3.1.1. 3 . . , 25% . , 7 . , ? , ?
. , 3 . ., - 7 , . ( ), .
3 3 3 3 3 3 3
0 1 2 3 4 5 6 7 t
7 (.. ) (116), r =0,25, 1 =2,.. = 7 =3. , (120), A = 3 . ., = 7:
. .
F(25%,1) . 3 3, , .
( ), 7 45,221 . ., . (121), :
. .
, (65):
. .
, , :
3 3 3 3 3 3 3
0 1 2 3 4 5 6 7 t
(118) (119) (126) (127) m = = 1
. .;
. .
3.1.2. , : ) 20 . . - ; ) 240 . . - . , 30% ? ?
. = 6 =20 . . :
20 20 20 20 20 20
0 1 2 3 4 5 6 t
30% (, ). (120), r = 30%:
|
|
. .
, , () .
, . (121) , :
. .
(65) Fn =240 . .:
. .
, : () .
, , . ., :
. .
. .
3.1.3. 8 . . , , 24% : ) ; ) ; ) .
. ) . , (122) = 8. ., = 3, r = 24%, m = 1, = 4 :
. .
, , , , r = 0,24:
, (129) :
. .
) (120), .
. .
) , (122) A = 8 . ., n = 3, r = 24%, m = 12, = 4, :
. .
, S 1 < S 2 < S S 1 < , ( ) (122), .
, , , ( ). , (122)-(124) A .
3.1.4. , , 30 . . . 32%. , , : ) ; ) ; ) .
. (123), = 30 . ., r = 32%, = 5, = 2.
) m = 2 , , mn =2 . 5 = 10, , . :
. .
) m = 4, mn = 4 5 = 20, , ,
. .
) m = 12, , , , . ,
. .
|
|
, .
3.1.5. 36% , 6 8 . ., , : ) ; ) ; ) ?
. = 8 . ., = 6.
) r = 36%, (121) :
. .
) , (123) = 12, = 1, :
. .
. r (12) = 0,36 (63):
(121) r = 0,4256:
. .
.
) (132) = 0,36, = 1, :
. .
3.1.6. 30% , 8 12 . ., 3 , , : ) ; ) ; ) ?
. p - p = 4, A = 12/4 = 3 . ., = 8.
) r = 30%, m = 1, (123) :
. .
) m = 2 , , mn = 2 8 =16, . (123):
. .
, , , .
) , = 0,3 (132):
. .
3.1.7. 15 10 . . , . , : ) ; ) 3 ; ) 4,5 , 4, 10 24% ?
. , , = 15 2 = 30. 2, 5 12%. h , . ( ) , (.. ), ( . .):
) h = 0:
10 10 10 10 10 10 10 10 10 10 10 10
0 1 2 3 4 5 6 7 8..27 28 29 30
t
) :
10 10 10 10 10 10 10 10
0 1 2 3 4 5 6 7 8 9 10 27 28 29 30
t
) :
10 10 10 10
0 1 2 3 4 5 6 7 8 9 10 28 29 30
t
) (121), F4(r, n) , . , = 10, r = 2%, :
. .
) (125), h = 6. vh = F 2(r, h), , , r = 5% (125):
|
|
. .
) (125), h = 9. , r = 12%:
. .
. ( . .) .
h | R | ||
2% | 5% | 12% | |
223,965 | 153,725 | 80,552 | |
198,881 | 114,710 | 40,808 | |
187,414 | 99,047 | 29,047 |
, , , . , 4,5 (.. 9 ) 24% , 29,047 . . (, , ).
, (125) h . , , (125) :
.. , . , h = 9, r = 12%:
. .
1 . , (125) 29,047 . ., .
, , h = 0 (125) (121).
3.1.8. 350 . . 60 . . 28% . , , : ) ; ) ; ) .
. ) , . -, (120) , :
. ., A = 60 . ., r = 0,28. :
.
-, F 3 (r, ), (120) . (120) :
,
, , :
,
(1,28)n = 2,6333. , :
, .. = 4. , (120), :
. .
, 58,183 . ., 4 350 . . , 350 FM 2(28%,4) = 130,385 . ., 4 . 130,385 . . , 58,183 . .
) , (122) , p =1, m = 2. :
(1,14)2n=2,748. : .
) m = 12, (122) :
, .
, .
3.1.9. , ( 65 ) 25 , 8000 . 18 . , 40 , 20%?
|
|
. A = 8000 . n = 18 . r = 20%, (121) :
.
. (120), .:
.
, 81 . 57 .
3.1.10. 5 400 . ., 20%. ( ) , , 400 . . , , , 24% .
. , R - . . ., R. = + 80. (120), . ., n = 5, r = 24%:
, . .
, R = 49,689 + 80 = 129,699 . .
3.1.11. 200 . . 4 ( 50 . .). 80 . . , 18% ()?
. . :
. .
, , , 50 . . , . , . :
) = 50, n = 4, r = 18% 80 . .;
) = 50, n = 3, r = 18% 50 80 . .
(120) :
. .
(126) :
. .
, . , (210,77 . .), (50 . .) (80 . .). , , 340,77 . . .
3.1.12. 8 . . . 37 . ., 20% ?
. (124) A = 8 . ., r = 0,2 p = m = 1, , . . , .
3.1.13. ( ) . , , 12 . ., : ) 28%; ) 28%; ) 28%.
. , A = 12 . . .
) r = 0,28, (124) = m = 1 :
. .
) (124) r = 0,28, m = 4, = 1, :
. .
) p = 1, = 0,28, (133) c:
. .
3.1.14. . 20 . . 40 . . 100 . . , 25% ? , ?
|
|
. , .
(124) r = 0,25 = m = 1, :
. .
(117) n = 2, 1 = 40 . ., 2 = 100 . . r = 25%:
. .
, .
, r, . :
.
, r 2 + 5 r - 1 < 0, , -5,1926< r <0,1926. , 19,26% . , , 17%. (124) (117) :
. .
. .
, 17% .
3.1.15. 800 . . 25% , . . .
. . , ., r = 25%, n = 6. (121), :
.
. 800000 ., , , 271 058 . , : 200 000 . (25% 800 000 .) 271058 - 200000 = 71058 . , , , , : 800000 71058 = 728942 . , 182 236 . (25% 728942 .), 271058 -182236 = 88822 . .. , , .
:
, , , .. 216826 ., 271058 - 216826 = 54232 . 25% 216826 ., 54207 . , : 800 000 .
, . , , k- , , k , ..
, , :
) ( ) (1 + r) r;
) ( ) (1 + r);
) ( ) (1 + r) .
, , ( ):
;
;
3.1.16. 300 . . 20% , . 102 . . . .
. , n , (121):
, . ., = 102 . ., r = 0,2, :
.
. 102 . ., () : .
:
(.)
(89453 .) . 74544 ., 14909 . (20% 74544 .), 74544 + 14909 = 89453 .
3.1.17. , 60 . . 5 , 24%. , 28%?
. , , 60 . . . ., n = 5, m = 2, = 1 r = 24%, (123) :
. .
, 5 , 22,512 . . , , (123) m = 4, r = 28%:
. .