50518497-simp1
TRANSCRIPT
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, .
, , , ,
, ...... ...,, 1.1. 1.1.2.. (...).
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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
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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
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(Mathematics for Economists) -
(Mathematics of Finance).
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Lanye Kroneke -
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2.1.
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100 .
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12E 0,12
100= = .
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13
__________________________________________________________
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12 30 360 -
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KEXT
360=
EX K 1
360
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365 ( 366 ).
_____________________________________________________________________
1
3.500 1
8%. ;
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2
10.000 2%. 45;
: 10.000 0,02 45
24,66365 365
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=
12
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400 3 6 .
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0,06 400 3
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6%.
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12=
365=
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14
4
1000 3% -
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12 12 10
4 1000 0,03
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=
12
=
365
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1 =
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365 =
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1 5% -
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100 2.000
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6
3% 5 -
4860 . ;
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4.800
12 12 0,03 5
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=
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15
7
500 7,3% 40 .
:
500 40 20000= = = :
365 5000
0,073= =
:
20000 4
5000= = = .
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16
1. () .
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100 .
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2. 2.000 8%. 3
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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% .
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17
2.3.
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1,6% 1,6% 1,6% 0,16% 1,44%100
= = .
:
1.500 0,0144 5 9
12 12
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(!!!)
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2.3.1.
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1. () ().
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2. 6%.
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3. 3.000 21 . 2%.
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4. 4%, 3.000 . 2 -
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5.
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2.4.
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5.000 30
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, :
5.000 49,32 4.950,68 = .
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22
10
1.500 2
14%. 0,5% -
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0, 05 1.500 7, 5 = .
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1.500 35 7,5 15 1.442,5 = .
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365 365 5.000K 4951,17
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4.951,17 4.950,68 0,49 = .
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12
1.400 12%
1340 . 3 -
165 . .
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1.400 1.340 60 = . 3 :
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1.400 0,12 3 42
12 12
= = = .
60 42 18 = 165 3 30 75 =
. :365 365 18
730 0,12 75
= = =
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:
1.400 730 670 = .
_________________________________________________________
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2.2.
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35 7,5 15 57,5+ + =
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12 12 57,5 690 0,24
1.442,5 2 2.885
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24%.
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14%.
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24
1. () () ().
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6. 2.000 12%
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7. 900 15% 836,25
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2.5.E
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10.000 .
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10.000 9.842,52 157,48 =
0,05 157,48 7,87 = .
:
9.842,52 7,87 9.850,39+ = .
10.000 .
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10.000 9.850,39 149,61 = .
:
12 12 149,61 0,0304 3,04%
9.850,36 6
= =
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__________________________________________________________
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4. 19.607 2% -
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5. 10.000 9.855
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2.6.
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1.000 0,980 989,9
0,99
.
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( ) ( ) ( ) ( )1 1 2 2 1 1 1 ... 1 = + + +
:1 2
1 2
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28
17
1 -
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=
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1 0,12 2 0,121 1
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18
1.000 1.500
73 146 100 .
8%; ()
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1 21 2
1 1 1
365 365 365
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100 0,08 73 0,08 145 0,08 1 1.000 1 1.500 1
365 365 365
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0 0,978 1.000 0,984 1.500 0,968 = +
0 0,978 984 1.452 = +
24360 0 2.490,8
0,978= .
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1 1 OA OA 1 T T E ... OA 1 T T E
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29
19
1.000 2
1 .
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1.000 1.500
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365 365
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365 365
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0 1.006 1.486,5= + 2492,5= .
-
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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%
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6. 1.000, 2.000 2.500
1, 2 3 2 .
11%
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800 1.200 70 100
. 10%.
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31
() ,
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,
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, 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.
. -
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3
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3.1.
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34
3.2.
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( )
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
-
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,
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(-
).
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= -
.
-
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1. () ()
)
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2. 15.000 -
8% 15 ;
3. 4% 12 ,
3.202 ;
4. 3500 5 5.636 .
;
5. 5.000 6%
7.970 ;
6.
5 ;
-
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3.3.
.
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-
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3
8.000 .
5 4%;
5 10 2%.:
( ) ( ) 10
1 8.000 1 0,02 9.751,56= + = + = .
-
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6 8 ;
6 2 1 13 + =
2 . 13 :
( ) ( ) 13
1 5.000 1 0,012 5.838,7= + = + =
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12 12
= + = + =
.
,
, -
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. -
.
-
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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 -
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1 , 3 4
6 12 3, 4, 62.
:
( ) ( ) ( ) ( ) ( )3 62 4 12
2 3 4 6 121 1 1 1 1 1 + = + = + = + = + = +
6 10%, -
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( ) ( ) ( )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%+ = + = .
-
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-
-
. 4 2
4,88 2 9,76% = 12 0,797 12 9,564% = . -
, -
.
7
6%.
3%. ;
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( ) ( )2 2
21 1 1 1 0,03+ = + + = +
( )2
1 0,03 1 1,0609 1 0,0609 6,09%= + = =
, .
-
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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% , -
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11. 3%, , -
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12. 12% ,
.
-
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13. 8% , -
.
14. 4,1%
4% .
;
-
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3.4.
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1 ,
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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 .
-
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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 .
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