6.6.3 ................................................................. 93

    6.7 ....................................................................................................... 94

    6.7.1 ....................................................................................... 95

    6.8 . ...................................................................... 95

    6.9 .............................................................................................. 96

    6.10 .. ......................................... 97

    6.11 ..................................................................................... 98

    6.11.1 ................................................................. 100

    6.12 ......................................................................................... 101

    6.12.1 ..................................................................................... 1036.13 .................................................................................................................... 104

    ................................................................................ 111

  • 7/30/2019 50518497-simp1

    7/42

    8

    1

    :

    .

    - , -

    () .

    -, (, , , , -

    ...)

    () .

    .

    -

    . -

    .

    .

    ,

    , -

    , ,

    ., , -

    .

    (Mathematics for Economists) -

    (Mathematics of Finance).

    -

    .

    ,

    ,

    .

  • 7/30/2019 50518497-simp1

    8/42

    , , -

    , :

    . -

    . -

    .

    - . -

    , .

    . 1711 -Joanne Gena -

    .

    Lanye Kroneke -

    . Antoine Augustin Gaurnot (1801-1877), , -

    ,

    :

    -

    .

    .

    , .

    -

    .

    . , , -

    .

    .

  • 7/30/2019 50518497-simp1

    9/42

    2

    :

    ,

    :

    2

    , , , ..,

    .

    :

    .

    2.1.

    , -

    . , .

    -

    .

    - .

    - , .

    .

  • 7/30/2019 50518497-simp1

    10/42

    12

    -.

    100 .

    -. 12% :

    12E 0,12

    100= = .

    .

    . . -

    ,

    .

    - .

    2.2.

    ,

    .

    ,

    T K E X=

    :

    ( ) K T K KEX K 1 EX= + = + = +

    ,:

    K E XT

    12

    =

    :

    EX K 1

    12

    = +

    .

    :K E X

    T365

    =

    :

    EX 1365 = +

    .

  • 7/30/2019 50518497-simp1

    11/42

    13

    __________________________________________________________

    -

    12 30 360 -

    :

    KEXT

    360=

    EX K 1

    360

    = +

    .

    .

    -

    .

    365 ( 366 ).

    _____________________________________________________________________

    1

    3.500 1

    8%. ;

    : ( ) ( ) K 1 EX 3.500 1 0,08 1 3.780= + = + = .

    2

    10.000 2%. 45;

    : 10.000 0,02 45

    24,66365 365

    = = .

    ,

    . :

    =

    12

    =

    365

    =

    3

    400 3 6 .

    ;

    :12 12 6

    0,06 400 3

    = = =

    6%.

    ,

    .

    :

    =

    12=

    365=

  • 7/30/2019 50518497-simp1

    12/42

    14

    4

    1000 3% -

    10 ;

    :

    12 12 10

    4 1000 0,03

    = = =

    .

    -

    .

    :

    =

    12

    =

    365

    =

    :

    1 =

    +

    12

    12 =

    +

    365

    365 =

    +

    5

    1 5% -

    100 ;

    :

    100 2.000

    0,05 1= = =

    .

    6

    3% 5 -

    4860 . ;

    :12 12 4860

    4.800

    12 12 0,03 5

    = = =

    + +

    .

    1

    -

    ( 12

    = 365

    = ).

    =

    .

  • 7/30/2019 50518497-simp1

    13/42

    15

    7

    500 7,3% 40 .

    :

    500 40 20000= = = :

    365 5000

    0,073= =

    :

    20000 4

    5000= = = .

  • 7/30/2019 50518497-simp1

    14/42

    16

    1. () .

    )

    .

    )

    .

    )

    .

    )

    100 .

    ) .

    ) .

    ) .

    2. 2.000 8%. 3

    ;

    3. 4.000 90 4%. ;

    4. 2.400 5 50 . ;

    5. 73.000 4% 73.520 ;

    6. 9% 8 210 .

    ;

    7. 5%. 1 -

    13.125 . ;

    8. 500 1 510 ,

    ;

    9. -

    3.500 35 3,65% .

    10. -

    1.200 50 14,6% .

  • 7/30/2019 50518497-simp1

    15/42

    17

    2.3.

    -

    :

    i) . .

    ii) . -

    ,.

    iii) . -

    .

    -

    . :

    i) .

    ii) ( )

    () (cash card).

    iii) , , , .

    .

    10%. -

    .

    - . -

    2%, 10

    2 2 2 0,2 1,8%100

    = = .

    8

    1.500 1,6% . -

    5 ;

    :

    10

    1,6% 1,6% 1,6% 0,16% 1,44%100

    = = .

    :

    1.500 0,0144 5 9

    12 12

    = = =

    (!!!)

    . :

  • 7/30/2019 50518497-simp1

    16/42

    18

    2.3.1.

    . -

    ()

    . , -

    , .

    .

    .

    -

    .

    ,

    500 .

    (

    ). -

    . -

    (-

    !).

    . :

    (cash card) ., , .. .

    .

    , -

    (, , ).

    .

    ,

    ( )

    ( 18 ). -

    . -

    ,

    .

  • 7/30/2019 50518497-simp1

    17/42

  • 7/30/2019 50518497-simp1

    18/42

    20

    1. () ().

    ) .

    ) .

    ) .

    ) .

    ) .

    ) .

    )

    .

    )

    . ) .

    2. 6%.

    ;

    3. 3.000 21 . 2%.

    ( ) 1;

    4. 4%, 3.000 . 2 -

    2.000 . 6 ;

    5.

    6%, 6 108 ;

  • 7/30/2019 50518497-simp1

    19/42

    21

    2.4.

    . ,

    .

    .

    ,

    . -

    .

    .

    , -

    .

    .

    -.

    , ,

    . .

    .

    . -

    -

    .

    .

    9

    5.000 30

    12%. ;

    :

    5.000 0,12 30

    49,32365 365

    = = = .

    , :

    5.000 49,32 4.950,68 = .

  • 7/30/2019 50518497-simp1

    20/42

    22

    10

    1.500 2

    14%. 0,5% -

    15 . ;

    :

    :

    1.500 0,14 2 35

    12 12

    = = = .

    0, 05 1.500 7, 5 = .

    :

    1.500 35 7,5 15 1.442,5 = .

    , .

    .

    ,

    .

    .

    11

    -

    1.

    :

    2.2

    :

    365 365 5.000K 4951,17

    365 365 0,12 30

    = = =

    + +

    4.951,17 4.950,68 0,49 = .

    .

    12

    1.400 12%

    1340 . 3 -

    165 . .

    :

    1.400 1.340 60 = . 3 :

  • 7/30/2019 50518497-simp1

    21/42

    23

    1.400 0,12 3 42

    12 12

    = = = .

    60 42 18 = 165 3 30 75 =

    . :365 365 18

    730 0,12 75

    = = =

    .

    :

    1.400 730 670 = .

    _________________________________________________________

    -

    , ,

    . -

    ,

    2.2.

    ____________________________________________________________________

    13

    -

    2 .

    :

    35 7,5 15 57,5+ + =

    :

    1.500 57,5 1.442,5 = .

    :

    12 12 57,5 690 0,24

    1.442,5 2 2.885

    = = =

    24%.

    ,

    14%.

  • 7/30/2019 50518497-simp1

    22/42

    24

    1. () () ().

    )

    .

    )

    .

    ) ,

    .

    ) .

    ) -

    .

    ) .

    ) .

    2. 1.000 15%, 2 .

    .

    3. 2.500 10%, 3 .

    .

    4. 50 -

    14% 1.790 . ;

    5. 400 3

    386 . ;

    6. 2.000 12%

    1.860 . ;

    7. 900 15% 836,25

    . 4 3 .

    ;

    8. 12% 1.400 , 8

    . ;

    9. 200 .

    205 . ;

    10. 1.500

    20 10%. 0,6% 12 .

  • 7/30/2019 50518497-simp1

    23/42

    25

    2.5.E

    -

    .

    ,

    . .

    . ,

    .

    -. , .

    . , -

    .

    - .

    15

    10.000 .

    3,2% 5% .

    ;

    :

    :

    12 12 10.000 9.842,52

    12 12 0,032 6

    = = =

    + +

    10.000 9.842,52 157,48 =

    0,05 157,48 7,87 = .

    :

    9.842,52 7,87 9.850,39+ = .

    10.000 .

    :

    10.000 9.850,39 149,61 = .

    :

    12 12 149,61 0,0304 3,04%

    9.850,36 6

    = =

    .

  • 7/30/2019 50518497-simp1

    24/42

    26

    __________________________________________________________

    ,

    . , , -

    . -

    ,

    . -

    , .

    ______________________________________________________________________

    1. () () ().

    ) .

    ) .

    )

    .

    )

    () . )

    .

    2. 15.000 ,

    3,5% ;

    ()

    3. -

    5%; ;

    4. 19.607 2% -

    . ;

    5. 10.000 9.855

    . ;

  • 7/30/2019 50518497-simp1

    25/42

    27

    2.6.

    -

    () .

    .

    .

    .

    .

    ()

    () .

    :

    . 1 2 OA ,OA ,...OA

    1 2 , ,..., .

    .:

    16

    1.000 2

    1 . -

    12%.

    ; (

    )

    :

    :

    1 0,12 2 0,12 1 1.000 1

    12 12

    =

    0 0,99 1.000 0,98 =

    1.000 0,980 989,9

    0,99

    .

    :

    ( ) ( ) ( ) ( )1 1 2 2 1 1 1 ... 1 = + + +

    :1 2

    1 2

    ...

    1 1 1 1 = + + +

    + + + +.

  • 7/30/2019 50518497-simp1

    26/42

    28

    17

    1 -

    ().

    :

    :

    1

    1

    1 1

    12 12

    =

    + +

    1000

    1 0,12 2 0,121 1

    12 12

    =

    + +

    1.000 1.000 1,01

    990,21,01 1,02 1,02

    = = = .

    18

    1.000 1.500

    73 146 100 .

    8%; ()

    :

    1 21 2

    1 1 1

    365 365 365

    = +

    100 0,08 73 0,08 145 0,08 1 1.000 1 1.500 1

    365 365 365

    = +

    0 0,978 1.000 0,984 1.500 0,968 = +

    0 0,978 984 1.452 = +

    24360 0 2.490,8

    0,978= .

    -.

    () . -

    :

    :

    1 1 OA OA 1 T T E ... OA 1 T T E

    :

    1 2

    1 2

    ...

    1 1 1 1 .

  • 7/30/2019 50518497-simp1

    27/42

    29

    19

    1.000 2

    1 .

    12%. ; (

    )

    :

    ( )11

    1

    12

    =

    ( )2 1 0,12 1.000 1

    12

    =

    0 1.000 0, 99 990= = .

    20

    19 (-

    ).

    :

    ( )1

    1

    1

    12

    =

    +

    ( )1.0002 1 0,12

    112

    =

    +

    990,1= .

    21

    1.000 1.500

    73 143 100

    . -

    8%; ()

    :

    ( ) ( )1 21 2

    1 1

    365 365

    = +

    ( ) ( )73 100 0,08 143 100 0,08 1.000 1 1.500 1

    365 365

    = +

    ( ) ( ) 1.000 1 0,006 1.500 1 0,009= + +

    0 1.006 1.486,5= + 2492,5= .

  • 7/30/2019 50518497-simp1

    28/42

    30

    1. 45

    2.500 60 . -

    10% .

    ;

    2. 1.800 2

    3 . 14%

    .

    ;

    3. 4.000 90 45 . 9%

    .

    ;

    4. 500 2

    4 . 12%

    .

    ;

    5. 2.000 4.000

    35 50 75 .

    7%

    . ;

    6. 1.000, 2.000 2.500

    1, 2 3 2 .

    11%

    . ;

    7. 900

    800 1.200 70 100

    . 10%.

  • 7/30/2019 50518497-simp1

    29/42

    31

    () ,

    .

    ,

    , .

    ,

    , , ,

    , .

    . ,

    , 1998. , , 1968

    . , , 1992

    . - ., , 1994

    . - . , , 2003

    Adekunle, J.O., The demand for Money: Evidence from Developed and less devel-

    oped Economies, IMF Staff Press, Vol. 15, 1968

    Davidson, P.Money and the Real World, London, 2ed., 1978

    . , , , 1993.

    . -

    . -

    ,

    .

  • 7/30/2019 50518497-simp1

    30/42

    32

  • 7/30/2019 50518497-simp1

    31/42

    3

    :

    / :

    ,

    , . - -

    .

    :

    -

    , -

    .

    3.1.

    ,

    .

    -

    .

    -.

    1 . -,

    .

  • 7/30/2019 50518497-simp1

    32/42

    34

    3.2.

    , -

    , :

    ( )

    1 = +

    . ( )

    1 +

    1 .

    1

    .

    1

    1% 2% 10% 15%

    1 1,01 1,05 1,1 1,15

    5 1,05 1,25 1,5 1,75

    10 1,1 1,5 2 2,5

    15 1,15 1,75 2,5 3,25

    20 1,2 2 3 4

    25 1,25 2,25 3,5 4,75

    50 1,5 3,5 6 8,5

    100 2 6 11 16

    1

    1% 2% 10% 15%

    1 1,01 1,05 1,1 1,15

    5 1,051 1,28 1,61 2,01

    10 1,104 1,63 2,59 4,05

    15 1,16 2,08 4,18 8,14

    20 1,22 2,65 6,73 16,37

    25 1,282 3,39 10,83 32,92

    50 1,645 11,47 117,39 1.083,65

    100 2,705 131,5 13.780,61 1.174.313,4

    -

    .

  • 7/30/2019 50518497-simp1

    33/42

    35

    ,

    .

    , , -

    . 15 1.174.313,4 !!!

    (-

    ).

    1

    1.000 5%.

    10 ;

    ( ) ( ) 10

    1 1.000 1 0,05 1.628,89= + = + = .

    2

    2.000 10%

    3.200 ;

    ( ) ( ) 1 3.200 2.000 1 0,1= + = +

    ( ) 3.200 1,1 1,6 1,1

    2.000= = .

    51,1 1, 6105= 5 . (

    -

    , 5= -

    .

  • 7/30/2019 50518497-simp1

    34/42

    36

    1. () ()

    )

    .

    )

    .

    )

    .

    )

    .

    )

    .

    2. 15.000 -

    8% 15 ;

    3. 4% 12 ,

    3.202 ;

    4. 3500 5 5.636 .

    ;

    5. 5.000 6%

    7.970 ;

    6.

    5 ;

  • 7/30/2019 50518497-simp1

    35/42

    37

    3.3.

    .

    , ,

    -

    .

    3

    8.000 .

    5 4%;

    5 10 2%.:

    ( ) ( ) 10

    1 8.000 1 0,02 9.751,56= + = + = .

    -

    ;

    . .

    4 5.000 2,4% .

    6 8 ;

    6 2 1 13 + =

    2 . 13 :

    ( ) ( ) 13

    1 5.000 1 0,012 5.838,7= + = + =

    :' ' 0,012 2 1 5.838,7 1 5.850,38

    12 12

    = + = + =

    .

    ,

    , -

    . -

    . -

    .

  • 7/30/2019 50518497-simp1

    36/42

    38

    5

    30.000 2 -

    6%. ;

    ( )

    1 = +

    ( )2

    30.000 1 0,06= = +

    30.000 1,1236= =

    30.000

    1,1236= 26.700 .

    26.700 , 30.000 26.700 3.300 = .

    1 ,

    ( ) 1 = + . -

    2

    . 2

    2.

    2 . -

    ( )2'

    2 1 = + . :

    ( ) ( ) ( )2 2'

    2 2

    1 1 1 1 = + = + + = +

    2 21 1 1 1+ = + = + .

    3 -

    . -

    1 , 3 4

    6 12 3, 4, 62.

    :

    ( ) ( ) ( ) ( ) ( )3 62 4 12

    2 3 4 6 121 1 1 1 1 1 + = + = + = + = + = +

    6 10%, -

    , ;

    ( ) ( ) ( )2 2 2

    2 2 21 1 1 0,1 1 1,1 1 + = + + = + = +

    2 21 1,1 1,1 1 0,0488 4,88%+ = = .

    :

    ( )4 4

    4 41 1 1,1 1 0,0241 2,41%+ = + =

    ( )12 1212 121 1 1,1 1 0,00797 0,797%+ = + = .

  • 7/30/2019 50518497-simp1

    37/42

    39

    -

    -

    . 4 2

    4,88 2 9,76% = 12 0,797 12 9,564% = . -

    , -

    .

    7

    6%.

    3%. ;

    :

    ( ) ( )2 2

    21 1 1 1 0,03+ = + + = +

    ( )2

    1 0,03 1 1,0609 1 0,0609 6,09%= + = =

    , .

  • 7/30/2019 50518497-simp1

    38/42

    40

    1. 4.000 5%.

    6 ;

    2. 4%. 3,5

    8.040 , ;

    3. 2.500 3%.

    2.816 ;

    4. 1.000 3 1.194 .;

    5. 4.500 4%.

    17 ;

    6. 6% 15

    16.033 .

    ;

    7. 20.000 , 3

    8%. -

    ; ()

    8. 2

    10% 13.605 . ;

    9.

    40.000 8% 34.192 ;

    10. 15% , -

    , , .

    11. 3%, , -

    , , .

    12. 12% ,

    .

  • 7/30/2019 50518497-simp1

    39/42

    41

    13. 8% , -

    .

    14. 4,1%

    4% .

    ;

  • 7/30/2019 50518497-simp1

    40/42

    42

    3.4.

    -

    1 ,

    .

    .

    .

    1, 2, , 1, 2, ,

    .

    ,

    :

    ( ) ( ) ( ) ( )1 2 1 2

    ...

    1 1 1 1 = + + +

    + + + +.

    8

    50.000 1

    2 . 4%. -

    ;

    ( ) ( )1

    2 1

    1 1 =

    + + ( )2

    50.0001 0,041 0,04

    = ++

    50.000

    1,0816 1,04= 52.000= .

    9

    10.000 30.000 -

    3 1 2 .

    6%.;

    ( ) ( )1 2

    2 3

    1 1 1 = +

    ++ +

    ( ) ( )2 3

    10.000 30.000

    1 0,061 0,06 1 0,06= +

    ++ +

    8.396 28.302

    1,1236= +

    36.698

    1,1236

    = 41.234 .

  • 7/30/2019 50518497-simp1

    41/42

    43

    1. 50.000 6

    8 . 8%

    ;

    2. 10.000 7

    5 . 7%

    ;

    3. 20.000 40.000 -

    1 4 2 . - 6%, ;

    4. 50.000 , 60.000 30.000

    1, 3 5 2 .

    6%, ;

    5. 11.025 10.000 5%.

    2 .

    .

    (2 3) -

    .

    :

    : ,

    .

    : -

    -

    .

  • 7/30/2019 50518497-simp1

    42/42