,,,
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>
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