15
Вежби по финансиска и актуарска математика Маја Сребренова 1. Каде фирма од Њујорк ќе купи, а каде ке продаде пченица ако пченицата котира во Бон 22,75 евра во 100 килограми, во Стокхолм 192,8 sek за 1000 килограми, во Лондон 120,81 GBP за 1016 килограми. Во Њујорк нотира девизата на Бон 0,9225, девизата на Стокхолм нотира 0,1079 а девизата на Лондон 1,7050. Трошоците за транспорт во Бон се 7% а во Стокхолм 3% и во Лондон се 4%. Решение: Бон: x $ 1kg. Пченица 100 kg. 22,75 € 100 € 107 € 1 € 0,9225 $ 9225 . 0 107 75 . 22 1 1 100 100 x 595 . 2245 10000 x 10000 595 . 2245 x $ 22 . 0 x Стокхолм: $ x 1kg пченица 100kg 192.822 sek 100 sek 103 sek 1 sek 0.1079 $ 1079 . 0 103 822 . 192 1 1 100 100 x 965 . 2142 10000 x 10000 965 . 2142 x $ 21 . 0 x Лондон: x $ 1 kg пченица 100 kg 11.89 GBP 100 GBP 104 GBP 1 GBP 1.7050 $ 1.7050 104 11.89 1 1 100 100 x 3348 . 2108 10000 x 10000 3348 . 2108 x $ 21 . 0 x

Vezbi Fin.mat

  • View
    263

  • Download
    13

Embed Size (px)

Citation preview

  • 1. ,

    22,75 100 , 192,8 sek 1000

    , 120,81 GBP 1016 .

    0,9225, 0,1079

    1,7050. 7%

    3% 4%.

    :

    :

    x $ 1kg.

    100 kg. 22,75

    100 107

    1 0,9225 $

    9225.010775.2211100100 x

    595.224510000x

    10000

    595.2245x

    $22.0x

    :

    $x 1kg

    100kg 192.822 sek

    100 sek 103 sek

    1 sek 0.1079 $

    1079.0103822.19211100100 x

    965.214210000x

    10000

    965.2142x

    $21.0x

    :

    x $ 1 kg

    100 kg 11.89 GBP

    100 GBP 104 GBP

    1 GBP 1.7050 $

    1.7050104 11.8911100100 x

    3348.210810000x

    10000

    3348.2108x

    $21.0x

  • 2. 20 30 , 10

    35 , 65 36 .

    1 ?

    :

    30 kg 30 . 1 kg = 600.

    10 kg 35 . 1 kg =350.

    65 kg 36 . 1 kg =2340 .

    95 kg x . 1 kg = 3290 .

    329095 x

    95

    3290x

    65.34x .

    3.

    35 48

    260 40

    ?

    :

    35 . kg 48-40=8

    40 kg

    48 kg 40-35=5

    13

    260 kg : 13 = 20 kg

    1 = 20 kg

    35 . 160208 kg

    48 . 100205 kg

  • 4. 70%, 40%, 62%, 52% 60%

    252 50%?

    :

    40% 2+10+12+20=44

    52% 10 l303

    60% 50% l30310

    62% l30310

    70% l30310

    84

    252 l : 84 = l3

    44 ll 1323

    5. 40 50 , 60

    55 170 .

    68 72

    60 ?

    :

    40 kg 50 . kg = 2000 .

    60 kg 55 . kg = 3300.

    100 kg kg = 5300 .

    kgx

    x

    x

    .53

    100

    5300

    5300100

    53 . 8+12=20 kg1005

  • 68. 60.

    72 .

    kg

    kg

    kg

    3557

    3557

    100520

    534:170

    3557

    3557

    1

    6. 48000

    03.03 13.07 5% 4,360?

    :

    :

    360,48000

    %5

    k

    S

    p

    VII

    VI

    V

    IV

    III

    13

    30

    31

    30

    28

    k

    k

    880

    360100

    132548000

    132

    7. 11% 3 9

    116370 . ? (30;360)

    :

    1200003630116370

    3630

    991136000

    9911116370

    116370

    9303

    %11

    S

    k

    k

    kS

    d

    p

    8. 2001 7%

    8,2%

  • 10,8%.

    .

    :

    %12.1100011215.0011215.01007100

    72.8

    100100100

    )%(8.10

    )_%(2.8

    %7

    *

    gggg

    i

    ipg

    p

    p

    i

    %55.3100035514.0035514.01007100

    78.10

    100100100

    *

    gg

    gg

    i

    ipg

    9. 10000 9%

    ?

    :

    .03.20381

    03.203810225.10225.0110000100

    4

    9

    110000

    1001

    4

    .8

    ).(.%9

    .10000

    3232

    48

    0

    0

    S

    S

    m

    p

    SS

    m

    n

    dapp

    S

    mn

    10. 35000 4%

    42000 ?

  • :

    .6.4

    04.1log

    2.1log

    2.1log04.1log

    04.12.1

    04.135000

    42000

    35000:/04.13500042000

    100

    413500042000

    1001

    ?

    ).(.%4

    .35000

    .42000

    0

    n

    n

    n

    pSS

    n

    dapp

    S

    S

    n

    n

    n

    n

    n

    n

    n

    11. 150000

    250000 ?

    :

    2001667.1

    2001667.1

    2001

    150000

    250000

    150000:/200

    1150000250000

    100

    21150000250000

    30

    30

    30

    30

    215

    p

    p

    p

    p

    p

    %4.3

    200200017.1

    200/200

    1017.1

    p

    p

    p

    mn

    m

    p

    SS

    p

    n

    m

    S

    S

    1001

    ?

    .15

    2

    .250000

    .150000

    0

    0

  • 12. 50000 8 6%

    ?

    :

    09.81098

    622.150000

    01522.0150000

    5.1100

    5.1150000

    4

    6100

    4

    6

    150000

    100

    1

    ?

    4

    %6

    8

    .50000

    32

    32

    48

    0

    0

    S

    S

    S

    S

    S

    m

    m

    SS

    S

    m

    n

    S

    mn

    13. 150000 15

    250000 ?

  • :

    215

    0

    0

    2100

    21150000250000

    100

    1

    250000

    2

    ?

    15

    .150000

    m

    m

    SS

    S

    m

    n

    S

    mn

    %377.3

    2400

    21017.1

    2

    20021017.1

    2100

    21017.1

    2100

    21

    017.1

    667.1

    667.1

    150000

    250000

    150:/150000250000

    30

    30

    30

    32

    14. 10000 5%

    12500 4,5% .

    ?

    :

  • nnn

    n

    n

    SS

    S

    S

    SS

    )05.1(12500:/047.112500)05.1(10000

    '

    047.112500'

    5.4100

    5.4112500'

    1001' 0

    .97

    997.0log

    8.0log

    8.0log997.0log

    8.0997.0

    8.005.1

    047.1

    8.005.1

    047.1

    05.112500

    047.112500

    05.1125000

    05.110000

    n

    n

    n

    n

    n

    n

    n

    n

    n

    n

    n

    15. 8 20000 6 15000

    4% .

    10 80000

    ? ( )

    :

    n

    n

    S

    S

    SS

    aap

    S

    aap

    S

    05.110000

    5100

    5110000

    1001

    ).(.%5,4

    .12500

    ).(.%5

    .10000

    0

    0

    0

    ).(.%4

    6

    15000

    ).(.%4

    8

    20000

    0

    0

    aap

    n

    S

    aap

    n

    S

  • 6.6299

    5041.1

    64.7052480000

    5041.164.7052480000

    5041.127.4688880000

    4100

    4127.4688880000

    1001

    ).(.%4

    10

    27.46888

    80000

    27.46888

    191644100

    4115000

    27.277240416.01200004100

    4120000

    1001

    10

    0

    0

    68

    6

    6

    8

    8

    8

    0

    x

    x

    x

    x

    x

    SS

    aap

    n

    xS

    S

    SS

    S

    S

    SS

    n

    n

    n

    n

    n

    16. 20 2000 8

    10000 .

    8% .

    5%

    20000 ?

    :

    2000 .( 20.) 10000.( 8.)

    m

    m

    SS

    m

    aap

    n

    S

    100

    1

    4

    ).(.%8

    .12

    .2000

    04,12

    0

    46.5274637.220000408.012000

    4

    8100

    4

    8

    1200048

    412

    4,12

    S

  • m

    m

    SS

    m

    aap

    n

    S

    100

    1

    4

    ).(.%8

    8

    46.15274

    04,8

    0

    94.29158637.246.152740408.0146.15274

    4

    8100

    4

    8

    146.1527448

    412

    4,8

    S

    :

    n

    n

    n

    SS

    S

    aap

    S

    1001

    .200000

    ).(.%5

    94,29158

    0

    0

    .38

    053.1log

    86.6log

    86.6log053.1log

    86.6053.1

    94.29158

    200000053.1

    053.194.29158200000

    053.0194.29158200000

    5100

    5194.29158200000

    n

    n

    n

    n

    n

    n

    n

    n

  • 17. B 250000

    15.05 , 06.04.

    :

    ) 8%

    ) 8%

    :

    at

    N

    39

    .250000

    )

    360001

    tp

    NE

    33.2478680086.1

    250000

    0086.01

    250000

    36000

    3981

    250000

    E

    END

    67.213133.247868250000 D

    ) t

    p

    NE

    360001

    75.247843

    0087.1

    250000

    00022.01

    250000

    36000

    81

    2500003939

    E

    END

    25.215675.247843250000 D

    18. B 250000

    15.05 , 06.04.

    :

    ) 8% ;

    ) 8% ;

    :

    at

    N

    39

    .250000

  • ) p=8%()

    93.780086.1

    8

    36000

    3981

    8

    d

    360001

    tdNE

    25.2478600855.0125000036000

    3993.71250000

    E

    ) p=8%()

    407.708.1

    8

    100

    81

    8

    d

    td

    NE

    360001

    7.24800100020575.0125000036000

    407.71250000

    39

    39

    E

    19.

    300000 20.05.

    23.03

    8%

    0.045% 100 .

    ?

    :

    d

    t

    N

    %045.0

    %8

    58

    03.23

    05.20

    .300000

    360001

    tdNE

  • 2961609872.03000000128.0130000036000

    5881300000

    E

    END

    3840296160300000 D

    - 23.03

    - 300000

    - 0,045%

    - 8% : 3840

    - : .135300000100

    045.0

    - : 100

    300000-3840-135-100=295925

    20. 25.01

    26.04

    40000000 .

    :

    - 1 5000000

    89,66;

    - 2 5000000

    89,73;

    - 3 22000000

    89,68;

    - 4 14000000

    89,75;

    - 5 5000000

    89,65;

    100000 .

    ?

    :

    100000 100000 4 89,75 14000000 14100000

  • 2 89,73 5000000 19100000 3 89,68 22000000 41100000 1 89,66 5000000 46100000 5 89,65 5000000 51100000

    2 4

    .

    , ..

    69.895

    47.448

    5

    65.8966.8968.8973.8975.89