. , , ,

,,,



1

 

1. , N = 1000 ., r = 28%, ND:

1 ND> r 10% = 30%;

2 ND< r 10% = 10%;

3 ND= r = 20%.

n = 10 .

( ) r n N, :

ND , %;

N , .;

r , %;

n , , .

1

 

1 = 0,30*1000 + 1000 = 300 + 1000 = 250+833,33=1083,33

(1+0,20)1 (1+0,20)1 1,20 1,20

2 = 0,30*1000 + 0,30*1000 + 1000 = 300 + 300 + 1000 =

(1+0,20)1 (1+0,20)2 (1+0,20)2 1,20 1,44 1,44

= 250 + 208,33 + 694,44 = 1152,77

3 = 0,30*1000 + 0,30*1000 + 0,30*1000 + 1000 = 300 + 300 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+020)3 1,20 1,44

+ 300 + 1000 = 250 + 208,33 + 173,61 + 578,70 = 1210,64

1,728 1,728

4 = 0,30*1000 + 0,30*1000 + 0,30*1000 + 0,30*1000 + 1000 =

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)4

= 300 + 300 + 300 + 300 + 1000 =

1,20 1,44 1,728 2,073 2,073

= 250 + 208,33 + 173,61 + 144,72 + 482,39 = 1259,05

5 = 0,30*1000 + 0,30*1000 + 0,30*1000 + 0,30*1000 + 0,30* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+020)4 (1+0,20)5

+ 1000 = 300 + 300 + 300 + 300 + 300 +

(1+0,20)5 1,20 1,44 1,728 2,073 2,488

+ 1000 = 250 + 208,33 + 173,61 + 144,72+120,58+401,93=

2,488

= 1299,17

6 = 0,30*1000 + 0,30*1000 + 0,30*1000 + 0,30*1000 + 0,30* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+020)4 (1+0,20)5

+ 0,30*1000 + 1000 = 300 + 300 + 300 + 300 +

(1+0,20)6 (1+0,20)6 1,20 1,44 1,728 2,073

+ 300 + 300 + 1000 = 250 + 208,33 + 173,61 +

2,488 2,985 2,985

+ 144,72+120,58+100,50+335= 1332,74

7 = 0,30*1000 + 0,30*1000 + 0,30*1000 + 0,30*1000 + 0,30* 1000 +

(1+0,28)1 (1+0,28)2 (1+0,28)3 (1+028)4 (1+0,08)5

+ 0,30*1000 + 0,30*1000 + 1000 = 300 + 300 + 300 +

(1+0,20)6 (1+0,20)7 (1+0,20)7 1,20 1,44 1,728

+ 300 + 300 + 300 + 300 + 1000 =

2,073 2,488 2,985 3,583 3,583

= 250 + 208,33 + 173,61 + 144,72+120,58+100,50+ 83,79+279,09 = 1360,56

8 = 0,30*1000 + 0,30*1000 + 0,30*1000 + 0,30*1000 + 0,30* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)5

+ 0,30*1000 + 0,30*1000 +0,30*1000 + 1000 = 300 + 300 +

(1+0,20)6 (1+0,20)7 (1+0,20)8 (1*0,20)8 1,20 1,44

+ 300 + 300 + 300 + 300 + 300 +

1,728 2,073 2,488 2,985 3,583

+ 300 + 1000 = 250 + 208,33 + 173,61 + 144,72+

4,299 4,299

+120,58+100,50+83,79+69,78+232,61=1383,92

9 = 0,30*1000 + 0,30*1000 + 0,30*1000 + 0,30*1000 + 0,30* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)5

+ 0,30*1000 + 0,30*1000 +0,30*1000 + 0,30*1000 + 1000 = 300 +

(1+0,20)6 (1+0,20)7 (1+0,20)8 (1*0,20)9 (1*0,20)9 1,20

+ 300 + 300 + 300 + 300 + 300 +

1,44 1,728 2,073 2,488 2,985

+ 300 + 300 + 300 + 1000 =

3,583 4,299 5,159 5,159

= 296,87 + 231,93 + 181,19 + 141,56 + 110,59 + 86,40 + 67,50 + 52,73 +

+ 58,15+193,83=1420,75

10 = 0,30*1000 + 0,30*1000 + 0,30*1000 + 0,30*1000 + 0,30* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+020)4 (1+0,20)5

+ 0,30*1000 + 0,30*1000 + 0,30*1000 + 0,30*1000 + 0,30*1000 +

(1+0,20)6 (1+0,20)7 (1+0,20)8 (1*0,20)9 (1*0,20)10

+ 1000 = 300 + 300 + 300 + 300 + 300 +

(1*0,20)10 1,20 1,44 1,728 2,073 2,488

+ 300 + 300 + 300 + 300 +

2,985 3,583 4,299 5,159

+ 300 + 1000 = 296,87 + 231,93 + 181,19 + 141,56 +

6,192 6,192

+ 110,59 + 86,40 + 67,50 + 52,73+58,15+48,44+161,49=1436,85


2

 

1 = 0,10*1000 + 1000 = 100 + 1000 = 83,33 + 833,33= 916,66

(1+0,20)1 (1+0,20)1 1,20 1,20

2 = 0,10*1000 + 0,10*1000 + 1000 = 100 + 100 + 1000 =

(1+0,20)1 (1+0,20)2 (1+0,20)2 1,20 1,44 1,44

= 83,33+69,44+694,44= 847,21

3 = 0,10*1000 + 0,10*1000 + 0,10*1000 + 1000 = 100 + 100 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+020)3 1,20 1,44

+ 100 + 1000 = 83,33 + 69,44+57,87+578,70= 789,34

1,728 1,728

4 = 0,10*1000 + 0,10*1000 + 0,10*1000 + 0,10*1000 + 1000 =

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)4

= 100 + 100 + 100 + 100 + 1000 = 83,33 + 69,44+

1,20 1,44 1,728 2,073 2,073

+ 57,87+48,24+482,39=741,27

5 = 0,10*1000 + 0,10*1000 + 0,10*1000 + 0,10*1000 + 0,10* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)5

+ 1000 = 100 + 100 + 100 + 100 + 100 +

(1+0,20)5 1,20 1,44 1,728 2,073 2,488

+ 1000 = 83,33 + 69,44+57,87+48,24+40,19+401,92=700,99

2,488

6 = 0,10*1000 + 0,10*1000 + 0,10*1000 + 0,10*1000 + 0,10* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)5

+ 0,10*1000 + 1000 = 100 + 100 + 100 + 100 +

(1+0,20)6 (1+0,20)6 1,20 1,44 1,728 2,073

+ 100 + 100 + 1000 = 83,33 + 69,44+57,87+48,24+

2,488 2,985 2,985

+ 72,34+33,50+335=666,22

7 = 0,10*1000 + 0,10*1000 + 0,10*1000 + 0,10*1000 + 0,10* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)5

+ 0,10*1000 + 0,10*1000 + 1000 = 100 + 100 + 100 +

(1+0,20)6 (1+0,20)7 (1+0,20)7 1,20 1,44 1,728

+ 100 + 100 + 100 + 100 + 1000 =

2,073 2,488 2,985 3,583 3,583

= 83,33 + 69,44+57,87+48,24+72,34+33,50+ 27,91 + 279,09 = 671,72

8 = 0,10*1000 + 0,10*1000 + 0,10*1000 + 0,10*1000 + 0,10* 1000 +

(1+0,28)1 (1+0,28)2 (1+0,28)3 (1+0,20)4 (1+0,20)5

+ 0,10*1000 + 0,10*1000 +0,10*1000 + 1000 = 100 + 100 +

(1+0,20)6 (1+0,20)7 (1+0,20)8 (1*0,20)8 1,20 1,44

+ 100 + 100 + 100 + 100 + 100 +

1,728 2,073 2,488 2,985 3,583

+ 100 + 1000 =83,33 + 69,44+57,87+48,24+72,34 +

4,299 4,299

+ 33,50+ 27,91+23,26+232,61= 648,50

9 = 0,10*1000 + 0,10*1000 + 0,10*1000 + 0,10*1000 + 0,10* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)5

+ 0,10*1000 + 0,10*1000 +0,10*1000 + 0,10*1000 + 1000 = 100 +

(1+0,20)6 (1+0,20)7 (1+0,20)8 (1*0,20)9 (1*0,20)9 1,20

+ 100 + 100 + 100 + 100 + 100 +

1,44 1,728 2,073 2,488 2,985

+ 100 + 100 + 100 + 1000 =

3,583 4,299 5,159 5,159

=83,33 + 69,44+57,87+48,24+72,34+33,50+27,91+23,26+19,38+193,83=

=629,10

10 = 0,10*1000 + 0,10*1000 + 0,10*1000 + 0,10*1000 + 0,10* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)5

+ 0,10*1000 + 0,10*1000 + 0,10*1000 + 0,10*1000 + 0,10*1000 +

(1+0,20)6 (1+0,20)7 (1+0,20)8 (1*0,20)9 (1*0,20)10

+ 1000 = 100 + 100 + 100 + 100 + 100 +

(1*0,20)10 1,20 1,44 1,728 2,073 2,488

+ 100 + 100 + 100 + 100 +

2,985 3,583 4,299 5,159

+ 100 + 1000 = 83,33 + 69,44+57,87+48,24+72,34+

6,192 6,192

+ 33,50+27,91+23,26+19,38+16,15+161,49=612,91

3

 

1 = 0,20*1000 + 1000 = 200 + 1000 = 166,66 + 833,33 = 999,99

(1+0,20)1 (1+0,20)1 1,20 1,20

2 = 0,20*1000 + 0,20*1000 + 1000 = 200 + 200 + 1000 =

(1+0,28)1 (1+0,20)2 (1+0,20)2 1,20 1,44 1,44

= 166,66 + 138,88+694,44= 999,98

3 = 0,20*1000 + 0,20*1000 + 0,20*1000 + 1000 = 200 + 200 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)3 1,20 1,44

+ 200 + 1000 = 166,66 + 138,88+115,74+578,70=999,98

1,728 1,728

4 = 0,20*1000 + 0,20*1000 + 0,20*1000 + 0,20*1000 + 1000 =

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)4

= 200 + 200 + 200 + 200 + 1000 =

1,20 1,44 1,728 2,073 2,073

= 166,66 + 138,88+115,74+96,48+482,39=1000,1

5 = 0,20*1000 + 0,20*1000 + 0,20*1000 + 0,20*1000 + 0,20* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)5

+ 1000 = 200 + 200 + 200 + 200 + 200 +

(1+0,20)5 1,20 1,44 1,728 2,073 2,488

+ 1000 = 166,66 + 138,88+115,74+96,48+ 80,38+ 401,93=1000,06

2,488

6 = 0,20*1000 + 0,20*1000 + 0,20*1000 + 0,20*1000 + 0,20* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)5

+ 0,20*1000 + 1000 = 200 + 200 + 200 + 200 +

(1+0,20)6 (1+0,20)6 1,20 1,44 1,728 2,073

+ 200 + 200 + 1000 = 166,66 + 138,88+115,74+

2,488 2,985 2,985

+ 96,48+ 80,38+ 67+ 335= 1000,14

7 = 0,20*1000 + 0,20*1000 + 0,20*1000 + 0,20*1000 + 0,20* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)5

+ 0,20*1000 + 0,20*1000 + 1000 = 200 + 200 + 200 +

(1+0,20)6 (1+0,20)7 (1+0,20)7 1,20 1,44 1,728

+ 200 + 200 + 200 + 200 + 1000 =

2,073 2,488 2,985 3,583 3,583

= 166,66 + 138,88+115,74+96,48+ 80,38+ 67+55,82+279,09 = 1000,05

8 = 0,20*1000 + 0,20*1000 + 0,20*1000 + 0,20*1000 + 0,20* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)5

+ 0,20*1000 + 0,20*1000 +0,20*1000 + 1000 = 200 + 200 +

(1+0,20)6 (1+0,20)7 (1+0,20)8 (1*0,20)8 1,20 1,44

+ 200 + 200 + 200 + 200 + 200 +

1,728 2,073 2,488 2,985 3,583

+ 200 + 1000 =166,66 + 138,88+115,74+96,48 +

4,299 4,299

+ 80,38+ 67+55,82+46,52+232,61=1000,09

9 = 0,20*1000 + 0,20*1000 + 0,20*1000 + 0,20*1000 + 0,20* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)5

+ 0,20*1000 + 0,20*1000 +0,20*1000 + 0,20*1000 + 1000 = 200 +

(1+0,20)6 (1+0,20)7 (1+0,20)8 (1*0,20)9 (1*0,20)9 1,20

+ 200 + 200 + 200 + 200 + 200 +

1,44 1,728 2,073 2,488 2,985


+ 200 + 200 + 200 + 1000 =

3,583 4,299 5,159 5,159

= 166,66 + 138,88+115,74+96,48+80,38+ 67+55,82+46,52+ 38,76 +193,84=

= 1000,07

10 = 0,20*1000 + 0,20*1000 + 0,20*1000 + 0,20*1000 + 0,20* 1000 +

(1+0,20)1 (1+0,20)2 (1+0,20)3 (1+0,20)4 (1+0,20)5

+ 0,20*1000 + 0,20*1000 + 0,20*1000 + 0,20*1000 + 0,20*1000 +

(1+0,20)6 (1+0,20)7 (1+0,20)8 (1*0,20)9 (1*0,20)10

+ 1000 = 200 + 200 + 200 + 200 + 200 +

(1*0,20)10 1,20 1,44 1,728 2,073 2,488

+ 200 + 200 + 200 + 200 +

2,985 3,583 4,299 5,159

+ 200 + 1000 = 166,66 + 138,88+115,74+96,48+

6,192 6,192

+ 80,38+ 67+55,82+46,52+ 38,76 +32,30+ 161,50 = 1000,03

2. :

: . , . 10%, , , 10%, .


2

, n1 . (Ij, %) , , . β1, β2, β3.

1

:

n1,

n2,

,

β1, %

β2, %

β3, %

9 57 12 27

18

14

1. (n) (, , ) :

Δn =

I , %;

j ;

n .

n 1 = 1,011779969 - 1,014277591 = 0,02497621 = 0,025 .

Δn 2 = 1,007838244 1,0094966213 = 0,01657969 = 0,017 .

Δn 3 = 1,003911606 1,00473705 = 0,000825444 = 0,001 .

.

2.         (Z)

:

Z = β/100 * /365 * ,

β , %;

, ;

, ..

Z = 27/100 * 12/365 * 1000 = 0,27 * 0,03 * 1000 = 8,1 .

Z = 18/100 * 12/365 * 1000 = 0,18 * 0,03 * 1000 = 5,4 .

Z = 14/100 * 12/365 * 1000 = 0,14 *0,03 * 1000 = 4,2 .

3. ( ) (, .) ;

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

= 0,2*8,125 + 0,5*5,417 + 0,3*4,201 = 1,625+2,708+1,260 = 5,593 = 5,59 .

4. (, %) , :

= ( / 1000) * 100,


= (5,593/1000) *100= 0,005593 *100= 0,5593 = 0,56

2

- -

(Ij), %

7,5 5,0 2,5
(), 12 12 12
(β), % 27 18 14
, 0,2 0,5 0,3
() (. 1 . .), 8,125 5,417 4,201

:

- , .

0,025 0,017 0,001
- , . 8,1 5,4 4,2

, , 0,56 ., , , .

1 1. , N = 1000 ., r = 28%, ND: 1 ND&gt;

 

 

 

! , , , .
. , :