. , , ,

,,,

1.1

, .

:

 

, , ..

 

 

 

 

 

, .

, - .

() , , , . 100 . .

( - ). .

, (, , , . .).

, (, , ). . , .

. , . . , .

:

1.            , , , :

.. = + + +

2.            :

. = ..

3.            :

. = .. * i .

4.            :

. . = . = * i .

, .

, .

.

. - . .

, . , .

, , . , .

:

= . * / 100

, , :

. = + . . . .

,

. . , :

. . = . *n /12

, .

12

. . , :

. . = . * n` /12

, n` -

( ).

:

= + . .

:

= *

,

.

:

1.              - . :

) ( ), :

= /

, ;

) , :

= /

;

)

. = . /

,

;

)

= /

)

= / .

,

;

)

= /

,

-

.

2.              :

)

= /

,

1 ;

)

= /

)

= . /

,

.

:

= . * / 100

.

:

= 100 . .

= 13%

= 100000 * 13 /100 = 13 000 .

.

:

. = 66 . .

= 13%

= 66000 * 13 / 100 = 8580 .

.

:

= 62 . .

= 13%

= 62000 * 13 / 10000 = 8060 .

1

1

/

.

.

1. 100000 13000
2. 66000 8580
3. 62000 8060
: 228000 29640

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.2

:

1.  ( ) - , )

2.  - , , , ..

3.  - (, )

4.  :

   () - ( ) :

= **:

- ;

- - , , .

= 1 + 1 + 2 + 2 + 3 + 3

(1 + 2 + 3)*1

1,2,3 -

= 1 + 2*0,95

100

2 - , :

2 = 100% - 1 ( )

0,95 - , ,

   () - , , :

= + + + +

, - , .

, - , ( )

   () - . :

= + - + -

  

=

:

1.  = + *

2.  = 1 + 2*0,95

100

3.   2 = 100 - 1

:

1.  .

2.  .

3.  .

.

= 129300

= 15,8

1 = 93%

2 = 100-93=7%

= (93 + 7*0,95)/100 = 0,997

= 129300*15,8*0,997 = 2036811

.

:

= 14720

= 18,2

1 = 93%

= 14720*18,2*0,997 = 267100

2.

2

 

1. 129300 14720
2. 0,997 0,997
3. 15.8 18,2
4. 2036811 267100

1.3. ,

 

: ( ) ( ). . . , :

1. 

2. 

3. 

4. 

5.  .

.

:

1.  - () - , . :

   - . -. , . - (, , , , ). 70% 90%.

   - () - . , . , .

   - , .

   - - , , .

   () - .

2.  () - , ( , , ).

.

- . . .

di = (Pi/P)*100%

di - ( %)

Pi -

P -

:

1. 

2.  (, , , )

3. 

4.  -

5.  .

1.3.1

, .

3

.

/
1 365
2 117
3 248
4 26
5 21
6 5
7 ..
8 222
9 1776

 

1.3.2 .

.

- , . :

1. 

= /*

-

-

- ( )

2.   .

= /(**)

-

-

-

-

- , , :

= *100/(100-n)

n - , :

n = (/)*100%

-

- ()

:

  

   -

   , ,

( )

:

= /*

:

= 22

= 2 /

= 2

= 22/2*2 = 22

= 22/2 = 11

( ).

:

= /(**)

:

= 14720

= 2 /

= 1,15

= 1776

= 14720/(2*1,15*1776) = 4

= 4/2 = 2

:

= - 100/(100-)

:

=(/)*100 = 26/222 * 100 = 11,71%

:

= 26

= 222

= ( *100)/(100-11,71) = 2200/88,29 = 25

= ( *100)/88,29 = 400/88,29 = 5

5 10
3 6
4 8
2 4
3 6

= 10*100/88,29 = 11

= 600/88,29 = 7

= 800/88,29 = 9

= 400/88,29 = 5

= 600/88,29 = 7

, .

1 1 1
- 2 4 5
3 6 7
1 1 1
1 1 1

4

/
1

:

n

n

6

5

11

2

13

22

4

26

25

5

30

2

:

n

n

n

n

n

4

5

5

3

140

5

3

2

4

3

17

10

6

4

8

6

34

11

7

5

9

7

39

3 30 60 69
4

, ,

n

n -

n

n

n

2000

1700

1500

1100

1150

1

2

3

1

1

8

1

4

6

1

1

13

1

5

7

1

1

15

5 38 73 84

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.4.

 

, . . . , . . .

.

, .

. , .

:

1.            , .. /

2.            , .. / , .

3.            - / , .

, . , . , , . . , :

1.            .

2.            .

3.            , .

, / 3 :

1 / .

2 ().

.

3 . .

/ :

1.             . , , , , .

2.             .

3.             /.

4.             .

5.             / .

/ , .

/:

)

)

I.                   . :

)

-               , . . ;

-               / . . , . - .

) :

-               () , 6

= *

, , :

= / = *

-               -, , , .. :

= +

= % *

-               - :

:

. = + + 1

-               - , .

. = . *

I.                   / :

-               ,

= .i *

-               -,

= +

/ () , /. : , , , , , , , . .

/, .

. = +

= + +

= *

= /

= % *

= * 2 * * 0,2 *

= +

= + +

= * *

= * %

= + +

= * 12 *

= % *

= * 12 / * 2 * * 0.2

 

1.4.1.

 

, .

 

()

 

:

Ϡ = +

= + +

= *

= /

= % *

= * 2 * * 0,2 *

= * %

+ / 12 /

 

:

6 = 1,05 = 1,05 / 2 = 0,525

= 2 / = 129300*0.525 = 67883

= 129300 = 67882,50*52% = 35299

% = 52 = 1,05 *2*0,2*222*11 = 1026

= 222 = 67883+3529+1026=104208

= 11 = 104208*7,8% = 8128

% = 7,8% = 104208+8128 = 112336 ᠠ

= 25 = 112336/12/25 = 374

 

:

5 = 0,89 = 0,89 / 2 = 0,445

= 2 / = 129300*0.445 = 6550

= 14720 = 6550*52% =3406

% = 52 = 0,89 *2*0,2*222*2 = 158

= 222 = 6550+3406+158=10114

= 2 = 10114*7,8% = 789

% = 7,8% = 10114+789 = 10903 ᠠ

= 5 = 10903/12/5 = 182

 

()

 

Ϡ :

= +

= + +

= i * *

= i * 2 * 0.2 * *

= * %

= /12/

 

:

5 = 0.89 = 0.89*1776*6 = 9484

= 1776 = 9484*31% = 2940

= 6 = 0.89 *2 *0.2 *222 *3 =237 = 3 = 9484+237+2940 =12661

= 7 񠠠 = 126612 * 7,8% = 988

% = 31 = 12661 + 988 = 13649

% = 7.8% = 13649 / 12 / 7 = 162

= 222

:

4 = 0.78 = 0.78*1776*10 = 13853

= 1776 = 13853*31% = 4294

= 10 = 0.78 *2 *0.2 *222 *5 =346

= 5 = 13853+4294+346 =18493

= 11 = 6025 * 7,8% = 1442

% = 31 = 18493 + 1442 = 19935

% = 7.8% = 19935 / 12 / 11 = 151

= 222

:

5 = 0.89 = 0.89*1776*4 = 6323

= 1776 = 6323*31% = 1960

= 4 = 0.89 *2 *0.2 *222 *2 =158

= 2 = 6323+1960+158 =8441

= 5 = 8441 * 7,8% = 658

% = 31 = 8441 +658 = 9099

% = 7.8% = 9099 / 12 / 5 = 152

= 222

:

4 = 0.78 = 0.65*1776*8 = 9235

= 1776 = 9235*31% = 2863

= 10 = 0.65 *2 *0.2 *222 *4 = 230

= 5 = 9235+2863 + 230=12128

= 11 = 12128 * 7,8% = 962

% = 31 = 12128 + 962 = 13290

% = 7.8% = 13290 / 12 /9 = 123

= 222

:

=

= + +

= * 12 *

= * %

= * 12 / * 2 * 0.2 * *

:

= 140 = 140 * 12 * *6 =

= 10 = 10080*31% = 3125

= 5 = 140/12/1776 *0.2 *222 *3 = 252

= 11 = 10080+3125+252 =13457

% = 31 = 13457 / 12 / 7 = 160

= 222

5

 

/ . . / . %

. .

. / / . . . / .

 

1

. ..

.

.

25

5

6

5

1.05

0.89

67883

6550

52

52

35299

3406

1026

158

104208

10114

8128

789

112336

10903

374

182

30 1.94 74433 38705 1184 114322 8917 123239 340
2

.

11

7

5

9

7

4

5

5

3

140.

0.78

0.89

089

0.65

13853

9484

6323

9235

10080

31

31

31

31

31

4294

2940

1960

2663

3125

346

237

158

230

252

18493

12661

8441

12128

13457

1442

988

658

962

19935

13649

9099

13090

13457

151

1162

1152

1121

1160

39 48975 14982 1223 65180 4050 69230 148

 

69 74433 48975 53687 2407 179502 12967 192469 232

 

1.4.2 , .

, , - . :

= + +

=*12*

Ϡ = *%

= *12/*2*0,2**

= /(12*)

= 2000

%: = 52%

= 1

= 1

= 1

=1776

= 2000*12*1 = 24000

= 24000*52% = 12480

= 24000 + 12480 = 36480

= 36480/12 = 3040

:

= 1700 .

%Ϡ = 52%

= 4

= 2

= 5

= 1700*12*4 = 81600

= 81600*52% = 42432

= 1700*12/1776*2*0,2*222*2 = 2040

= 81600 + 42432 + 2040 = 126072

= 126072/60 = 2110

:

= 1500

% = 52%

= 3

= 6

= 7

= 1500*12*6 = 108000

= 108000*52% = 561600

= 1500*12/1776*2*0,2*222*3 = 2700

= 108000 + 56160 + 2700 = 166860

= 166860/84 = 1986

:

= 1100

% = 52%

= 1

= 1

= 1

= 1100*12*1 = 13200

= 13200*52% = 6864

= 13200 + 6864 = 20064

= 20064/12 = 1672

:

= 1150

% = 52%

= 1

= 1

= 1

= 1150*12*1 = 13800

= 13800*52% = 7176

= 13800 + 7176 = 20976

= 20976/12 = 1748

6

 

6

, ,

 

/
1. 1 24000 12480 36480
2. 5 81600 2040 42432 126072
3. 7 108000 2700 56160 166860
4. 1 13200 6864 20064
5. 1 13800 7176 20976
15 240600 4740 125112 370452

5 6

7

.

1. 30 114322 8917 123239
2. 39 65180 4050 69230
3. , , 15 370452 370452
84 549954 12967 562921

1.4.3

 

8.

.

 

/
1. 2303911
2.

-

..

84

69

3. 33390
4. 27428
5. 562921
6. 558

 

 

 

1.5

.

- . . .

: ( , . ), ( ) , .

:

1.  ;

2.  ;

3.  ;

4. 

:

1.  :

  

   , , .

2.  - , , , .

3.  () ()

4.  .

, ( , / ..)

, (, / , ). .

5.  

- :

   - .

   - ( + )

   - ( + )

   - ( + )

6.   :

   - - , .

   - - , , , .

7.   , , 2- :

   -

   - % , ( , ).

1.5.1 , , ,

 

9.

.

 

-
129300 0,63 81459 8030 676110
14720 0,59 8685 8,10 70349

1.5.2 , .

10.

.

 

 

/ .

1.

1.1

1.2

1.3

1.4

.

, , .

.

.

.

97164

1280

65180

4050

26654

2. . 3840
3. . 16640
4. , . 17647
: 135291

10

1.           : 1280 +65180 + 4050 +26654 = 97164

1.1 ..: (66000 + 62000 )*1% = 1280

1.2 :65180

1.3 : 4050

1.4 : (65180 + 4050)*38,5% = 26654

2.   : (66000+ 62000)*3% = 3840

3.   : 8580 +8060 = 16640

4.   , : 117644 *15% = 17647

: 117644 + 17647 = 135291

11.

.

 

/ .

1.

1.1

1.2.

.

513076

370452

142624

2.

2.1

2.3

2.4

.

, , , .

.

.

20000

5000

2000

13000

3. 13800
4. 1-3: 546876
5. 82031
: 628907

11

1. :

370452 + 142624 =513076

1.1 : 370452

1.2 : 370452*38,5% = 142624

2.   :

5000 + 2000 + 13000 = 20000

2.1      , , , :100000*5% =5000

2.2 :

100000*2% = 2000

2.3 :13000

3.   : 69*200 = 13800

4.   513076 + 20000 + 13800 = 546876

5.   : 546876*15% = 82031

6.   : 546876 + 82031 = 6289075

1.5.3

12.

.

- -
1.     676110 5,23 70349 4,78
2. 13522 0,11 1407 0,10
3. 87924 0,68 11482 0,78
4. / 104208 0,81 10114 0,69
5. / 8128 0,06 789 0,05
6. - 43249 0,33 4198 0,29
7. 119056 0,92 16235 1,10
8. 553438 4,28 75469 5,13
9. 1605635 12,42 190043 12,91
10. 53146 0,41 5158 0,35
11. 1658781 12,83 195201 13,26
12. 134361 1,04 15811 1,07
13. 1793142 13,87 211012 14,34

12

1.

= 676110

= 70349

2.  

= 676110*2% = 13522

= 70349*2% = 1407

3.

= 129300*0,68=87924

= 14720*0,78=11482

4.

= 104208

= 10114

5.

= 8128

= 789

6.

=112336 *38,5% = 43249

= 10903*38,5% = 4198

7.

:

=2036811/(2036811+267100)*100% = 88%

=135291*88% = 119056

= 135291- 119056 =16235

8.

=628907*88% = 553438

= 628907 - 553438 = 75469

9.

=

676110+13522+87924+104208+8128+43249+119056+553438=1605635

= 70349+1407+11482+10114+789+4198+16235+75469=190043

10.

= 104208*51% = 53146

= 10114*51% = 5158

11.

= 1605635 + 53146 = 1658781

=190043 + 5158 = 195201

12.

=1658781*8,1% = 134361

= 195201*8,1% = 15811

13.

= 1658781 + 134361 = 1793142

=195201+ 15811 = 211012

6

 

- .

- , .. ,

:

1.           , ,

2.           , . . - . , .

3.          

:

. () . :

1.           ()

2.          

3.          

. . :

= +- +- +-

= ---

= *

, -

:

= - * i

,

I

:

=

, . :

1.           . .

2.           . .

3.           . .

. 2 :

1.           :

= / ()*100%

,

2.           :

= /(+)*100%

.

.

13

1.

15,8*,997 = 15,75

18,2*0,997 = 18,15

2.

13,87

14,34

3.

15,75- 13,87 =1,88

18,15 14,34 = 3,81

4.

= / *100%

1,88/13,87*100% = 13,55%

3,81/14,34*100% = 26,57%

1 .

Z = C/

13,87/15,75= 0,88

14,34/18,5 = 0,79

13.

1. 15,75 18,15
2. 13,87 14,34
3. 1,88 3,81
% 13,55 26,57
1.1 , . :

 

 

 

! , , , .
. , :