( ) 158,,,,,, ( CIP) /. :, 1996. 12 ISBN 7 302 02353 0... :. F275 CIP ( 96) 20860 : ( :, 100084) : : : 850 1168 1/ 32 : 13. 25 : 344 : 1996 12 1 1996 12 1 : ISBN 7 302 02353 0/ F 130 : 0001 5000 : 16. 00
,,,,,,, ;,,,,, 1996. 6
1 3 1. 1 3 1. 2 9 1. 3 12 1. 4 18 1. 5 25 2 29 2. 1 29 2. 2 48 3 70 3. 1 70 3. 2 92 3. 3 99 3. 4 107 4 115 4. 1 115 4. 2 131
4. 3 146 5 169 5. 1 169 5. 2 173 5. 3 199 5. 4 210 5. 5 217 6 228 6. 1 229 6. 2 237 7 263 7. 1 263 7. 2 278 7. 3 284 7. 4 300 7. 5 310 8 327 8. 1 327 8. 2 332 8. 3 348 8. 4 360 9 369 9. 1 369 9. 2 379 9. 3 382
9. 4 387 ( S/ P,, ) 404 ( P / S,, ) 407 ( S/ A,, ) 410 ( P / A,, ) 413 417
1,,,,,,,,,,, 1. 1,,,,,,,, : 3
( ),,,,,,,,,,,,,,, ( ),,,,,,,, ( ),, 4
,,,,,,, ( ),,,,,,,,,,,,,,,,,,,,,, 5
( ), 1., 100, 500, 400,,, 2.,, 100,,,,, 100 100 3., 500, 100,,,,, 4.,,,,,, 1, 2 3 4 ( ), 6
, V= P 1 ( 1+ 1) - 1 + P 2 ( 1+ 2) - 2 + + P ( 1+ ) - +, V, P,,, P P,,, V = P ( 1 + ) - = P / = 1 : V P,,,,,,,,,,,,,,,,,, ( ),, 7
,,,,,,,,,, ( ),,,, ( ),,,,,,,,,, ( ), 8
,,,,,,,,,,,, 1. 2,,,,, ( ), 9
,,,,,,,,,, ( ),,,,,,,,, ( 10
),,,,,,,,, ;,,,,,,,,,,,,,,,,,, ( ) 11
,,,,,,,,,, 1. 3,,,,,,,, ( ), : 1. :,,,,, 2. :,,,, 12
, 3. :,,,,, 4. ;,,,,, ( ) : 1. :,, ;,, 2. :,, 3. :,,, 4. :,,, 13
, 5. :, ( ),,,,, ;,,,,,,,,,,,,,,,,,,, ( ), 1. 14
,,,,,,,,,,,,,,,,, 2.,,, 3.,,,,,,, 15
, :,, ( ),,,, ( ),,,,,,,,, ( ),,,,,, 16
,,,, ( ),,,,,,,, ( ),,,,,,,, ( ),,,,,,,, ( ),, 17
,,, ( ),,,,,,,,,,,, : 1., ; 2., ; 3., 1. 4,,,,, 18
,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 19
,,,,,,,,,,,,,,,,,,,,,,,,,, ;,,,,,,, ;,, 20
,,,,,,,,,, ;, ;,,,,,, ;,,,, ;,,,,,,,,,,,, 21
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 22
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, 23
,,,,,,,,,, ; ;,, ;,,, ;,,,,,,,,,,,,,,,,, 24
1. 5,,,,,, : ( ), 1992 11, 1994 7 1,, ;, : 1. 2. 25
3.,, 4.,,,, ( ),,,,,, ( ),,,,,,, 26
,,,,,,,,,,,,,,,,,,,,, 1 1 1 1 27
, : 1. :, 2. : 3. : 4. : 5. :,,,,,, 28
2,,,, 2. 1,, 1, 1,, 20 ;, 22 12%,? 20,, 20 1+ 12 12% = 22. 4, 12, 20 22. 4, 22. 4-22= 0. 4 20, 29
,,,,,,,,,,,,,,,,,,,,,,,,,,, 30
,,, ;,, ;,,,, ;,,,,, ;,,,,,, 12%, 1, 1 200, 100, 3. 3, 1 390, 23 1,,,,, 1, 23, ( ),, 1. 31
, I ; : I = P t P, ;,, ; t,, 1 1 000, 6, 12% : I = 1 000 12% 6 = 60( ) 12,,, 12 360, ;, : 2.,, S = P + I = P + P t = P ( 1+ t) 1, : 3. S = 1 000 1+ 12% 6 12 = 1 060( ),, 32
,, : P = S- I = S- S t = S( 1- t), P, ; S, ;, ; t, 1, 4, 15% : ( ) P = 1 060 1-15% 4 12 = 1 007( ), 1.,,,,, P, S = P + P = P ( 1+ ),, 33
S = P ( 1+ ) + P ( 1+ ) = P ( 1+ ) ( 1+ ) = P ( 1+ ) 2, P S = P ( 1+ ) = P ( S/ P,, ), S, ; P, ;, ;, ( 1+ ) 1, ( S/ P,, ), x y,, P, S, 2 1,, :, ;, 2 1 34
2 1 000, 10%, S = 1 000 ( 1+ 10% ) 3 = 1 000 1. 331 = 1 331( ) ( 1+ 10% ) 3 = ( S/ P, 10%, 3) = 1. 331, 3, 8%, : ( 1+ 8% ) = 2 ln 1. 08= ln 2 ln2 = ln 1. 08 = 0. 6931 9( ) 7. 696 10-2, = 8% 2 1. 999, = 9 4, 18 4, : ( 1 + ) 18 = 4, ( 1 + ) = 4 1 1 8 1. 08 = 8% 4 1 1 8 x y, = 18 4 3. 996, = 8% 2.,,, : S = P ( 1 + P = ) S ( 1 + ) = S ( 1 + ) - = S ( P / S,, ) 35
( 1+ ) -,, 1, ( P / S,, ) x y, 5 4 4 000, 10%, : P = 4 000 ( 1+ 10% ) - 4 = 4 000 0. 6830 = 2 732( ) ( 1+ 10% ) - 4 = ( P / S, 10%, 4) = 0. 6830, ( ), : ; ; ; 1.,, 2 2, ( 1) 2 2, 36
, 2 3 2 3 A,,, : S= A+ A( 1+ ) + A( 1+ ) 2 + + A( 1+ ) - 1 ( 1+ ), ( 1+ ) S= A( 1+ ) + A ( 1+ ) 2 + A( 1+ ) 3 + + A ( 1+ ), ( 1+ ) S- S= A( 1+ ) - A, S = A ( 1+ ) - 1 = A( S / A,, ) ( S/ A,, ) = ( 1+ ) - 1, 1,,, 6 5 1000, 9%, 5? S = 1 000 ( 1+ 9% ) 5-1 9% = 1 000 5. 985 = 5 985( ) 37
, ( S / A, 9%, 5) = 5. 985, S = 1 000 5. 985 = 5 985( ) ( S/ A, 9%, 5) = 5. 985> 5 : ( S / A,, ) >, x > 0 : ( 1+ x ) = 1+ x + ( - 1) 2! ( 1+ x ) > 1+ x, x 1 : ( 1+ x ) 1+ x x 2 + + x - 1 + x,, 1,, ( S/ A,, ) = ( 1+ ) - 1 1+ - 1 =. 6, ( S/ A, 9%, 5) = 5. 985 = 5, ( S/ A,, ), ( 2) 38
( A/ S,, ) = S= A ( 1+ ) - 1 A = S ( 1+ ) - 1 = S( A / S,, ), ( 1+ ) - 1 ( A/ S,, ) = 1 ( S / A,, ),, 7, 10, 10, 10%,, A = 100 000 ( A/ S, 10%, 10) 1 = 100 000 ( S / A, 10%, 10) = 100 000 1 15. 937 = 6 275( ) 10 = 1 / 10, 8 3 300 000, 39
?, 8%, A = 300 000 ( A / S, 8%, 3) 1 = 300 000 ( S/ A, 8%, 3) = 300 000 1 3. 2464 = 92 410( ) 300 000 3= 100 000( ) ( 3),, 2 4 2 4, P = A( 1+ ) - 1 + A ( 1+ ) - 2 + + A ( 1+ ) - ( - 1) + A( 1+ ) -, ( 1+ ), P ( 1+ ) = A+ A( 1+ ) - 1 + + A( 1+ ) - ( - 2 ) + A ( 1+ ) - ( - 1)., 40 P ( 1+ ) - P = A - A ( 1+ ) -,
P = A 1- ( 1+ ) - = A( P / A,, ) - 1- ( 1+ ) ( P / A,, ) =,,, x > 0 ( 1+ x ) - > 1- x x 1 ( 1+ x ) - 1- x, 1,,,, : ( P / A,, ) = 1- ( 1+ ) - 1- ( 1- ) =. ( P / A,, ) ( P / A,, ), 9 5 1 000, 6%,? ( P / A, 6%, 5) = 1- ( 1+ 6% ) - 5 = 4. 2124 6% = 5 P = 1 000 ( P / A, 6%, 5) = 1 000 4. 2124= 4 212( ) 10 10 1 000, 20%,? ( P / A, 20%, 10) = 1- ( 1+ 20% ) - 10 = 4. 1925 20% 41
P = 1 000 ( P / A, 20%, 10) = 1 000 4. 1925= 4 193( ), 9, 4. 2124 5 ; 10, 4. 1925 10, ( 4), P = A ( P / A,, ) = A A= P, 1- ( 1+ ) - 1- ( 1+ ) - = P ( A/ P,, ) ( A/ P,, ) = 1- ( 1+ ) - ( P / A,, ) = 1- ( 1+ ) - 11 10% 150 000 15,? 42 ( A / P, 10%, 15) = 1 = 0. 13147 7. 6061 A = 150 000 ( A/ P, 10%, 15) = 150 000 0. 13147= 19 721( )
2., 2 5 2 5 ( 1), 2 6 2 6 A,,, : S = A( 1+ ) + A( 1+ ) 2 + + A ( 1+ ) S = A+ A( 1+ ) + + A ( 1+ ) - 1, ( 1+ ), ( 1+ ) : 43
S= A ( S/ A,, ) ( 1+ ) = A ( 1+ ) - 1 ( 1+ ) 2 6 2 3, 2 3 2 6, ( 1+ ) 12 1 000, 10%, 8? S = 1 000 ( S / A, 10%, 8) ( 1+ 10% ) = 1 000 11. 436 1. 1 = 12 580( ) ( 2),, 2 7 2 7, P = A+ A( 1+ ) - 1 + + A( 1+ ) - ( - 1 ) = [ A ( 1+ ) - 1 + A ( 1+ ) - 2 + + A ( 1+ ) - ] ( 1+ ) = A( P / A,, ) ( 1+ ) = A 1- ( 1+ ) - ( 1+ ), ( 1+ 44
),, 2 7 2 4, 2 4 2 7, ( 1+ ) 13 3, 100 000, 10%,? P = 100 000 ( P / A, 10%, 3) ( 1+ 10% ) = 100 000 2. 487 1. 1 = 273 570( ) 3. m, 2 8 m= 3, = 4 2 8 m, : S= A( S / A,, ) m, 1,, P = A( P / A,, ) ( 1+ ) -, ( m+ ) m m 45
P = A ( P / A,, m+ ) - A( P / A,, m) = A 1- ( 1+ ) - m - - A 1- ( 1+ ) - m = A 1- ( 1+ ) - ( 1+ ) - m = A ( P / A,, ) ( 1+ ) - m 14 100, 7 12%,? 4. P = 100 ( P / A, 12%, 7) ( 1+ 12% ) - 2 = 100 4. 5638 0. 79719 = 364( ),,,,,, ( 1+ ) - 0, P = A 1- ( 1+ ) - P = A 15, 10 000 10%,? P = 10 000 = 100 000( ) 10% 16 6 000, 1 200 8%, 46
? P = 1 200 = 15 000( ) 8% ( ),,,, 1 M, r, r M, 1 1 1+ = 1+ r M r 17 12%,?, M= 2 = 1+ 12% 2 M 2-1= 12. 36%,, M= 4, = 1+ 12% 4 4-1= 12. 55%, M= 12 = 1+ 12% 12, M, 12-1= 12. 68% M,, 47
, = lim 1+ r M M - 1 17 r= 12%, = lim 1+ r M = e r - 1 M r r - 1 = e 0. 12-1= 12. 75%,,,,, 2. 2,,,,,,,, ( ),,,, 48
,,,,, ( ), 1.,,,, : ( 1) 100 15%, 15% 100% ( 2), 100, 20% 10% 5%, 30% 40% 30% ( 3), 100,,, 100, 100% 60% 20%,,,,, 49
,, 2.,, ( 1),,,,,,, ( 2),,, 3.,,, ( 1),,, :,,,, 50
,,,,,,,, ( 2),,,,,,,,,,,,, : ( 3), : ; : ; :, ;,, ;,, 51
,,,, ( ),,,, 1 100%, 0,, ;,,,, 1 000, 1 000, 100%,, 1 000,, 1 000, 1 00%, 80%, 1 000 20%, 40%, 60%, 1 000, 1 000 100%, 80% 20%, 200 200 30% 50% 20% 52
( ),,,,,,,,,,,,,,, 1, : P = 1( :, P ) = 1 0 P dk = 1 ( : K, P ) ( ),,,, 53
, : K =,, P K = 1 = P K = 1 P = 1 K ; P ; 18 A B 2 1, 2-1 A B ( P ) A ( K ) B 0. 30 30% 90% 0. 50 26% 26% 0. 20 20% - 70%, 2 9,, 2 10 P,, 0. 3, A 30%, A 30% 0. 3 A 54
2 9 A B 2 10 K A = 0. 30 30% + 0. 50 26% + 0. 20 20% = 26% B K B= 0. 30 90% + 0. 50 26% + 0. 20 ( - 70% ) = 26%, 26%, A, 20% 30%, B, - 70% 90%, 55
, 1, P d K = 1, 0,,, ( ),, = ( K - K ) 2 P = 1,,, 18 A B A B: A = ( 30% - 26% ) 2 0. 30 + ( 26% - 26% ) 2 0. 50 + ( 20% - 26% ) 2 0. 10 = 15. 49% B = ( 90% - 26% ) 2 0. 30 + ( 26% - 26% ) 2 0. 50 + ( - 70% - 26% ) 2 0. 20 = 55. 43% B A, ( ),,, 56
, :, V= E 100% V, ; ; E 18, A VA = B V B= 15. 49% 26% 55. 43% 26% = 59. 58% = 213. 19%,,,,, 19 A 13%, 15. 49% ; B 52%, 55. 43% A B 18, A, B VA = VB = 15. 49% 13% = 119. 15% 55. 43% 52% = 106. 60% 18, A B 57
( ), :,, :, ;, : :, K ; K F K R ; K = K F + K R, : K F K 0 ; K F = K 0+ I P,, ; I P,, 58
,,, ( ), : K R b V K R = bv V b, : 1. 20%, 10%, 100%, K = K F + K R b= K - K F V K R = bv = 20% - 10% 100% = 0. 1 2.,,, ;,, 3.,,, 20 19, A V A = 119. 15%, B 59
V B = 106. 60% 10%, A B ba = 0. 05 bb = 0. 08. A B K A = K F + ba V A = 10% + 0. 05 119. 15% = 15. 96% K B = K F + bbvb = 10% + 0. 08 106. 60% = 18. 53%, ba = bb, VA > V B, K A > K B ba < bb, K A < K B b,, b,, K, K, K > K, 19, K A = 13%, K B = 52%, K A = 13% < K A = 15. 96% K B = 52% > K B= 18. 53% A, B 21 18, A B K A = K B = 26%, A B 15. 49% 55. 43%, ba bb 0. 05 0. 08, K F 10% 60
V A= A = K A V B= B = K B 15. 49% 26% 55. 43% 26%, K A K B = 15. 49% 26% = 213. 19% = K F + ba V A = 59. 58% = 10% + 0. 05 59. 58% = 12. 98% = K F + bbvb = 10% + 0. 08 213. 19% = 27. 06% K A = 26% > K A = 12. 98%, A ; K B= 26% < K B = 27. 06%, B ( ), K = K F + K R K = K F + bv C, K C= K F C+ bvc P P F P R P = P F + P R 61
, : P R = K RC= bvc K P C, : P R K = P / C P = K R K = P K R K K R bv = P = P K F + K R K F + bv 22 21, A B 1000 P R A = ba V AC = 5% 59. 58% 1000 = 29. 79( ) P R B = bbv BC = 8% 213. 19% 1000 = 170. 55( ) B 23 1 000 A, 129. 8 ; B, 270. 6 A 2. 98% 12. 98%, B 17. 06% 27. 06% P R A = P A P R B = P B K R A K A K R B K B 2. 98% = 129. 8 = 29. 8( ) 12. 98% 17. 06% = 270. 6 = 170. 6( ) 27. 06% 62
,,,,,,,,,, ( ), 1.,,,,,,, r = - 1, 2 2,, 2 11 2., 63
2 2 A B 1991 30% - 6% 12% 1992-6% 30% 12% 1993 40% - 16% 12% 1994-16% 40% 12% 1995 12% 12% 12% 12% 12% 12% 21. 1% 21. 1% 0 2 11,,,,,, r = 1, 2 3,, 2 11 A 64
2 3 A B 1991 30% 30% 30% 1992-6% - 6% - 6% 1993 40% 40% 40% 1994-16% - 16% - 16% 1995 12% 12% 12% 12% 12% 12% 21. 1% 21. 1% 21. 1%,,, 0. 5 0. 7,,,,,,, ( ) 1.,,,, K R = K = R = K R = K R 65
K R ; = K R, K R, : = K R : K R = K R + K R = K R + K = R K R,, 2 12 K R= + K = R 2 12,, K R, : K R=, : 66 + K = R + = ( + ) + K = R K R = +
, :, K F, K = K F + K R= K F + + + K = R, 2.,, :, K = K ; X K = 1 X ; K ;, K R = +, K = X K = = 1 = X K F + = 1 = 1 = K F + ( X ) = K R = 1 X ( K F + + + = K R ) = 1 X ( + ) + = 1 X K = R, K = R, : = X = 1, : 67
K R = K = R K R K = R : K = K F + K R = K F + K = R, = 1, : = K = K F + = K R : K = K F + K = R = K F + ( = K - K F ) 24 A B C, 1. 5 1. 0 0. 5, 50% 30% 20%, 15%, 10%, 3 = = 1 X = 50% 1. 5 + 30% 1. 0 + 20% 0. 5 = 1. 15 K R = ( = K - K F ) = 1. 15 ( 15% - 10% ) = 5. 75% K = K F + K R = 10% + 5. 75% = 15. 75% 25 24 A B C 20% 68
30% 50%, 3 = K R= = 1 X = 20% 1. 5 + 30% 1. 0 + 50% 0. 5 = 0. 85 ( = K - K F ) = 0. 85 ( 15% - 10% ) = 4. 25% K = K F + K R = 10% + 4. 25% = 14. 25% 3. = K R = = K R = K R = K R = = 1, < 1, > 1,,, : K = K F + + + K = R ( ) K = K F + K = R ( ),,, 69
3,,,,, :, 3. 1,,,,,,,,,,,, 70
,,,,,,,, 3 1 3 2 3 1 : C 19 12 31 : : : 50 100 90 120 24 12 8 10 22 16 218 200 400 800 8 20 : 2 4 24 14 398 796 2 4 8 44 32 24 44 24 16 14 652 238 20 56 14 64 2 14 8 16 10 18 0 90 0 100 1220 1400 10 6 : 90 60 440 600 : 3234 4000 490 900 : 1324 1524 520 480 1910 2476 120 100 24 0 30 40 50 20 1160 1520 20 16 : 2004 2512 1400 1400 : 140 150 71
16 12 120 160 30 10 100 170 : 0 6 1760 1880 3360 4000 3360 4000 3 2 : C 19 : 5700 6000 : 5006 5288 40 44 56 56 598 612 : 72 40 : 80 92 192 220 398 340 : 48 80 34 20 : 10 40 470 400 : 150 128 320 272 72
( ),, 1., 3 1, C = : 1 220 = 2. 77 440 : 1 400 = 2. 33 600, 2. 77, 2. 33,,,, : = -,,,,,, 2, 73
,,,,, 2,,,, 2.,, = = - - -,,,, 3 1, C = 546 = 1. 24 440 = 1 054 = 1. 76 600, 1. 24, 1. 76,,, 74
,, 1, ;,,, 1,,,,, 1,,, 1,,,,, 3.,,,, + + = 3 1, C = 96 = 0. 218 440 = 218 = 0. 363 600, 75
, ( ), ;,,,,,,,, 1.,, = 3 1, C = 1 600 = 0. 476 3 360 = 2 120 = 0. 530 4 000 : ( 1),,,, 1,, ( 2), 76
,, ( 3),,, ;, 2.,,,,, = 3 1, C = 1 760 = 0. 524 3 360 = 1 880 = 0. 470 4 000, 1, : + =,,,,,,,,, 3 1, C = 3 360 1 760 = 1. 909 77
= 4 000 = 2. 128 1 880 3.,,,,,, = 3 1, C = 1 600 = 0. 909 1 760 = 2 120 = 1. 128 1 880 : =, - = 1, - = 1 4.,,,,,, + = 3 2, C = 662 = 3. 45 192 78
= 620 = 2. 82 220,,,,,,,,,,,,, : ( ) 1.,,, = + = 2,, 79
,,,,,,,,,,,,,,,,,,,,,,,, = = =,,,, 360 = = 360 80
,, 3 1 3 2, C = 5 288 = 11. 9( ) 445 = 445 360 = 30. 3( ) 5 288 2., = = - - - - = + 2,,,,,,,,,,,,, = 360 81
360 =,, : = +,,,,,, 3 1 3 2,, C = 6 000 = 10. 1( ) 597 = 597 360 = 35. 8( ) 6 000 = 30. 3+ 35. 8 = 66. 1( ) 3., = = ( + ) 2, = 82 360
360 =,,,,,,,, 3 1 3 2, C = 6 000 = 4. 58( ) 1 310 = 1 310 360 = 78. 6( ) 6 000, ( ),, = = + 2,,,,,,, 83
,,, ;, 3 1 3 2, C = 6 000 = 2. 74( ) 2 193 = 6 000 = 2. 42( ) 2 476 ( ), =,,,,, 3 1 3 2, C = 6 000 = 1. 63( ) 3 680 = 6 000 = 1. 50( ) 4 000 84
,,,,, ( ), 1., = 100%,, 3 2, C = 470 100% = 8. 25% 5 700 = 400 100% = 6. 67% 6 000,, : 85
= 100% = -,,, 3 2, C = 594 100% = 10. 42% 5 700 = 712 100% = 11. 87% 6 000, = 100%, 3 2, C = 320 100% = 5. 61% 5 700 = 272 100% = 4. 53% 6 000 2., = 100% = + + + + 86
= - +,,,,, 3 2, C = 470 = 8. 75% 5 374 = 400 = 7. 02% 5 700 3.,,, = 100% = ( + ) 2,,,, 3 1 3 2, C = 400 100% = 10. 87% 3 680 = 400 100% = 10% 4 000,,,,,,, = 100% 87
, 3 1 3 2, C = 272 100% = 7. 39% 3 680 = 272 100% = 6. 8% 4 000 4.,,, : = 100%,, 3 1 3 2, C = 470 100% = 33. 6% 1 400 = 400 100% = 28. 6% 1 400,,, = 100% 3 1 3 2, C = 470 100% = 26. 7% 1 760 88
= 400 100% = 21. 3% 1 880,,,, = 100% 3 1 3 2, C = 320 100% = 22. 9% 1 400 = 272 100% = 19. 4% 1 400,,, = 100% 3 1 3 2, C = 320 100% = 18. 2% 1 760 = 272 100% = 14. 5% 1 880 ( ), 1.,,, 89
- = ;, 3 200, 200, 2 000, : 3 200-200 = = 1. 50( ) 2 000,,, 2.,,, =,,,, ;, 600, 2 000, : = 600 = 0. 30( ) 2 000 3.,, = 90 -
,,, ;,, 6 100, 60, 2 000, : 6 100-60 = = 3. 02( ) 2 000 4.,,, = 100% 1. 50, 0. 30, : 0. 30 = 100% = 20% 1. 50 5., = 100% 0. 30, 7. 50, : = 6. 0. 30 100% = 4% 7. 50,, 91
, =,, 3. 2 1. 50, 7. 50, = 7. 50 1. 50 = 5,,,,,,,, :,,,,,,, 5, 10, 92
3 3 4, 3 4 3 3 D : 1992 1993 1994 1995 5 700 6 270 6 646 6 778 : 2 850 3 162 3 370 3 932 2 850 3 108 3 276 2 846 : 800 860 1 200 1 040 2 050 2 248 2 076 1 806 : 150 130 234 134 2 200 2 378 2 310 1 940 : 726 784 762 640 1 474 1 594 1 548 1 300 : 526 1 114 1 750 2 370 2 000 2 708 3 298 3 670 : 148 160 154 130 738 798 774 650 1 114 1 750 2 370 2 890 3 4 1993 1994 1995 % % % 570 10 376 6 132 2 312 11 208 7 562 17 258 9 168 5-430 - 13 60 8 340 40-160 - 13 198 10-172 - 8-270 - 13-20 - 13 104 80-100 - 43 178 8-68 - 3-370 - 16 58 8-22 - 3-122 - 16 120 8-46 - 3-248 - 16 93
: = - = 3 4, : ( 1) ; ( 2), 1995 17% ; ( 3) ; ( 4), 1995 ; ( 5), ; ( 6), 1995,,,,,,, : = 100%,,, 3 5 D, 3 6 3 6, 94
, 70% ;, 10% 20%,,,, 1994 D 3 5 : 1993 1994 1995 1. 1 594 1 548 1 300 2. 220 354 402 3. 82 44 126 4. 160 154 130 2 056 2 100 1 958 1. 160 154 130 2. 798 774 650 3. 800 1 800 600 4. 1 758 2 728 1 380 298-628 578 1993 1994 1995 1. 200-100 - 100 2. 100 100 100 300 0 0 2 628-578 298-628 578 95
D 3 6 : 1993 1994 1995 1. 77 74 66 2. 11 17 21 3. 4 2 6 4. 8 7 7 100 100 100 1. 8 7 7 2. 39 37 33 3. 39 86 30 4. 86 130 70 14-30 30 1993 1994 1995 1. 10-5 - 5 2. 5 5 5 15 0 0 0 30-30 15-30 30,,,,, 96
, 100,,, : = 100 3 7 D, 3 8 D 3 7 : 1992 1993 1994 1995 600 800 700 600 600 700 800 900 1 800 2 600 4 400 5 000 : 200 420 774 1 176 2 800 3 680 5 126 5 324 300 302 930 352 238 320 364 490 1 000 1 000 1 000 1 000 148 308 462 592 1 114 1 950 2 390 2 890 2 800 3 680 5 126 5 324 97
3 8 D : 1992 1993 1994 1995 100 ( 600) 133 117 100 100 ( 600) 116 133 150 100 ( 1600) 136 227 239 100 ( 2800) 131 183 190 100 ( 300) 100 310 117 100 ( 238) 134 153 206 100 ( 1000) 100 100 100 100 ( 148) 208 312 400 100 ( 1114) 157 213 259 100 ( 2800) 131 183 190 3 8 : ( 1) ; ( 2), ; ( 3), ; ( 4),, ; ; 3 8 : ( 1) ; ( 2), ( 3),, ; 98
( 4) 1994,, 1995,,,,,,,,,,,,, 3. 3 3. 1, 3. 2,,,,,,,,,,,,, 99
,,,,,,,,,,,,,,, 3 9 67 3 9 0. 58 0. 73 0. 60 0. 80 0. 57 0. 25 0. 10 0. 008 0. 32 0. 17 2. 93 5. 16 288 4. 93 1. 6 1. 34 4. 52 169 4. 77 1. 36 0. 42 0. 27 0. 40 0. 20 0. 43 6. 62 116 117 35 39. 6 0. 64 1. 11 0. 07 0. 45 0. 29 0. 61 0. 73 0. 60 0. 80 0. 57 ( % ) 96. 7 43. 3 59. 8 53. 1 52. 2 2. 44 3. 86 2. 18 2. 03 4. 26 : 1992 = = 100
,,,,,,,,,,, : ( ),,, 1. 3 10 60% 30% 30% 3 10 40% 30% 10% 40% 60% 20% 30% 10% 100% 100% 101
, : ( 1) 100%,,,, 40%, 60% 40%,,, 60% 40%,, 0. 4, 0. 6 ( 2),, ;, 2/ 3, 1/ 3 ( 1), 60% 60% 2/ 3= 40%, 40%, 60% ( 3) 2, ( 2), 60%, 30% ( 1), 40%, 10% ( 4), 1 2,, 3, 1/ 3, 60% 1/ 3= 20% 40%,, 30% 10% ( 5) 1 102
,, 30%, ( 3) 60%,, 30% 2.,, 3 11 3. 1 C,, 3 11 C : ( 60% ) 2400 1400-1000 ( 40% ) 1600 2120 520 : ( 30% ) 1200 924-276 : 1200 600-600 ( 30% ) 1200 476-724 400 1520 1120 ( 40% ) 1600 2600 1000 ( 60% ) 2400 1880-520 : ( 20% ) 800 1400 600 ( 30% ) 1200 310-890 ( 10% ) 400 170-230 4000 4000 4000 4000 3., : ( 1) :,,,,,,,,,,, 103
( 2) :,,,,, ;,,,,,, ( 3) :,,,, ( 4) :,,, ( ),,,, 1. 3 12, : ( 1) 100%,, C 25%, 25%, 75% ( 2),, C, 13%, 12% ( 3),,, 104
1% ( 4) 33%,, 6%, 5% 3 12 100% 75% 25% 13% 12% 1% 11% 6% 5% 2., 3. 1C, 3 13, +, - 3. 3 13, 28 888, 468, ( ) 120, 40, ( 888-468- 120-40) = 260, 232, ( 260-232) = 28, 105
3 13 ( 100% ) 6 000 6 000 0 ( 75% ) 4 500 5 388-888 ( 25% ) 1 500 612-888 ( 13% ) 780 312 + 468 40 + 40 ( 12% ) 720 340-380 (, 1% ) 60-60 + 120 ( 11% ) 660 400-260 ( 6% ) 360 128 + 232 ( 5% ) 300 272-28 ( ),,,, C 2, 100%, 200%, C 4 000, 8 000, 3 14 106
3 14 ( ) ( 200% ) 8 000 6 000-2 000 ( 150% ) 6 000 5 388 + 612 ( 50% ) 2 000 612-1 388 ( 26% ) 1 040 312 + 728 0 40 + 40 ( 24% ) 960 340-620 (, 2% ) 80-60 + 140 ( 22% ) 880 400-480 ( 12% ) 480 128 + 352 ( 10% ) 400 272-128 3 14,, 2 000,,,, C,,, 3. 4,, 107
,, C, 3 15 3 15 1 2 3 4 5= 4 3 6= 2 5 0. 15 2. 00 2. 33 1. 165 0. 1748 0. 10 1. 00 1. 73 1. 730 0. 1730 0. 10 0. 40 0. 53 1. 325 0. 1325 0. 05 10. 00 10. 05 1. 005 0. 0503 0. 10 12. 00 11. 88 0. 940 0. 0940 0. 15 2. 00 1. 63 0. 8150 0. 1223 0. 10 11. 00% 6. 67% 0. 6064 0. 0606 0. 15 12. 50% 7. 02% 0. 5616 0. 0842 0. 10 35. 00% 21. 28% 0. 6080 0. 0608 1. 00 0. 9525 : 1.,, 2.,, 1, 108
3., 4. 3 15 3. 1 C 5., 6.,, 1, ; 1,, 3 15, 0. 9525, C,,,, 3 1, : 1. = 109
3 1 C = 2. = 110
= 3. =, : 1.,,,,, 2.,, 3.,,,,,,,,, 4.,,,,,, ;,, 5. 111
,,,,,,,, 112
4,,, 4. 1,,,, ( ), : 1., 115
,,,,,,, 2.,,,,, ;, 3.,,,,,,,,,,, ( ),,,,,, 116
( ) : 1., ; 2.,,, ; 3.,, ; 4., : 4 1 4 1,, 4 1 117
4 1 : 1 ( ) 2 ( 1) 3 600 4 600 5 1 200 6 ( 2) 7 100 8 80 9 50 10 70 11 300 12 ( 3) ( 3) = ( 1) + ( 2) 1 500 13 ( ) 14 ( 4) 15 500 16 250 17 250 18 100 19 80 20 80 21 40 22 800 23 ( 5) 24 200 25 50 26 50 27 60 28 100 29 40 118
30 500 31 ( 6) ( 6) = ( 4) + ( 5) 1 300 32 ( ) 33 ( 7) ( 7) = ( 3) - ( 6) 200 34 ( ) 35 ( 8) 100 36 ( 9) 200 37 ( 10) ( 10) = ( 8) + ( 9) = ( 8) + ( 3) - ( 6) 300 38 ( 11) 160 39 ( 12) ( 12) = ( 10) - ( 11) 140 : ( ) 1.,,,, : ( 1), ; ( 2), 2., 119
( ) 1., : ( 1),,, ( 2), ( 3), ( 4),,,,,,,,,, 2., 120
( ) : = - = + - + ( ) ( ),, ;,, : = = - + = + - - -, ( ),, 121
1.,,,,,, 2.,, 2/ 10, / 30, 10, 10, 30,,, ;,,,, 1 2 3 4 5 5 20% 40% 20% 10% 5% 5%,, 3.,,,,,, : ( 1) ; ( 2) ; ( 3) ; ( 4) 122
; ( 5) ; ( 6) ; ( 7) ; ( 8) ( ), 1.,, ; ; 2.,,, : ( 1),, ( 2),,,,,, ( 3 ) 123
, : ( 1), ( 2),,, ( 3), 3.,,,,,,,,, 4.,,,, ;,,,, ( ),,,,,,,, : ( 1) ; ( 2) ; ( 3), 124
1.,,, : ( 1),, ( 2) ( 3), : ( 1),,,, ( 2),, : ( 1),,, ( 2),,, 1 1000,,, 8, 100, 9%,, 100 125
9% = 9, 8 1, 2., : ( 1) ; ( 2) ; ( 3),,,,,,,, ;, 3.,,,,,, 126
,,,,,, ( ), : = / 360 = / 360 = / 360,, 4 2 4 2, 127
4 2, : = + -, : = 360, 2 100, 50, 30, 900, = 100+ 50-30= 120( ) = 900 120= 300( ) 360,, ( ), :,,,, 4 3, 4 3, N, 0- t1,, t 1 N t 1- t2 t 2,, N,, N, 128
4 3 N, N / 2, N, N^ : ( 1),, ( 2),, : T C ; T C= N 2 + T N b N, ; ; T ; b, N, N N,, 4 4 129
4 4 N^, : T C N,, T C = 2 - T b = 0, N 2 N 2 = 2T b, N^ = 2T b 3 2 0%, 1 0 0, 1 0 00, N^ = 2 10 000 000 100 = 100 000( ) 20% 10, : 130 T / N^ = 1 000 = 100( ) 10
TC ^ = 100 000 2 20% + 10 000 000 100= 20 000( ) 100 000 ( ), : = - 1 4 1 000, 30, 20%, ( 1 000-30) ( 1+ 20% ) = 1 164( ),,,,,, 4. 2,,,,,, 131
,,, ( ) : 1.,,,,, 2.,, ( 1),, ( 2), ( 3) : ; ; ; ( 4),, ( ) 132
,,, ( ) : 1., ; 2.,, ; 3. 4 5 4 5,,,, ( ),,,, 133
,, ;,,,, 6%, 15% ( ),,, 2/ 10, / 30, : 10, 2% ;, 30, 30, 10, 2%,,, ( ),,,,,, ;,,,,, :, ;, ;, 134
,,,,, ( ),,, : 1.,, ;, 2., : ( 1),, ( 2), :,,, ;, 135
; :, AAA AA A BBB BB B CCC CC C, AAA, C ;, AAA AA A ( 3),,,,, ( 4), ( ),,,, 5C 1. 5C 5C, C, 5C ( 1),,,, ( 2),,,, 136
( 3), ( 4),,, ( 5),,, 2.,,, :, 1) ; Y = a1x 1 + a 2x 2 + + a x = a x = 1 Y ; a ( a = = 1 x 4 2 4 2 ( 1), ( 2), ( 3) ( 2), ( 4) 84. 50, 137
4 2 ( x ) ( a ) ( 1) ( 2) 0 100 ( 3) ( a x ) ( 4) = ( 1) ( 3) 0. 20 1. 9 90 18. 00 ( % ) 0. 10 60 75 7. 50 ( % ) 0. 05 15 90 4. 50 0. 25 AA 85 21. 25 0. 30 85 25. 50 0. 05 75 3. 75 0. 05 80 4. 00 1. 00 84. 50,, 80, 60 80, 60 ( ),,, 1.,,,,,, : ; ; ;, ;, ;, ;, 138
2.,, :,,,, : ( 1),,,,,, ( 2),,, ( 3),,,,, ( 4),,, ( 5),, ( 6),,, : ( 1),,, ( 2), 139
, 3.,,,,,, 4 3 19 12 31 4 3 ( ) ( % ) 127 118 51. 53 1 30 61 50 21. 83 31 180 34 29 12. 66 181 360 26 22 9. 61 360 15 10 4. 37 263 229 100. 00,,,,,,,,,,, 140
( ), ;,, :, = - = + :, ; P = S K - + + C SR0- S B- SDR D - S M 360 P, ; S ( ) ; K ( ) ; C, ; R 0, ; C S, ; 360 B, ; D, R D, ; M, 141
,,,,, ( ) 5 5, 4 4 4 4 ( % ) ( ) ( ) 5. 7 40 90 000 8. 7 90 10 000 12 75 15 000 10%, A B A B 6% 15% 4 5 20%, 15%,,, A B, P = 100 000 20% - 45 100 000 15% - 100 000 6% 360 = 100 000 20% - 12 500 15% - 100 000 6% = 12 125( ), 12500 P A = 90 000 20% - 142 40 90 000 15% - 90 000 5. 7% 360
= 90 000 20% - 10 000 15% - 90 000 5. 7% = 11 370( ) P B = 115 000 20% - - 115 000 6. 78% 49 115 000 15% 360 = 115 000 20% - 15 653 15% - 115 000 6. 78% = 12 855( ) 4 5 A ( ) ( ) 90 000 5. 7% 100 000 + 10 000 8 7% = 6% 100 000 5. 7% 90 000 100 000 40 + 40 10 000 90= 45 100 000 100 000 90 000 B 100 000 115 000 6% 100 000 115 000 45 115 000 + 15 000 12% = 6. 78% 115 000 + 15 000 75= 49 115 000, B, 12 855-12 125= 730 A, 12 125-11 370= 755 B ( ) 6 6, A B, 4 6 143
4 6 A B 30, 45, 2/ 10, / 30 S ( ) 100 000 120 000 130 000 C ( ) 45 60 30 B 6% 8% 4% D 0 0 50% R D 0 0 2% P 20% 20% 20% R 0 15% 15% 15%, A B, P = 100 000 20% - = 12 125( ) P A = 120 000 20% - = 11 400( ) 45 100 000 15% - 100 000 6% 360 60 120 000 15% - 120 000 8% 360 30 P B = 130 000 20% - 130 000 15% - 130 000 4% 360-130 000 50% 2% = 17 875( ), B, 17 875-12 125= 5 750, A, 12 125-11 400= 725 B 144
( ), 7 7 1 200 000, 20%, 10%, 4 7, 4 7 ( ) 10 000 15 000 ( ) 60 30 ( % ) 4 2, 60 P 1 = 1 200 000 20% - 1 200 000 10% 360-1 200 000 4% - 10 000 = 162 000( ) 30 P 2 = 1 20 0000 20% - 1 20 0000 10% 360-1 20 0000 2% - 1 5000 = 191 000( ), 191 000-162 000= 29 000, ( ),,, 145
,,,,,, 4. 3,, 50%,,,,, ( ) 1., ( 1),,,,,,,, 146
( 2),,,,, ( 3),,,, 2.,,,, : ( 1),, D, U, D U ( 2),,,, F 1,, K, Q, D Q K + F 1,, T Ca : 147
T Ca = F 1+ D Q K + DU ( 3),,,, K c, Q 2 K c F 2, T Cc : T Cc = F 2+ Q 2 K c ( 4),,, K u, S, TCs T Cs= K us D Q ( ),,,, 148
( ) : 1. ; 2. ; 3. 4 6 4 6, ( ),,,, : = : 1. 149
: = =,, 360, 90, 30 2. 3.,, : = + + + + : ( 1), ( 2), ( 3) ( 4) : =,, 150
,,, 50%,,, : =, ( 5) 8, 1kg, 360000, 6 /, 5, 1, 30, 50%, 2, 3? 360 000 1 6 ( 5+ 1+ 2+ 30 50% + 3) = 156 000( ) 360 ( ),, : =, : 1. 151
2. 3. 4. 9 4 8, 4 8 ( ) ( ) ( ) ( % ) 5 12 000 50 5 5 12 000 100 2 5 17 000 60 8 5 17 000 100 2 5 20 000 80 3 20 = 5 12 000 50% 5+ 5 12 000 100% 2 + 5 17 000 60% 8+ 5 17 000 100% 2+ 5 20 000 80% 3= 1 088 000( ),,, ( ), : 152
= : 1.,,, 2. 3.,, ( 1) ( 2) ( 3) 10 5, 30 000, 6, 2, 3 5 30 000 ( 6+ 2+ 3) = 1 650 000( ) ( ),, ;,, 153
, 4 9 19 4 9 : 80 000 65 000 6 000 5 000 4 000 50 000 28 000 20 000 2 000 30 000 25 000 5 000 160 000,,,,,,, : = 154-1 %
1- %,,, : = - 1-, =,,,, : ( 1) ; ( 2), ; ( 3), ; ( 4), 155
, ( ),, : 1.,,,,,,, 2.,,,,,, 3.,,,,, 4., 156
5., ( ),, 1., 2., 3., 4. 5. ( ),,,,,,,,, 157
A BC, ABC, : 1. ( ) ; 2.,, : 3., A, B, C, ; 4. A, B, C 11 40, 1 600 000, ABC 4 10, 4 7, 4 11 4 10 ( ) ( ) ( ) ( ) ( % ) ( ABC) 1 3 000 60 180 000 11. 25 A 2 2 000 22 44 000 2. 75 C 3 15 000 18 270 000 16. 88 A 4 11 000 20 220 000 13. 75 A 5 10 000 17 170 000 10. 62 A 6 30 000 3 90 000 5. 62 B 7 2 000 10 20 000 1. 25 C 8 8 000 15 120 000 7. 5 A 9 5 000 12 60 000 3. 75 B 10 45 000 2 90 000 5. 62 B 11 60 000 1 60 000 3. 75 B 158
( ) ( ) ( ) ( ) ( % ) ( ABC) 12 18 000 2 36 000 2. 25 C 13 20 000 3 60 000 3. 75 B 14 24 000 1 24 000 1. 50 C 15 6 000 8 48 000 3. 00 C 16 5 000 4 20 000 1. 25 C 17 4 500 2 9 000 0. 56 C 18 7 200 3 21 600 1. 35 C 19 8 000 1 8 000 0. 50 C 20 6 000 2 12 000 0. 75 C 21-40 37 400 2. 34 C 1600 000 100 4 7, A 60%, 12. 5%, B 82. 5%, 25% 4 7 ABC 4 11 159
4 11 ( ) ( ) ( % ) ( ) ( % ) ( ) ( % ) 1 180 000 11. 25 A 3 270 000 16. 88 A 4 220 000 13. 75 A 5 12. 5 960 000 60. 0 5 170 000 10. 62 A 8 120 000 7. 50 A 6 90 000 5. 62 B 9 60 000 3. 75 B 10 90 000 5. 62 B 5 12. 5 360 000 22. 5 11 60 000 3. 75 B 13 60 000 3. 75 B 2 44 000 2. 75 C 7 20 000 1. 25 C 12 36 000 2. 25 C 14 24 000 1. 50 C 15 48 000 3. 00 C 16 20 000 1. 25 C 30 75 280 000 17. 5 17 9 000 0. 56 C 18 21 600 1. 35 C 19 8 000 0. 50 C 20 12 000 0. 75 C 21 40 37 400 2. 34 C 1 600 000 100 40 100 1 600 000 100,,,,, 160
,,, ( ),,, T C= TCa + T Cc + TCs = F 1 + D Q K + D U + F 2 + K c : ( 1), ; ( 2) ; ( 3), ; ( 4) D U K K c F 1 F 2, T C= F 1+ F 2+ DU + D Q K + K c Q 2 + K us D Q T C Q T C, T C Q : T C = - D Q 2 K + K c 2 = 0, Q 2 ^ Q = 2K D K c, Q^, 161
N^ = D Q^ = D 2K D / K c = D K c/ 2K T C ^ Q = + 360 T^ = = 360 2K / DK c N^ DK 2K D/ K c + K c 2 2K D / K c = + 2K D / K c, F 1+ F 2+ D U, Q, 4 8 4 8 4 8,, : : Q^ Q= 2 = K D 2K c 162
^ I = Q^2 U = K D U 2K c 12 8 100, 36, 2, 12 Q^ = N^ = 8 100 540 2 8 100 36 2 = 15( ) = 540( ) T C ^ Q = 2 36 8 100 2 = 1 080( ) T^ = 360 2 36/ 8 100 2 = 24( ) ^ I = 36 8 100 12 = 3 240( ) 2 2 ( ),,,, ;,, 13, 675, 2%,? Q 1= 540 Q 2= 675 T C1 = 8 100 540 36 + 540 2 2 + 8 100 12 163
= 98 280( ) T C2= 8 100 675 36 + 2 + 8 100 12 ( 1-2% ) 675 2 = 96 363( ) T C2 < T C1 675 ( ),,, 4 9, 4 9 P, d, Q/ P, Q d, E = Q - P E = 1 2 Q- Q P d, T C= D Q K + 1 2 Q - Q P d K c Q P d, 164
T C = - DK + K c Q 2 2 1 - d P = 0 Q^ = 2K D K c P P - d, N^ = DK c 2K 1 - d P T C ^ Q = 2K D K c 1 - d P T^ = 360 2K D K c P P - d ^ I = K D 2K c P P - d U ( ),,, Q^ N^, B, B^, Q^ + B^, T C( S B) : K u T C( S B) = K us N^ + BK c S, ^ N 165
B K c,,,,,,, L, d, L, R R= Ld B, R R= Ld + B,,, 14 D 3600, K c 2, K u 4, L 10, 10 Q^ 300, N^ 12 4 12 4 12 ( 10d ) 70 80 90 100 110 120 130 ( P ) 0. 01 0. 04 0. 20 0. 50 0. 20 0. 04 0. 01 ( 1) B= 0, R= Ld + B= 10 10+ 0= 100( ) 166
4 13 4 13 70 80 90 100 110 120 130 0 10 20 30 0. 75 0. 20 0. 04 0. 01 S = 10 0. 2+ 20 0. 04+ 30 0. 01= 3. 1( ), T C( S, B) = 4 3. 1 12+ 0= 148. 8( ) 10 B= 10, R= 10 10+ 10= 110( ) 4 14 70 80 90 100 110 120 130 0 10 20 0. 95 0. 04 0. 01 S = 10 0. 04+ 20 0. 01= 0. 6( ), T C( S, B) = 4 0. 6 12+ 10 2= 48. 8( ) 20 B= 20, R= 10 10+ 20= 120( ) 4 15 70 80 90 100 110 120 130 0 10 0. 99 0. 01 S = 10 0. 01= 0. 1, T C( S, B) = 4 0. 1 12+ 20 2= 44. 8( ) 167
30 B= 30 R= 10 10+ 30= 130( ), S = 0 T C( S, B) = 0+ 30 2= 60( ) ( 2), B= 20, T C( S, B) = 44. 8, 20, 120, 300+ 20= 320 168
5,,,,,,,, 5. 1,, ( ), : 1. 2., 169
3., 4., ( ), : 1., 2. 3. ( ), : 1. 2. 3. 4. 5. 6. 170
( ) 1., :, 2.,,,,,,,, ( 1) ( 2), ( 3) ( 4) 171
( 5) ( 6),,, ( 7), ; ( ),,,,,, ( ),,,,,, ( ),,,,, 172
,,, : ( ), ( ), 5. 2,,,, ( ), 173
, : 1., ( 1) ( 2), ( 3) ( 4) 2.,, : = - = - ( + + ) = - 3. = - ( + ) = +, 174
( 1) ; ( 2) ; ( 3),,,, 1, 27 000, 5,, 5 2 000, 18 000, 5 000, 5 000 10 000, 5,, 5 2 000, 11 400, 3 000, 3 000, 400 40%, 5 1, 5 2 5 1 : 1 2 3 4 5 ( 1) 18 000 18 000 18 000 18 000 18 000 ( 2) 5 000 5 000 5 000 5 000 5 000 ( 3) 5 000 5 000 5 000 5 000 5 000 ( 4) 8 000 8 000 8 000 8 000 8 000 ( 4) = ( 1) - ( 2) - ( 3) ( 5) 3 200 3 200 3 200 3 200 3 200 ( 5) = ( 4) 40% ( 6) 4 800 4 800 4 800 4 800 4 800 ( 6) = ( 4) - ( 5) ( 7) 9 800 9 800 9 800 9 800 9 800 ( 7) = ( 6) + ( 3) 175
1 2 3 4 5 ( 1) 11 400 11 400 11 400 11 400 11 400 ( 2) 3 000 3 400 3 800 4 200 4 600 ( 3) 1 600 1 600 1 600 1 600 1 600 ( 4) 6 800 6 400 6 000 5 600 5 200 ( 4) = ( 1) - ( 2) - ( 3) ( 5) 2 720 2 560 2 400 2 240 2 080 ( 5) = ( 4) 40% ( 6) 4 080 3 840 3 600 3 360 3 120 ( 6) = ( 4) - ( 5) ( 7) 5 680 5 440 5 200 4 960 4 720 ( 7) = ( 6) + ( 3) 5 2 : 0 1 2 3 4 5-27 000-5 000 9 800 9 800 9 800 9 800 9 800 2 000 5 000-32 000 9 800 9 800 9 800 9 800 16 800-10 000-3 000 5 680 5 440 5 200 4 960 4 720 2 000 3 000-13 000 5 680 5 440 5 200 4 960 9 720 176
,, 1, 0,,,,,,, 5 2, 5 1 5 2 5 1 5 2, 177
: ( 1), ;, ( 2),, ( 3),,,,,, ( ),,,,,,,,,,,, :, N P V= N CF 0 + = t = 0 N CF t ( 1 + ) t N P V 178 N CF 1 ( 1 + ) + N CF 2 ( 1 + ) 2 + + N CF ( 1 + )
N CF t t 2 1 5 2,, 10%,,,,,,,,,,, 3 1 5 2,,, = 0 10% 20% 30% 40%, 5 3,, :, 9. 1%, 10 560 ;, 20. 2%, ;, 34. 9%, ( ), 179
1., : : 3, 6 3, 25%, N P V ( 25% ) < 0, 25%, N P V ( 25% ) > 0, 2.,, : 5 3, 10%,, 8%, N P V > N P V N P V > N P V 4,, 40%, 10%, 5 4,,, : ( 1) = - 180 = - ( + ) = + = ( - - ) ( 1- ) +
= ( 1- ) - ( 1- ) +, :, ( 1- ) ;, 5 4 : 60 000 50 000 ( 10% ) 6 000 5 000 ( ) 6 4 3 0 4 4 8 600 5 000 28 000 7 000 10 000 10 000 1 9 000 18 000 2 9 000 13 500 3 9 000 9 000 4 9 000 4 500 ( 2),,,,, ( 3) 181
,,,,, : 0 : - 10 000+ [ 10 000- ( 60 000-9 000 3) ] 40% = - 19 200( ) 1 : - 8 600 ( 1-40% ) + 9 000 40% = - 1 560( ) 2 : - 8 600 ( 1-40% ) + 9 000 40% - 28 000 ( 1-40% ) = - 18 360( ) 3 : - 8 600 ( 1-40% ) + 9 000 40% = - 1 560( ) 4 : - 8 600 ( 1-40% ) + 7 000- ( 7 000-6 000) 40% = 1 440( ) 5 4 5 4 : 0 : - 50 000( ) 1 : - 5 000 ( 1-40% ) + 18 000 40% = 4 200( ) 2 : - 5 000 ( 1-40% ) + 13 500 40% = 2 400( ) 3 : - 5 000 ( 1-40% ) + 9 000 40% = 600( ) 182
4 : - 5 000 ( 1-40% ) + 4 500 40% + 10 000 - ( 1 000-5 000) 40% = 6 800( ) 5 5 5 5, N P V = - 19 200-1 560 ( P / S, 10%, 1) - 18 360 ( P / S, 10%, 2) - 1 560 ( P / S, 10%, 3) + 1 440 ( P / S, 10%, 4) = - 19 200-1 560 0. 909-18 360 0. 826-1 560 0. 751+ 1 440 0. 683 = - 35 971( ) N P V = - 50 000+ 4 200 ( P / S, 10%, 1) + 2 400 ( P / S, 10%, 2) + 600 ( P / S, 10%, 3) + 6 800 ( P / S, 10%, 4) = - 50 000+ 4 200 0. 909+ 2 400 0. 826 + 600 0. 751+ 6 800 0. 683 = - 39 105( ) N P V > N P V,, 35 971 183
, 39 105, 3.,, : 5 5 A 1 B 1 B2 C1 C2, B 1 B2 C1 C2, 800 000 5 5 5 5 : A 1 245 000 135 000 B1 300 000 160 000 B2 595 000 220 000 C1 250 000 42 000 C 2 205 000 36 000,, 5 6 5 6,, A 1B 1C1, 337 000 4.,, : 184
5 6 : A1B1C1 795 000 337 000 A1B1C2 750 000 331 000 A1 B1 545 000 295 000 A 1C1 495 000 177 000 A 1C2 450 000 171 000 B1 C1 550 000 202 000 B 2 C 2 800 000 256 000 6, 5 7, 15%,?, 5 7 : 2 200 10 4 200 600 700 2 400 10 0 300 2 400 400 5 6 5 6 5 7 185
5 7 : N P V - 600-700 ( P / A, 15%, 6) + 200 ( P / S, 15%, 6) = ( P / A, 15%, 6) - 600-700 3. 784+ 200 0. 432 = 3. 784 = - 836( ) : N P V - 2 400-400 ( P / A, 15%, 10) + 300 ( P / S, 15%, 10) = ( P / A, 15%, 10) - 2 400-400 5. 019+ 300 0. 247 = 5. 019 = - 863( ),,,, ( ),, 186
,,, 1.,,,,,,,,,,, 2.,,,,,,,,,,,,,,,,,, : 187
, P I = P I ; t = 0 I t t ; Q t t ; ; I t ( 1 + ) t ( 1 + ) t t = 0, : 1,,,,,,,,,, 7 A B, 5 8 14%, Q t 5 8 : A B 0 110 000 10 000 1 50 000 5 050 2 50 000 5 050 3 50 000 5 050 A B 5 8 5 9, 188
5 8 A 5 9 B 50 000 ( P / A, 14%, 3) 50 000 2. 322 P I A = = = 1. 06 110 000 110 000 5 050 ( P / A, 14%, 3) 5 050 2. 322 P I B = = = 1. 17 10 000 10 000, A B 1,,, B A, B, N P V A = 50 000 ( P / A, 14%, 3) - 110 000 N P V B = 50 000 2. 322-110 000= 6 100( ) = 5 050 ( P / A, 14%, 3) - 10 000 = 5 050 2. 322-10 000= 1 726( ) N P V A> N P VB, A 189
,,,, ( ) :, t = 0 I RR ; N CF t t ; N CF t = 0 ( 1 + I RR) t ( ),,,, ;,,,, 8 5 1 5 2 1, 5 3, : 190
5 3, N P V ( 20% ) = 125 N P V ( 30% ) = - 6242, I RR 20% 30% 20%, 21% N P V ( 21% ) = - 627,, 20% 21% : I RR = 20% + : 125 ( 21% - 20% ) = 20. 2% 125- ( - 627) 5 3, N P V ( 30% ) = 1 310 N P V ( 40% ) = - 1174, I RR 30% 40% 35% N P V ( 35% ) = - 33, 35% ; 34% N P V ( 34% ) = 218,, : IRR = 34% + 218 ( 35% - 34% ) = 34. 9% 218- ( - 33), 5 3 ( ),,, 5 3,,,, 9 5 9,,, 191
6,,,,,,,,,,,,,,,,,,,,,, 192
,,,,,, 6 1,,,,,,,, ( ),,,,,,,,,,,,,, ( ),,,,,,,, 193
,,, ( ),,,,,,,,, ( ) : 1. 2.,, 194
3.,,,,,, ( ),, : 1., 2.,, 3.,,, ;,, ( ),, 195
,,,,, 1,, 1. 12 500, 50%, 5, 5 2 500, 3 500,, 5 2. 8 200, 1 3 000, 400 20%, 80% 5 2 000 3. 1 060, 200, 600, 300, 100 4. 10%, 8% 6% 30%, 30% 196
( ) 1. 6 1 6 1 : 1 2 3 4 5 ( 1) 8 200 8 200 8 200 8 200 8 200 ( 2) 3 000 3 400 3 800 4 200 4 600 ( 3) 2 000 2 000 2 000 2 000 2 000 ( 4) = ( 1) - ( 2) + ( 3) 3 200 2 800 2 400 2 000 1 600 ( 5) = ( 4) 30% 960 840 720 600 480 ( 6) = ( 4) - ( 5) 2 240 1 960 1 680 1 400 1 120 ( 7) = ( 1) - ( 2) - ( 5) = ( 3) + ( 6) 4 240 3 960 3 680 3 400 3 120 2. 6 2 6 2 : 0 1 2 3 4 5-12 500-3 500 4 240 3 960 3 680 3 400 3 120 2 500 2 000 3 500-16 000 4 240 3 960 3 680 3 400 11 120 197
3. N P V = - 16 000+ 4 240 ( P / S, 10%, 1) + 3 960 ( P / S, 10%, 2) + 3 680 ( P / S, 10%, 3) + 3 400 ( P / S, 10%, 4) + 11 120 ( P / S, 10%, 5) = - 16 000+ 4 240 0. 909+ 3 960 0. 826 + 3 680 0. 751+ 3 400 0. 683+ 11 120 0. 621 = 3 117( ) 3 117, ( ) 1.,, 6 3 6 3 : 1 2 3 4 5 1 060 1 060 1 060 1 060 1 060 200 200 200 200 200 860 860 860 860 860 258 258 258 258 258 602 602 602 602 602 2. 6 4,, 20%, 2 3. N P V = - 6 250+ 1 498 ( P / S, 8%, 1) + 1 386 198 ( P / S, 8%, 2) + 1 274 ( P / S, 8%, 3) + 1 162 ( P / S, 8%, 4) + 3 360 ( P / S, 8%, 5)
= - 6 250+ 1 498 0. 926+ 1 386 0. 857+ 1 174 0. 794+ 1 162 0. 735+ 3 300 0. 681 = 438( ) 438, 6 4 : 0 1 2 3 4 5-6 250 602 602 602 602 602 896 784 672 560 448 1 250 1 000-6 250 1 498 1 386 1 274 1 162 3 300 ( ) 1. 6 5 6 5 : 1 2 3 4 5 600 600 600 600 600 200 200 200 200 200 800 800 800 800 800 240 240 240 240 240 560 560 560 560 560 2. 6 6 199
6 6 : 0 1 2 3 4 5-6 250 560 560 560 560 560 896 784 672 560 448 1 250 1 000-6 250 1 456 1 344 1 232 1 120 3 258 3. N P V = - 6 250+ 1 456 ( P / S, 6%, 1) + 1 344 ( P / S, 6%, 2) + 1 232 ( P / S, 6%, 3) + 1 120 ( P / S, 6%, 4) + 3 258 ( P / S, 6%, 5) = - 6 250+ 1 456 0. 943+ 1 344 0. 890+ 1 232 0. 840+ 1 120 0. 792+ 3 258 0. 747 = 675( ) 675,,, : ( ), 200
,,,, ( ),,,,,, ( ),,,,,,,, 6 2,, 201
( ), 1.,,,,,,,, ;, 2.,,,,,,, ;, 3.,,,,, ; 202
,,,,,,, 4.,,,,,, ( ), 1.,, ;,,,,,,,,,,,, 2. :,,, 203
,,,,,,,,,,, ( ), 1.,, ( 1),, :,,,,,,,, ( 2),, 204
:,,,, : 2.,, ( 1),,,,,,,,,,,, : ( 2),,,,,,, 205
( ), : = ( 1 + ) + t = 1 ( 1 + ) t,,,, t,, t 2 1 000, 8%, 5,, 10%,? 1 000 ( 1 + 10% ) 5 + 5 t = 1 1 000 8% ( 1 + 10% ) t = 1 000 ( P / S, 10%, 5) + 1 000 8% ( P / A, 10%, 5) = 1 000 0. 621 + 1 000 8% 3. 791 = 924( ) 3,, 4%, 5%, 10, t 206
1 000 ( 1 + 5% ) 10 + 10 t = 1 1 000 4% ( 1 + 5% ) t = 1 000 ( P / S, 5%, 10) + 1 000 4% ( P / A, 5%, 10) = 1 000 0. 614 + 1 000 4% 7. 722 = 923( ),,, = ( 1+ ) 4 1 000, 5,, 10%,? 1 000 ( 1+ 10% ) 5 = 1 000 ( P / S, 10%, 5) ( ) = 1 000 0. 621= 621( ),,,,,, : P = D 1 1 + K + D 2 ( 1 + K ) 2 + + = t = 1 D t ( 1 + K ) t, P ; D t ( 1 + K ) t + 207
D t t ; K, : 1.,,,, : P = t = 1 D t ( 1 + K ) t + P ( 1 + K ),, P 5 3 3 10 000, 3 100 000 12%,? 3 P = t = 1 10 000 + ( 1 + 12% ) t 100 000 ( 1 + 12% ) 3 = 10 000 ( P / A, 12%, 3) + 100 000 ( P / S, 12%, 3) = 10 000 2. 402 + 100 000 0. 712 = 95 220( ) 2., D,, : 1 1 + K P = : P = 208 t = 1 D = ( 1 + K ) t t = 1 D ( 1 + K ) t D 1 + K D 1 + K 1 -, 1 = D 1 K 1 + K
, 1 1+ K 6,,? P = 10 000 12% = 83 333( ) 3.,, t, G, D 1 G K D t= D 1( 1+ G) t - 1, : P = = t = 1 D 1 D t ( 1 + K ) t = t = 1 1 + G 1 + K 1 + K t = 1 1, D 1( 1 + G) t - 1 ( 1 + K ) t t- 1 1 + G D 1, G 1 + K 1 + K < K 1 + G 1,, 1 + K P = t = 1 D t ( 1 + K ) t = D 1 1 + G 1 + K 1 + K t = 1 D 1 1 D 1 = = 1 + K 1 + G K - G 1-1 + K 7, 3, 5% 12%,? P = 3 ( 1 + 5% ) 12% - 5% = 45( ) 45 t- 1 209
,,,, ( ),,,,,,, 6 1 6 1,, - P 0 + P 1 + ( 1 + R) D t t = 1 1 = 0 ( 1 + R) t, 210
P 0 ; P ; D t t ; ; R R,, D t = D, : - P 0+ P + D ( 1+ R) R 1-1 = 0 ( 1+ R),,, R,, P P 0 : ( 1+ R) - 1- R - P 0+ P - P R+ D 0 D + ( P - P 0) / R P, D + ( P - P 0) / R ( P + P 0) / 2 :, 8 95 220, 3, 3 10 000, 3 100 000, - 95 220+ 100 000 ( 1+ R) 3 + 10 000 R 1-1 ( 1+ R) 3 = 0, 211
, 5, R= 12%, 10 000+ ( 100 000-95 220) / 3 R = 11. 9% ( 100 000+ 95 220) / 2 9 924 5, 1 000, 8%, 950, 6 2, 1 000 8% = 80( ) N P V= - 924+ 80 ( 950+ 80) + 1+ ( 1+ ) 2 = 9%, N P V( 9% ) = 16. 32( ) = 11%, N P V( 11% ) = - 15. 96( ),, = R= 9% + 6 2 16. 32 ( 11% - 9% ) = 10. 0% 16. 32_ ( - 15. 96) 2, 80+ ( 950-924) / 2 R = 9. 9% ( 950+ 924) / 2 10, 1 000,? 212
, 80+ ( 1 000-924) / 2 R = 12. 3% ( 1 000+ 924) / 2,, N P V( 12. 3% ) = - 924+, = 3. 61( ) N P V( 13% ) = - 924+, : R= 12. 3% + = - 7. 41( ) 80 ( 80+ 1 000) + 1+ 12. 3% ( 1+ 12. 3% ) 2 80 ( 80+ 1 000) + 1+ 13% ( 1+ 13% ) 2 3. 61 ( 13% - 12. 3% ) = 12. 5% 3. 61- ( - 7. 41) 11, 1 000, 3? 3 6 3 6 3, 80+ ( 1 000-1 000) / 3 R = 8% ( 1 000+ 1 000) / 2 213
N P V( 8% ) = - 1 000+ 8%, 80 1+ 8% + 80 + ( 1+ 8% ) 2 ( 80+ 1 000) ( 1+ 8% ) 3 = 0 ( ),,, 1.,,,,,,, 2.,,,,,,,, 3.,,,, ;,,,,, 214
4.,,,, : ( 1) ; ( 2), ; ( 3) ; ( 4), ; ( 5), 5.,,,,, 12 3 100 1 100, 14%,, : ( 1) 1 20% ; ( 2) 1 10%, : ( 1) 1 20% 1 : 100 ( 1+ 14% ) = 114( ) 3 100 ( 1+ 14% 3) - 100 2 20% = 102( ) 3 : 114-102= 12( ),, 215
: ( 2) 1 10% 1 : 100 ( 1+ 14% ) = 114( ) 3 1 100 ( 1+ 14% 3) - 100 2 10% = 122( ) : 122-114= 8( ),, ( ), 1., : ( 1) ; ( 2) ; ( 3) AAA AA A BBB BB B CCC CC C9,, 4,,, 5,, 2. : ( 1) ; ( 2) ; ( 3) 216
3., 1, A B C D 4 A, A 1 2 3 B, C D 4.,,, 4 8, : A + ; A ; A - ; B + ; B - ; B ; C ; D 217
( ) 1., ( 1) ( ), ;, ( 2), :,,,,,,,,,,,,, ( 3),,,,, ;,,, ;,,,,, 218
, ;,,,,, 2 ( 1), 4,,, ( 2), 4,,,,,,,,,,,,, ( 3),, : ; ; ; ; 219
; ; ; ; ;,, ( ),, 1,,,, : =, : =,, ;, ;,, 13 3, 15, 10,? = 15 3= 45( ) = 10 3= 30( ),, 220
2,,, 1,,,, 20,,,, 1, 5,, 10 11, 5 20,,,, ( ),,,,,,, : 1,,,, ;, ;, ;,, 221
,,,,,,,, 40,, 12, 10, 1/ 3, 1/ 3, 1/ 3, 1/ 3,,,,,,,,, 2,,,,,,,, 3,,,,, 222
,,,,, ( ),,,,,, ( ),,, : 1,,, 2,,, 223
, 3,,,,, 224
7,,,,, 7 1,, 1, 1 1992 1995 20%, 1995 1 000, 1996, 1996 20%, 1996 227
: 1 000 ( 1+ 20% ) = 1 200( ), ;, 2,,,,,,,,,,,,,,, ( ),, 10%, 10% 10%, 10%, 10%, 228
, 10%, 10%,, 10%, 10%,,, ;, : = - - ( ) = - = + + : = - - : ; ( ),, 229
: 1, ; 2,, ; 3, 2 1995 7 1 1996 19 000 000, 50%, 1996 7 1 1995 : ( % ) 17 000 000 100. 0 : 11 730 000 69. 0 85 000 0. 5 1 360 000 8. 0 3 825 000 22. 5 : 3 111 000 18. 3 34 000 0. 2 680 000 4. 0 : 272 000 1. 6 408 000 2. 4 1995, 1996, 7 2 7 2, 456 000, 456 000 50% = 228 000( ) 230
7 2 1996 1995 ( % ) 1996 17 000 000 100. 0 19 000 000 : 11 730 000 69. 0 13 110 000 85 000 0. 5 95 000 1 360 000 8. 0 1 520 000 3 825 000 22. 5 4 275 000 : 3 111 000 18. 3 3 477 000 34 000 0. 2 38 000 680 000 4. 0 760 000 : 272 000 1. 6 304 000 408 000 2. 4 456 000 ( ), : 1, 2, 3 3, 1995, 7 3, 1996 231
7 3 1995 : ( % ) : 221 000 1. 3 3 060 000 18. 0 2 720 000 16. 0 10 000 500 000 289 000 1. 7 6 800 000 37. 0 : 1 010 000 2 618 000 15. 4 153 000 0. 9 269 000 4 050 000 16. 3 800 000 1 950 000 2 750 000 6 800 000, 1996 7 4 7 4 1996 : 1995 1995 ( % ) 1996 : 221 000 1. 3 247 000 3 060 000 18 3 420 000 2 720 000 16 3 040 000 232
1995 1995 ( % ) 1996 10 000 10 000 500 000 500 000 289 000 1. 7 323 000 6 800 000 37. 0 7 540 000 1 010 000 1 010 000 2 618 000 15. 4 2 926 000 153 000 0. 9 171 000 269 000 269 000 4 050 000 16. 3 4 376 000 800 000 800 000 1 950 000 2 178 000 2 750 000 2 978 000 186 000 6 800 000 7 540 000 7 4, = - + = 7 540 000- ( 4 376 000+ 2 978 000) = 186 000( ) 1996 1995 1996, : 1 950 000+ 228 000= 2 178 000( ) ( ) : 233
, = = + = + = - + - = - - - -,, + - - - = - -, : ( 221000+ 3060000+ 2720000+ 289000) - ( 2618000+ 153000) = 17000000 ( 19 000 000-17 000 000) - 228 000 = 3 519 000 2 000 000-228 000 17 000 000 234
= 414 000-228 000 = 186 000( ) 4 1996 4 500 000, 40% 20%, 1996 530 000 = ( 40% - 20% ) 4 500 000-530 000= 370 000( ), :, y a y= a + bx b x,,,,,,, y= a + bx, a b, x y 235
( ) a b,,, y 1= a + bx 1,, y 2= a + bx 2 b= y 2- y 1 x 2- x 1 a = y 1- bx 1 = y 2- bx 2, x 1 y 1 x 2 y 2 :,, 7 1 x P 1 x P 6 L, L L 1 P 2 P 3, L 2 P 3 P 4,,, : y y, x x, 236
7 1 5 7 5 1996 79 000, 7 5 ( x ) ( ) ( y ) ( ) 1991 6. 0 495 1992 5. 5 480 1993 5. 0 450 1994 6. 5 520 1995 7. 0 550 1993, x 1= 5. 0, y 1 = 450, 1995, x 2 = 7. 0, y 2= 550 : b= 550-450 7. 0-5. 0 = 50 a = 450-50 5. 0= 200 237
y = 200+ 50x 1996 : y= 200+ 50 7. 9= 595( ) ( ), a, b, 7 2 5, 7 2 y a 210 ; ( 5, 450), : : b= 1996 : 238 450-210 = 48( / ) 5. 0 y = 210+ 48x
y = 210+ 48 7. 9= 589. 2( ) 595,,,, ( ),,,,,,,,, 7 3, : 7 3 D = 1, D, 239
D = cos = 2 cos, y, x, D = 1 Q = 2 = 1,, y = a+ bx Q= 2 = [ y - ( a + bx ) ] 2 = ( y 2 + a 2 + b 2 x 2 + 2a bx - 2a y - 2bx y ) Q, Q a b, Q a = ( 2a + 2bx - 2y) = 2( a + b x - y) = 0 Q b = ( 2bx 2 + 2ax - 2x y) = 2( b x 2 + a x - x y) = 0 y = a + b x x y = a x + b x 2, y = a + bx a b a b,, 240
6 5, 1996 7 5 7 6 7 6 x( ) y ( ) xy x 2 1991 6. 0 495 2 970 36 1992 5. 5 480 2 640 30. 25 1993 5. 0 450 2 250 25 1994 6. 5 520 3 380 42. 25 1995 7. 0 550 3 850 49 = 5 x = 30 y = 2495 xy = 15090 x 2 = 182. 5 7 8, y = 211+ 48x 2 495 = 5a + 30b 15 090 = 30a + 182. 5b a = 211 b= 48 1996 79 000 7. 9, 1996 : y = 211+ 48 7. 9 = 590. 2( ),,,,,,, 241
7 2,, 6, 7,, 6 ( ), : 1, 2,, 3 4, 242
, ( ),, : 1 2 3 4 ( ),, 6,, 4,,, 243
, ( ) : 1,,, 2,,,,,, : 1,,, 2,,, ( ),,,,,, 244
, 1. 5/ 10, / 30, 10, 1. 5% ; 10 30, ;, 30, 30, 10, : 1,, 2,,,,,, : = - 360 - = 1-360 - 3,,,,, 245
7 1. 5/ 10, / 30, 1, 10, 0 2 : = 1. 5% 360 = 27. 1% 1-1. 5% 30-10, 30, 10, 20 3 55, : 1. 5% 360 = 12. 1% 1-1. 5% 55-10, 55, 10, 20, 25 ( ),, 246
( ) 1,,,,,,,,,,,,,,, 2 1,,,, 247
1989 100 3 000, 3 6 9 3, 1,,,,,,,, 7 3, ( ),,,,,, 1. 248
,, 2.,,,,,,, : K ; D ; P ; f ; F K = ( ) K = D P - f D P ( 1- F ), 1. 249
( 1), ( 2), ( 3),, 2.,,,,,,,, 3., ;,,, ;, ( ),, : 250
- = ( 1- ) 1. : :, K l ; D l ; I l ; T ; D l= I l ( 1- T ) K l = I l ( 1- T ) L( 1- F l ) L, ; F l : K l=, R l Rl ( 1- T ) 1- F l,,,, K l = Rl ( 1- T ) 8 3 300, 12%,, 0. 2%, 33%,? 12% ( 1-33% ) 1-0. 2% = 8. 06% 251
, 2. 12% ( 1-33% ) = 8. 04%,,,,, : K b ; I b ; T ; K b= I b( 1- T ) B( 1- F b) B, ; F b, 3, 9 500, 14%, 560, 5%, 33%, : 500 14% ( 1-33% ) 560 ( 1-5% ), : 252 500 14% ( 1-33% ) 500 ( 1-5% ) = 8. 82% = 9. 87%
( ) 450, : 500 14% ( 1-33% ) 450 ( 1-5% ) = 10. 97%,,, 1. K p D p P p F p ; ; ; K p = D p P p ( 1- F p ), 10 100, 130, 15%, 6? : ; 100 15% 130-6 = 12. 10%, ( 1), ( 2), 253
, 2.,,, G, G K c : D 1 D 2, D, P c =, D 1 ( 1 + K c) + D 2 ( 1 + K c) 2 + + = t = 1 D t ( 1 + K c) t D t= D 1( 1+ G) t - 1 1,, P c= = t = 1 D 1( 1 + G) t - 1 = ( 1 + K c) t 1 + G D 1 1 + G 1 + K c = 1 + G 1-1 + K c K c= D 1 + G P c D 1 1 + G D 1 K c - t = 1 G D ( 1 + K c) 1 + G 1 + K c, : t, 254 K c= D 1 P c( 1- F c) + G
K c ; D 1 1 ; P c ; F c ; G 11 500, 600, 5%, 1 12%, 6% 3. 500 12% + 6% = 16. 53% 600 ( 1-5% ),,, :, K r P r D 1 ; ; 1 ; K r= D 1 + P G r G,,,,,, 255
, ;,,, :, : K w ; K ; K w = K W = 1 W,, W = 1; = 1, W 3 1.,, 2.,, 3.,,, 256
12 1000, 100 250 100 350 200, 5. 65% 7. 00% 10. 63% 15. 80% 15. 15% :, : Wl = 100 = 0. 10 1 000 : Wb= 250 = 0. 25 1 000 : Wp = 100 = 0. 10 1 000 : Wc= 350 = 0. 35 1 000 : Wr = 200 = 0. 20 1 000, K W = 5. 65% 0. 10+ 7. 00% 0. 25+ 10. 63 0. 10 + 15. 80% 0. 35+ 15. 15% 0. 20 = 0. 57% + 1. 75% + 1. 06% + 5. 53% + 3. 03% = 11. 94% 7 7 7 7 ( ) ( % ) ( % ) 100 5. 65 0. 10 0. 57 250 7. 00 0. 25 1. 75 100 10. 63 0. 10 1. 06 350 15. 80 0. 35 5. 53 200 15. 15 0. 20 3. 03 1 000-1. 00 11. 94 257
13, 100 300 125 525 300, 7 8 7 8 ( ) ( % ) ( % ) 100 5. 65 0. 074 0. 42 300 7. 00 0. 222 1. 55 125 10. 63 0. 093 0. 99 525 15. 80 0. 389 6. 15 300 15. 15 0. 222 3. 36 13 50-1. 000 12. 47 14, 5 100 320 130 560 320, 7 9 7 9 ( ) ( % ) ( % ) 100 5. 65 0. 070 0. 40 320 7. 00 0. 224 1. 57 130 10. 63 0. 091 0. 97 560 15. 80 0. 392 6. 19 320 15. 15 0. 224 3. 39 1430-1. 000 12. 52 258
,,,,, ( ), K w ; K w = K W K ; W, W = 1; = 1 15 600, 15% 25% 60%, 5% 11% 14%, K w = 5% 15% + 11% 25% + 14% 60% = 11. 9%, 7 10 259
7 10 ( % ) ( % ) 0. 15 90 5 0. 75 0. 25 150 11 2. 75 0. 60 360 14 8. 40 1. 00 600-11. 90 ( ),,,,, 16 10000, : 0. 15 0. 25 0. 60, : 1.,,,,, : 0. 15 0. 25 0. 60 2.,,,,, 7 11 260
7 11 0. 15 45 5% 45-105 6% 105 7% 0. 25 250 11% 250-500 12% 500 13% 0. 60 330 14% 330-900 15% 900 16% 3. 7 11,,,,,,,, : BP = T F W, BP ; T F ; W, 7 12,,, 3 2, 6 261
7 12 0. 15 45 45-105 105 0. 25 250 250-500 500 0. 60 330 330-900 900 5% 6% 7% 11% 12% 13% 14% 15% 16% 45 = 300 0. 15 105 = 700 0. 15 250 = 1000 0. 25 500 = 2000 0. 25 330 = 550 0. 60 900 = 1500 0. 60 4.,,,, 6 7 7 13, 7 4 7 13 1 300 0. 15 5% 0. 75% 0. 25 11% 2. 75% 0. 60 14% 8. 40% 11. 90% 2 300-550 0. 15 6% 0. 90% 262 0. 25 11% 2. 75% 0. 60 14% 8. 40% 12. 05%
3 550-700 0. 15 6% 0. 90% 0. 25 11% 2. 75% 0. 60 15% 9. 00% 12. 65% 4 700-1000 0. 15 7% 1. 05% 0. 25 11% 2. 75% 0. 60 15% 9. 00% 12. 80% 5 1000-1500 0. 15 7% 1. 05% 0. 25 12% 3. 00% 0. 60 15% 9. 00% 13. 05% 6 1500-2000 0. 15 7% 1. 05% 0. 25 12% 3. 00% 0. 60 16% 9. 60% 13. 65% 7 2000 0. 15 7% 1. 05% 0. 25 13% 3. 25% 0. 60 16% 9. 60% 13. 90% ( ),,, 1 600, 1 600 1 500 100, 100 263
7 4 0. 6,,, 1 500, 13. 05%,, 1 600,,,,, 2 000, 7 4,,, 264
,,,,,,, ( ),,, :,,,, :,,,,,, 7 14 7 14 : ( 1) ( 2) ( 3) ( 4) = ( 1) - [ ( 2) + ( 3) ] 10 6 3 1 15 9 3 3 20 12 3 5 265
7 14, 3, 10 1. 5 2. 0 15 20, 1. 5 2. 0 6 9 12, 6+ 3= 9 9+ 3= 12 12+ 3 = 15, 12/ 9= 1. 33 15/ 9= 1. 66,, 10 15 1. 5, 1 3, 3 10 20 2. 0, 1 5, 5,, ( ) : V E BI T = Q( P - V) - F = S 1- P - F E BIT ; Q ; P ; V ; F ; S, S= QP,, : 266 EBIT = 1-1 - E BI T E BI T = S 1 - V P S V P S V P - F
= S S S 1 - V P S 1 - V P - F = S Q( P - V) S Q( P - V) - F = S D OL S, DOL,, : D OL = D OL = DOL = D OL = D OL = E BI T / E BI T S / S S 1 - V P S 1 - V P - F EBI T + F E BI T Q( P - V) Q( P - V) - F S - VC S - VC - F, VC= QV,,, DOL > 1 267
( ),,,,,,,,,,, : 1. F F,, DOL,, 2. Q Q,, DOL,, 3. P P,, DOL,, 4. V V,, D OL,,, F, V, Q P,,,,, F,,, 268
,,,, 17 80, 480, 300, D OL= 480-300 480-300 - 80 = 1. 8 : 1, 1. 8 ;, 1, 1. 8,,,,, ( ),,, :,,,, :,,,,, 269
,, 7 15 7 15 : ( 33% ) ( 1) ( 2) ( 3) = [ ( 1) - ( 2) ] 33% ( 4) = ( 1) - [ ( 2) + ( 3) ] 10 8 0. 66 1. 34 15 8 2. 31 4. 69 20 8 3. 96 8. 04 7 15, 8, 10 1. 5 2. 0 15 20, 8+ 0. 66= 8. 66 8+ 2. 31= 10. 31 8+ 3. 96 = 11. 96 10. 31/ 8. 66= 1. 19 11. 96/ 8. 66 = 1. 38, 1. 5 2. 0, 1. 5 2. 0, 4. 69/ 1. 34= 3. 5 8. 04/ 1. 34= 6 ( ) :, E P S = N P - P D N E P S ; N P ; 270 = ( E BI T - I ) ( 1 - T ) - P D N
P D N ; E BIT ; I ;, ; T, 33%,, : EP S= E P S E P S = ( 1 - T ) E BI T N E P S = ( 1- T ) EBI T N ( 1 - T ) E BI T ( E BI T - I ) ( 1 - T ) - P D = E BI T E BI T E BI T E BI T - I - P D / ( 1 - T ), : E P S E P S = EBI T E BIT E BI T E BI T - I EBI T,, 1 EBI T - I,, : D F L = : DF L = DF L = E P S / E P S E BI T / E BI T EBI T EBI T - I > 1 Q( P - V) - F Q( P - V) - F - I 271
D F L = S - VC - F S - VC - F - I ( ),,,,,,,,,,, : 1, I,, 2 E BI T, E BI T = Q( P - V) - F,,,,, 18 800, 350, 14%, 98, DF L= 98 98-350 14% = 2, 2 1, 2 ;, 272
1, 2,,,,,,,, : D CL DT L= DOL DF L = EBI T / EBI T E P S / E P S S/ S E BI T / E BI T = EP S / E P S S / S : D CL DT L= D OL= EBIT + F E BI T DF L= E BI T E BI T - I E BI T + F EBI T = E BI T + F E BI T - I E BI T EBI T - I 273
DCL DT L= Q( P - V) Q( P - V) - F - I S - VC DCL DT L= S - VC- F - I 19 300, 100, 1 000, 500, E BI T = 1 000-500 - 300 = 200( ) D OL = D F L = D CL = 200 + 300 200 = 2 5 200 200-100 = 2 200 + 300 200-100 = 5 7 5,, ;, ( ),, 10 000, 1 500 2 500 4 000 2 000, 0 15 0 25 0 40 0 20 274
,,, ( ), : 1,,,, 2,,,,,, ( ), 1, ;, 2,,,, 3 275
, ;, 4,, 5,,,,,, ( ),,,,,,,, 1,,,,,, S K S 276 SK S= ( EBI T - BK b) ( 1- T )
E BIT B K b T, S K S = EBIT ( 1- T ) - BK b( 1- T ), E BIT ( 1- T ) = SK S + BK b( 1- T ) V, VK v= SK S + BK b( 1- T ) K v= S V K S+ B K b( 1- T ) V V= S K s + B K b ( 1- T ) K v K v VK v= E BI T ( 1- T ) K v= V= EBI T ( 1- T ) V EBI T ( 1- T ) K v,,, MM 2,,,?,,,,, 277
,,,,,,, :,,,,,,,,,,,,,,, ( ), 1,, 278
20, 3, 1, 7 16 7 16 : ( % ) ( % ) ( % ) 35 12 45 12 5 75 13 100 13 150 14 110 13 5 65 17 105 17 55 17 300 20 200 20 260 20 500 500 500 3,, K w 1 = 35 100 65 12% + 13% + 500 500 500 17% + 300 500 20% = 17 65% K w 2 = 45 150 105 12 5% + 14% + 500 500 500 17% + 200 500 20% = 16 90% 279
K w 3 = 75 500 + 260 500 20% = 17 19% 13% + 110 55 13 5% + 500 500 17%,,, 2,,, 21, 7 17 7 17 : ( % ) ( % ) 50 12 5 60 13 5 20 18 20 18 30 21 20 21 100 100 280 K w 1 = 50 20 30 12 5% + 18% + 100 100 100 21% = 16 4%
K w 2 = 60 20 20 13 5% + 18% + 100 100 100 21% = 15 9%,,,, 20 : 500, 45 150 105 200, 12 5% 14% 17% 20% 7 18 7 18 : ( % ) ( % ) ( % ) ( % ) ( % ) 45 12 5 50 13 95 12 76 60 13 5 105 13 07 150 14 150 14 150 14 105 17 20 18 125 17 16 20 18 125 17 16 200 20 30 21 230 20 13 20 21 220 20 09 500 100 600 16 81 100 600 16 73, 45+ 50 + 50 13% K w 1 = 45 12 5% 600 45+ 50 105+ 20 + 20 18% + 105 17% + 600 105+ 20 200 20% + 30 21% 200+ 30 = 95 150 125 12 76% + 14% + 600 600 + 150 600 14% 200+ 30 600 600 17 16% 281
+ 230 600 20 13% = 16. 81% 45+ 60 + 60 13. 5% K w 2 = 45 12 5% 600 45+ 60 105+ 20 + 20 18% + 105 17% 600 105+ 20 200+ 20 + 20 21% + 200 20% 600 200+ 20 = 105 150 125 13 07% + 14% + 600 600 + 220 600 20 09% = 16. 73% + 150 600 14% 600 17 16%,,, ( ),, 1 ( 1), E P S= E P S E BIT I 282 ( EBI T - I ) ( 1- T ) - DP N
T D P N y = AX + B : EP S = 1- T N EBI T - A B : A = 1 - T N B = - > 0 1- T N I + 1 N D P 1 - T N I + 1 N DP < 0 7 5,, 7 5, 1 7 5, EP S P O OP, B, B E P S, EP S BP OP, 283
EP S EBIT > E P S E BI T E P S E BI T, DF L = E P S E BI T E BI T EP S > 1 E P S / EP S EBI T / EBI T > 1 ( 2) E P S 1- T N, I EP S A =, B = - 1 - T N I + 1 D P N, EP S, b I : 7 6 b= 1- T N I 7 6 7 7, DP E P S 284
:,, D P D P D P = 1 N D P 7 7 N, EP S A = 1 - T,, N, 7 8 7 8 E P S, EP S, N, : EP S= 0 EBI T = I + DP 1- T, N,, EP S ( 3),,,,,, 285
, ( 1- T ), EP S,, D P = 1 N D P b = 1 - T N I, E P S,,, 7 9 7 9, EP S 7 10, EP S EP S 7 10, EP S,,,,, 286
7 10, 7 10,, E P S,, ;, E P S,, 2,,, :, E P S = E P S, 1 - T N E BI T = E BI T - 1 - T N I / N - I / N 1/ N - 1/ N E BIT ; I = 1 - T N E BI T - 1 - T N I, 287
T ; N, ; I, ; N ; I, : 1 - T N EBI T - 1 - T N I + 1 N DP = 1 - T N E BI T - 1 - T N I + 1 N D P, E BI T = ( 1 - T ) ( I / N - I / N ) + ( 1/ N - 1/ N ) D P ( 1 - T ) ( 1/ N - 1/ N ), DP,, : E P S= EP S, E BI T = 1 - T N EBI T - 1 - T N I + 1 DP N = 1 - T N E BI T - 1 - T N I + 1 N D P, ( 1 - T ) I ( 1/ N - 1/ N ) + ( DP / N - DP / N ) ( 1 - T ) ( 1/ N - 1/ N ), D P, : E P S= E P S, 1 - T N E BI T = ( 1-288 E BI T - 1 - T N I + 1 N D P = 1 - T N E BI T - 1 - T N I + 1 N D P, T ) ( I I / N ) + ( DP D P / N ( 1 - T ) ( 1/ N - 1/ N )
22 850, : 100, 700, 50 150, : 10, 150 3 12%, 10%, 40%, E P S, EP S, E P S E P S : D P = 1 N DP = 1 10 150 12% = 1 8( ) b = 1- T N I 1-40% = 10 150 10% = 0 9( ) b< D P, E P S,,, 7 11 7 11 EP S, : E BI T = ( 1-40% ) ( 25/ 10-10/ 13) + ( 1/ 10-1/ 13) 6 ( 1-40% ) ( 1/ 10-1/ 13) = 85( ) 289
7 11, E BI T 85, E BI T 85 290
8,, 8 1,, ( ),,,,,,,,,,, 291
:, ;,,,,, ( ),, 1,,,,,,, 2,,, ;,,, 292
, ( ),,,,,, :,,, : ( 1) ; ( 2),,,, : ( 1),,,, ( 2), ( 3),, ( 4),,,, 293
( 5),, ( 6),,,, ( 7),,, ( ),,,,, 1,,,,,,,,,,,,,,,,,, 294
,, 2,, : ( 1),,, ( 2),,,,,,,,, ;,,,,, 2/ 10, / 30, 20 36 7% 2% 1-2% 360 20 = 36 7%,, 295
8 2,, ( ),, 1,, ( 1),,,, ( 2), ;, ;, ; ( 3),, 296
, ( 4), ( 5),,,,, 2,, ( 1) : ; ; ; ( 2) : ; ; ; ; ; ; ( 3),, : ( 1),, ; ( 2) ; ( 3), 297
3,, : ( 1), ( 2),,, ( 3), ( ),,,,,,,,,, 1, 5 000, 2 3 4 3, 12, 8 1, 8 1 : ( ) A B C D E F G H I J K L ( 0 2) 8 12 4 15 10 12 7 9 8 8 13 5 111 ( 0 6) 14 17 12 25 16 16 15 17 10 16 15 7 180 298
( ) A B C D E F G H I J K L ( 0 2) 25 25 14 30 20 26 20 22 12 20 18 10 242 = 111/ 12= 9 25( ) = 180/ 12= 15 00( ) = 242 12= 20 17 = 9 25 0 2+ 15 00 0 6+ 20 17 0 2 = 14 88( ) = 5 000 10 000 14 88= 744 000 000( ) ( ),,,,,, 1,, :, x ; x = x 1 + x 2 + + x = x j j = 1 299
x j j ( j = 1 2, ) 2 1 6 8 2, 7 8 2 : 1 2 3 4 5 6 131 153 168 145 170 155 x = 131+ 153+ 168+ 145+ 170+ 155 = 154( ) 6 7 154,,, 2., :, x = w j x j ( j = j = 1 x ; x j j ; ; w j j w j = 1 j = 1 1, 2,, w j = 1) j = 1 3 8 3, 300
8 3 ( ) xj w j w j x j 1991 100 1/ 15 6. 67 1992 115 2/ 15 15. 33 1993 124 3/ 15 24. 80 1994 131 4/ 15 34. 93 1995 128 5/ 15 42. 67 598 1 124, 124,,, 598/ 5= 120, 5, 124,, 3.,, 4 1 5, 6 5 0. 10, 0. 15, 0. 20, 0. 25, 0. 30 6, 1 5, 6 12,, 8 4 : 6 301
33. 6= ( 30+ 32+ 35+ 37+ 34) 5 6 34. 25 = 30 0. 10+ 32 0. 15+ 35 0. 20 + 37 0. 25+ 34 0. 30 8 4 ( ) 1 30 2 32 3 35 4 37 5 34 6 40 33. 6 34. 25 7 42 35. 6 36. 35 8 45 37. 6 38. 45 9 41 39. 6 40. 80 10 49 40. 4 41. 35 11 50 43. 4 44. 25 12 52 45. 4 46. 40 4.,, : ( 1),,, ( 2), ( 3), 302
( 4) : = +, 5 4 1 8 5 8 5 ( ) 5 3 1 30 2 32 3 35 33. 6 4 37 35. 6 + 2. 0 5 34 37. 6 + 2. 0 + 2. 0 6 40 39. 6 + 2. 0 + 1. 6 7 42 40. 4 + 0. 8 + 1. 9 8 45 43. 4 + 3. 0 + 1. 9 9 41 45. 4 + 2. 0 + 2. 3 10 49 47. 4 + 2. 0 11 50 12 52 8 5, 10, 1 3 10 47. 4, 8 10 2. 3, 1 : 47. 4+ 3 2. 3= 54. 3( ), 303
,, 2 1,, 5.,,, :, F t = F t- F t t ; F t - X t - 1 t- 1 ; 1 t- 1 ; 1+ ( X t - 1- F t - 1) = X t - 1+ ( 1- ) F t - 1, 0 1 6 5 240, 230, = 0. 2, 9 F 9= 0. 2 240+ ( 1-0. 2) 230= 232( ) : ( 1) F t- F t-,, 1, 1= X t- 2+ ( 1- ) F t - 2 F t= X t- 1+ ( 1- ) X t - 2+ ( 1- ) 2 F t- 2 F t= X t - 1+ ( 1- ) X t - 2+ ( 1- ) 2 X t- 3+ ( 1- ) 3 F t - 3, F t= X t- 1+ ( 1- ) X t - 2+ + ( 1- ) - 1 X t - + ( 1- ) F t -, 1: 304
+ ( 1- ) + + ( 1- ) - 1 + ( 1- ) = [ 1+ ( 1- ) + + ( 1- ) - 1 ] + ( 1- ) 1- ( 1- = ) + ( 1- ) = 1- ( 1- ) + ( 1- ) = 1, 1 ( 1- ) ( 2) F t = F t- 1+ ( X t - 1- F t- 1),,, = 1 F t= X t - 1,,,,,,,, 0. 1 0. 3 7 1 8 8 6, 0. 1 0. 9 8 6 1 2 3 4 5 6 7 8 ( ) 980 650 930 630 890 610 850 560 = 0. 1 0. 9 2 8 2, 1 980 8 7 305
8 7 1 2 3 4 5 6 7 8 ( ) 980 650 930 630 890 610 850 560 = 0 1 980 947 945 914 912 882 879 = 0. 9 980 683 905 658 867 636 829 8 7, = 0. 1, ; = 0. 9,, ( ),,,,,,,,,,,, 1. 306
,,, y ; x ; a b y= a + bx : y 1= a + bx 1 y 2 = a + bx 2 y = a + bx, x, a b y= a+ b x xy = a x + b x 2 a = x 2 y - x y x x 2 - ( x ) 2 b = x y - x y x 2 - ( x ) 2 x = 0, : a = y, b = x y x 2 8 5 307
, 8 8, 36. 5 8 8 ( ) ( ) 1991 14. 0 436 1992 15. 6 521 1993 20. 0 589 1994 23. 8 648 1995 26. 6 706 x = 0, x = 0 : = 5 ( 14. 0 + 15. 6 + 20. 0 + 23. 8 + 26. 6) 5 = 100 5 = 20( ) x y, 8 9 y 8 9 x y xy x 2 1991-6. 0 436-2 616. 0 36. 00 1992-4. 4 521-2 292. 4 19. 36 1993 0. 0 589 0. 0 0. 00 1994 3. 8 648 2 462. 4 14. 44 1995 6. 6 706 4 659. 6 43. 56 = 5 x = 0 y = 2 900 xy = 2 213. 6 x 2 = 113. 36 8 9 y a = = 2 900 = 580 5 308
: b= xy x = 2 213. 6 2 113. 36 y = 580+ 19. 527x 36. 5, : x 6= 36. 5-20. 0= 16. 5 = 19. 527 y 6= 580+ 19. 527 16. 5= 902. 20( ) 902. 20 2.,, : : y= a + bx + cx 2 2 y 1= a + bx 1+ cx 1 y 2 = a + bx 2+ cx 2 2 y = a+ bx + cx 2, x x 2, a b c : y = a + b x + c x 2 xy= a x + b x 2 + c x 3 x 2 y = a x 2 + b x 3 + c x 4, x : 309
, :, : : x = 0 x 3 = 0, y = a + c x 2 xy= b x 2 x 2 y= a x 2 + c x 4 a = y - c x 2 b = x y x 2 c = x 2 y - ( x 2 ) ( y) x 4 - ( x 2 ) 2 9 5, 8 10 35 8 10 1991 1992 1993 1994 1995 ( ) 10. 2 14. 9 20. 0 25. 3 31. 1 ( ) 129 258 450 675 954 y, x, x : 10. 2+ 14. 9+ 20. 0+ 25. 3+ 31. 1 = 20. 3( ) 5, 8 11 310
8 11 y( ) x xy x 2 x 2 y x 4 1991 129-10. 1-1 302. 9 102. 01 13159. 29 10 406. 0401 1992 258-5. 4-1 393. 2 29. 16 7 523. 28 850. 3056 1993 450-0. 3-135. 0 0. 09 40. 50 0. 0081 1994 675 5. 0 3 375. 0 25. 00 16 875. 00 625. 0000 1995 954 10. 8 10 303. 2 116. 64 111 274. 56 13 604. 8896 = 5 2466 0 10 847. 1 272. 90 148 872. 63 25 486. 2434 8 11 : c= 5 148 872. 63-272. 90 2 466 5 25 486. 2434- ( 272. 90) 2 = 1. 348 10 847. 1 b= = 39. 75 272. 9 2 466-1. 348 272. 90 a = = 419. 63 5 : y= 419. 63+ 39. 75x + 1. 348x 2 35, : x 6= 35-20. 3= 14. 7 y 6= 419. 63+ 39. 75 14. 7+ 1. 348 14. 7 2 = 1 295( ),,,, 311
,,, 8 12 8 12 ( ) ( ) 7 700 000 : 220 5 600 1 232 000 310 12 000 3 348 000 10% 40 78 000 3 120 000 2 538 400 : 2 000kg 5. 20 10 400 1 400 20 28 000 100 km 20 000 2 000 000 5 100 000 500 000 10 238 400 8. 3,,,,,, c V M, c 312
V M,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, : 313
1.,,, 2.,,,,, 3.,,,,,, ;,,,,,,,,,,, 314
( ),,,,,,,,,,, ( ), 8 1 315
,, 8 1 ( ) :, 1., : : = ( 1), ;, ( 2), ;, 2., 3.,, 316
4., ;,,,, ;, 5., ( ), 1.,,, = + + + = + + +, + = 1- - ( 1+ ) = 1- -,,, 317
,,, : ( 1) ; ( 2) ; ( 3) : ( 1),,, ; ( 2), 10, 20, 13 10%, 0. 7% 15% = 20+ 13 = 44. 41( ) 1-15% - ( 10% + 0. 7% ) 11, 100, 25%, 0. 7% 500 000, 5 000 000, = 2. 100 ( 1+ 25% ) = 139. 98( ) 500 000 1-5 000 000-0. 7%, : = - - 318
= ( 1- ) ( 1- ),,, 12, 5%, 3 000, 10%, 5%,? = 3 000 ( 1+ 5% ) ( 1-10% ) ( 1-5% ) = 2 693( ),,,,, 3.,, :, = + + + = = 319
, =, = + + +, + = 1- + ( 1- ) 13 2 000, 200 000, 40, 80 000, 0. 7% 200 000 40+ = 2 000 1-0. 7% + 80 000 = 181. 27( ) 2 000 ( 1-0. 7% ), = : + ( + ) ( 1+ ) = 1-,,, ;,, 320
4.,,,,,,,,,,,,,,,,,,,,, ;,,,,, : : ( 1),, > ( 2),,, : > + ( 3),, : > + : 321
( 1+ ) = 1-14, 500, 20%, 25%, = 5. 500 ( 1+ 20% ) 1-25% = 800( ),, 160, 210, 60%, 40%, 190 : ( ) 160+ ( 210-160) 60% = 190( ),,,,,,,, : 1., ( 1),,,, : ;, ; 322
( 2),,, :, ; ; ;,, 2., ( 1),,, ( 2),,,,, 3., ( 1),,,,, ( 2) 100 99. 80, 100, 99. 80, 8 6 ( 3),,,, ( 4), 323
8 4,,,, ;,,,, : ( 1) ( 2),,, ; ( 3),, ( 4) 324
( 5),,,, : ( ),,,,, ;,,, : 1., ; 2. ; 3. ; 4., ( ),,,,, 325
,,,,,, ( ),,,,,,,,,,,, ( ),,,,,,,,,,,,,, 326
( ),,,, ;,,,,,,,,, ;,,,, ;,,,,, ( ),,,,,,,,,,, : 327
( ),,,,,,,,,,,,,,,,,,,,,,, ( ),,,,,,,,,,,,, 328
,,,,,, 10 5 2,,,, ( ),,,,,,,,,, ( ) : 1.,, 2. 329
,,,, 15 215, 198 A 2 300 B 880, A 2 300 B 836, = 198 100% = 92% 215 A = 2 300 100% = 100% 2 300 B = 836 100% = 95% 880 B 100%, ; A 100%,,,, ( ),, ;, : 330
= 100% ( ) = ( ) 100% = - 1 100% 16 8 13 8 13 : ( ) ( % ) ( % ) 7000 7500 100 100 700000 750000 750000 107. 14 107. 14 5000 4500 121 124 605000 544500 558000 90 92. 23 2000 2500 200 200 400000 500000 500000 125 125 1705000 1794500 1808000 105. 25 106. 04 8 13,, 1 808 000-1 705 000 = 103 000, 106. 04%, 6. 04% ;, 5. 25%, 25%, ; 92. 23%,, 90%,,,,, : 331
= - = ( 7 500-7 000) 100+ ( 4 500-5 000) 121 + ( 2 500-2 000) 200 = 50 000-60 500+ 100 000 = 89 500( ), 500, 5 ; 500, 6. 05 ; 500, 10 = - = ( 100-100) 7 500+ ( 124-121) 4 500 + ( 200-200) 2 500 = 13 500( ),, ; 3, 13 500,, 895 000 ;, 13 500,, 89 500+ 13 500= 103 000 332
9,,,,,,,,,,, 9 1,,, ( ) : 1 = + +,, 333
: :, = + - - = + - - ( 1), = - - -,,,, ( 2) = - 334
,,,, ( 3), ( 4), ( ) ( ),,, 2, : = -,, 3, : 335
= -,, ( ) : = -,,,, ( ),, : ( 1), ( 2),,, ( 3), 336
( 4),,, : 1,, : ( 1) 17% ; ( 2) 13% ; ( 3) = - = -, : ( 1) ; ( 2) ; ( 3),,,,, : = 6% 2 337
( 1),,,,,, 11,,, : = =, 3% 45% 10, 4 ( 2) : = ( + + ) : 7% 5% 1%, ( 3), : 338
= ( + 3 + ) 3%,,,,,,,,, :,, 3% 5%, 5% 20% ;,,, ;, : 4 = ( ) ( 1 1 12 31 ),, 33%,,,, ( 1) 339
33%, = 33%, =, a b, 5,,, a, ; b ; c ; d, 3%, ; e ; f,, ; g,,, 340
( 2),,, 15, 4, ( ), : ( ) ( ) = 33% ( ) ( ) = - ( ) 1 130 000 000, 11 270 000 4 000 000, 5 120 000 330 000, 200 000 56 000, 780 000 33%,? : 11 270 000-56 000-780 000+ ( 5 120 000-4 000 000) + ( 330 000-130 000 000 1 ) + 200 000 = 11 954 000( ) : 11 954 000 33% = 3 944 820( ), 341
( ),,,,, ( ),,,,, ( ),,,,,,,, ( ),, 342
,,,,,,,,,,,, 9 2,,,,,,, ( ) : = - - - 343
= 1- - - 2 5000, 1200, 10%, 7 %, 3%, 700, 80 5 000 1 200 1-10% ( 1+ 7% + 3% ) - 700-800 000 = 1 040 000( ) ( ),,, ;,, = ( 1- ) - = = ( 1- ) -,, = ( - ) = ( - ) = ( - ) 3, = 1 200 [ 1-10% ( 1+ 7% + 3% ) ] - 700 = 368( ) = 800 000 368= 2 174( ) = ( 5 000-2 174) 368= 1 039 968( ) 344
( ), = = = 1+ : = ( 1+ ) 4 15%, 1 000, 1 000 15% = 150( ) 5 260, 20%, 260 ( 1+ 20% ) = 312( ),,,, 9 1 345
9 1 19 : 2 535 000 3 042 000 : 1 215 000 1 500 000 130 000 150 000 210 000 252 000 980 000 1 140 000 : 10 000 13 000 : 125 000 141 000 83 000 95 000 782 000 917 000 : 250 000 300 000 69 000 72 000 : 46 000 71 000 1 055 000 1 218 000 : 369 000 426 000 686 000 792 000 9 3,,, ( ),,, 346
,,,,,, ( ),,,,,,, ( ),,,, : 1,,,, 2,,,,, 347
: 1 ; 2 ; 3 ; 4 ; 5 ; 6, ( ),,,,,,, 5,,,, 5,,,,,,,, 348
, ( ),, 10% 50%,, : ( 1), ( 2),,,, 6%,, 25% ( 3), 25%,,, ;, 349
( ),,,,,,,,,,, ( ),,,,,,,, 6 : ( 1) 4 800, 33% ; ( 2) 2 000 ; 350
( 3), 10%, 5% ; ( 4) 1 300, 9 2 9 2 : 48 000 000 : - 20 000 000 28 000 000 : 9 240 000 1 876 000 1 876 000 15 008 000 : 938 000 13 000 000 1 070 000 9. 4, ;,,, 351
( ),, 1,,,,,,,, 2 10%,, 50%,,, 3,,,,,,,, :,, 352
( ),, 1,,,,,, 2,,,,,,,,,,, 3,,,,,, 353
( ) 1,,,,,,,,,,,, 2,,,,,,,,, 3,, 354
,,,,,,,, 20%,,, 4,, :, ;,, ( ),,, 5,,,,,,, :, ;, 355
( ) 1961 :, MM MM : ( 1),,,, ( 2), ( 3) ( 4), MM,,,,,,,,,, MM,,, MM, 356
, MM,,, MM,,, MM,,,,,,, MM, ( ),, MM,,,,,,,,,,,,,,,, 357
( ),,, : ( 1),, ( 2), ( 3),, ;,,,,,,,,, 7 2 500 000, 70% 30%, : 2 200 000 3 200 000 4 200 000,?, : ( 1) 2 200 000, : 358 2 200 000 70% = 1 540 000( )
: 2 500 000-1 540 000= 960 000( ) : 960 000 2 500 000= 38 4% ( 2) 3 200 000, : 3 200 000 70% = 2 240 000( ) 2 500 000-2 240 000= 260 000( ) : 260 000 2 500 000= 10 4% ( 3) 4 200 000, : 4 200 000 70% = 2 940 000( ) 2 940 000-2 500 000= 440 000( ),,,,,,,,,,,,,, ( ),,,, 359
, 8 40%,, 9 3 9 3 : 1979 4 50 1 80 50 00 1980 2 00 0 80 46 00 1981-1 50 0 00 38 00 1982 1 75 0 70 48 00 1983 3 00 1 20 52 00 1984-0 50 0 00 42 00 ( ),,,,,,,,,,,,,, : 360
( 1),,,, ( 2),,,, ( 3),, ( 4),,, ( ),, : ( 1), ; ( 2) :,,,, 361
( ), ( ),,,,,,,,, 9 10%, 1, 20, 9 4 9 4 : ( 1, 100 000 ) 100 000 200 000 1 000 000 1 300 000 10%, 100 000 10% = 10 000( ) 10 000 20= 200 000( ) 1, 10 000, 190 000,, 362
200 000 9 5 9 5 : ( 1, 110 000 ) 110 000 390 000 800 000 1 300 000,,,,, : 10 000 20= 200 000( ), 20/ ( 1+ 10% ), : 11 000 20/ ( 1+ 10% ) = 200 000( ),,,,,,, ( ),, 363
,,,,,,, 10 9 6 9 6 : ( 400 000, 2 ) 800 000 4 000 000 4 000 000 8 800 000,?, 2 1, 400 000 800 000, 800 000,,,,,,, 25%,,,,, 5,, 4 1, 5 20 364
( ),,,,,,, 11 5 000 000, 1 000 000 2 000 000, 32 62 500 30, 2,?, 9 7 9 7 ( 1) 5 000 000 5 000 000 ( 2) 1 000 000 937 500 ( 3) [ ( 1) / ( 2) ] 5 5 33 ( 4) 6 6 ( 5) [ ( 3) ( 4) ] 30 32 ( 6) 2 0 9 7,, 32 ( 30 + 2 ),, 32, 2, 365
,,,,,,,,,,,, ( ),, ( ),,,,, ( ),, 4,, 366
, T + 0 T, T, + 0,,,,, ( ),,,,,,,,, 12 1994 12 15, : 1994 12 15 1994, 1994 2, 1995 1 15, 1995 2 1 : 1994 12 15 ; 1995 1 15 ; 1995 1 12, 1 11 1 11 ; 1995 2 1 367
( S/ P, i, n) \ ( % ) 1 2 3 4 5 6 7 1 1. 010 1. 020 1. 030 1. 040 1. 050 1. 060 1. 070 2 1. 020 1. 040 1. 061 1. 082 1. 103 1. 124 1. 145 3 1. 030 1. 061 1. 093 1. 125 1. 158 1. 191 1. 225 4 1. 041 1. 082 1. 126 1. 170 1. 216 1. 262 1. 311 5 1. 051 1. 104 1. 159 1. 217 1. 276 1. 338 1. 403 6 1. 062 1. 126 1. 194 1. 265 1. 340 1. 419 1. 501 7 1. 072 1. 149 1. 230 1. 316 1. 407 1. 504 1. 606 8 1. 083 1. 172 1. 267 1. 369 1. 477 1. 594 1. 718 9 1. 094 1. 195 1. 305 1. 423 1. 551 1. 689 1. 838 10 1. 105 1. 219 1. 344 1. 480 1. 629 1. 791 1. 967 11 1. 116 1. 243 1. 384 1. 539 1. 710 1. 898 2. 105 12 1. 127 1. 268 1. 426 1. 601 1. 796 2. 012 2. 252 13 1. 138 1. 294 1. 469 1. 665 1. 886 2. 133 2. 410 14 1. 149 1. 319 1. 513 1. 732 1. 980 2. 261 2. 579 15 1. 161 1. 346 1. 558 1. 801 2. 079 2. 397 2. 759 16 1. 173 1. 373 1. 605 1. 873 2. 183 2. 540 2. 952 17 1. 184 1. 400 1. 653 1. 948 2. 292 2. 693 3. 159 18 1. 196 1. 428 1. 702 2. 206 2. 407 2. 854 3. 380 19 1. 208 1. 457 1. 754 2. 107 2. 527 3. 026 3. 617 20 1. 220 1. 486 1. 806 2. 191 2. 653 3. 207 3. 870 368
\ ( % ) 1 2 3 4 5 6 7 25 1. 282 1. 641 2. 094 2. 666 3. 386 4. 292 5. 427 30 1. 348 1. 811 2. 427 3. 243 4. 322 5. 743 7. 612 40 1. 489 2. 208 3. 262 4. 801 7. 040 10. 286 14. 974 50 1. 645 2. 692 4. 384 7. 107 11. 467 18. 420 29. 457 8 9 10 11 12 13 14 1 1. 080 1. 090 1. 100 1. 110 1. 120 1. 130 1. 140 2 1. 166 1. 188 1. 210 1. 232 1. 254 1. 277 1. 300 3 1. 260 1. 295 1. 331 1. 368 1. 405 1. 443 1. 482 4 1. 360 1. 412 1. 464 1. 518 1. 574 1. 630 1. 689 5 1. 469 1. 539 1. 611 1. 685 1. 762 1. 842 1. 925 6 1. 587 1. 677 1. 772 1. 870 1. 974 2. 082 2. 195 7 1. 714 1. 828 1. 949 2. 076 2. 211 2. 353 2. 502 8 1. 851 1. 993 2. 144 2. 305 2. 467 2. 658 2. 853 9 1. 999 2. 172 2. 358 2. 558 2. 773 3. 004 3. 252 10 2. 159 2. 367 2. 594 2. 839 3. 106 3. 395 3. 707 11 2. 332 2. 580 2. 853 3. 152 3. 479 3. 836 4. 226 12 2. 518 2. 813 3. 138 3. 498 3. 896 4. 335 4. 818 13 2. 720 3. 066 3. 452 3. 883 4. 363 4. 898 5. 492 14 2. 937 3. 342 3. 797 4. 310 3. 887 5. 535 6. 261 15 3. 172 3. 642 4. 177 4. 785 5. 474 6. 254 7. 138 16 3. 426 3. 970 4. 595 5. 311 6. 130 7. 067 8. 137 17 3. 700 4. 328 5. 054 5. 895 6. 866 7. 986 9. 276 18 3. 996 4. 717 5. 560 6. 544 7. 690 9. 024 10. 575 19 4. 316 5. 142 6. 116 7. 263 8. 613 10. 197 12. 056 20 4. 661 5. 604 6. 727 8. 062 9. 646 11. 523 13. 743 369
\ ( % ) 8 9 10 11 12 13 14 25 6. 848 8. 623 10. 835 13. 585 17. 000 21. 231 26. 462 30 10. 063 13. 268 17. 449 22. 892 29. 960 39. 116 50. 950 40 21. 725 31. 409 45. 259 65. 001 93. 051 132. 78 188. 88 50 46. 902 71. 358 117. 39 184. 57 289. 00 450. 74 700. 23 15 16 17 18 19 20 25 30 1 1. 150 1. 160 1. 170 1. 180 1. 190 1. 200 1. 250 1. 300 2 1. 323 1. 346 1. 369 1. 392 1. 416 1. 440 1. 563 1. 690 3 1. 521 1. 561 1. 602 1. 643 1. 685 1. 728 1. 953 2. 197 4 1. 749 1. 811 1. 874 1. 939 2. 005 2. 074 2. 441 2. 856 5 2. 011 2. 100 2. 192 2. 288 2. 386 2. 488 3. 052 3. 713 6 2. 313 2. 436 2. 565 2. 700 2. 840 2. 986 3. 815 4. 827 7 2. 660 2. 826 3. 001 3. 185 3. 379 3. 583 4. 768 6. 276 8 3. 059 3. 278 3. 511 3. 759 4. 021 4. 300 5. 960 8. 157 9 3. 518 3. 803 4. 108 4. 435 4. 785 5. 160 7. 451 10. 604 10 4. 046 4. 411 4. 807 5. 234 5. 696 6. 192 9. 313 13. 786 11 4. 652 5. 117 5. 624 6. 176 6. 777 7. 430 11. 642 17. 922 12 5. 350 5. 936 6. 580 7. 288 8. 064 8. 916 14. 552 23. 298 13 6. 153 6. 886 7. 699 8. 599 9. 596 10. 699 18. 190 30. 288 14 7. 076 7. 988 9. 007 10. 147 11. 420 12. 839 22. 737 39. 374 15 8. 137 9. 266 10. 539 11. 974 13. 590 15. 407 28. 422 51. 186 16 9. 358 10. 748 12. 330 14. 129 16. 172 18. 488 35. 527 66. 542 17 10. 761 12. 468 14. 426 46. 672 19. 244 22. 186 44. 409 86. 504 18 12. 375 14. 463 16. 879 19. 673 22. 091 26. 623 55. 511 112. 46 19 14. 232 16. 777 19. 748 23. 214 27. 252 31. 948 69. 389 146. 19 20 16. 367 19. 461 23. 106 27. 393 32. 429 38. 338 86. 736 190. 05 370
\ ( % ) 15 16 17 18 19 20 25 30 25 32. 919 40. 874 50. 658 62. 669 77. 388 95. 396 264. 70 705. 64 30 66. 212 85. 850 111. 07 143. 37 134. 68 237. 38 807. 79 2, 620. 0 40 267. 86 378. 72 533. 87 750. 38 1 051. 7 1 469. 8 7 523. 2 36 119. 50 1 083. 7 1 670. 7 2 566. 2 3 927. 4 5 988. 9 9 100. 4 70 065. 497 929. ( P / S, i, n) \ ( % ) 1 2 3 4 5 6 7 8 9 1 0. 990 0. 980 0. 971 0. 962 0. 952 0. 943 0. 935 0. 926 0. 917 2 0. 980 0. 961 0. 943 0. 925 0. 907 0. 890 0. 873 0. 857 0. 842 3 0. 971 0. 942 0. 915 0. 889 0. 864 0. 840 0. 816 0. 794 0. 772 4 0. 961 0. 924 0. 888 0. 855 0. 823 0. 792 0. 763 0. 735 0. 708 5 0. 951 0. 906 0. 863 0. 822 0. 784 0. 747 0. 713 0. 681 0. 650 6 0. 942 0. 888 0. 837 0. 790 0. 746 0. 705 0. 666 0. 630 0. 596 7 0. 933 0. 871 0. 813 0. 760 0. 711 0. 665 0. 623 0. 583 0. 547 8 0. 923 0. 853 0. 789 0. 731 0. 677 0. 627 0. 582 0. 540 0. 502 9 0. 914 0. 837 0. 766 0. 703 0. 645 0. 592 0. 544 0. 500 0. 460 10 0. 905 0. 820 0. 744 0. 676 0. 614 0. 558 0. 508 0. 463 0. 422 11 0. 896 0. 804 0. 722 0. 650 0. 585 0. 527 0. 475 0. 429 0. 388 12 0. 887 0. 788 0. 701 0. 625 0. 557 0. 497 0. 444 0. 397 0. 356 13 0. 879 0. 773 0. 681 0. 601 0. 530 0. 469 0. 415 0. 368 0. 326 14 0. 870 0. 758 0. 661 0. 577 0. 505 0. 442 0. 388 0. 340 0. 299 15 0. 861 0. 743 0. 642 0. 555 0. 481 0. 417 0. 362 0. 315 0. 275 16 0. 853 0. 728 0. 623 0. 534 0. 458 0. 394 0. 339 0. 292 0. 252 17 0. 844 0. 714 0. 605 0. 513 0. 436 0. 371 0. 317 0. 270 0. 231 18 0. 836 0. 700 0. 587 0. 494 0. 416 0. 350 0. 296 0. 250 0. 212 371
\ ( % ) 1 2 3 4 5 6 7 8 9 19 0. 828 0. 686 0. 570 0. 475 0. 396 0. 331 0. 277 0. 232 0. 194 20 0. 820 0. 673 0. 554 0. 456 0. 377 0. 312 0. 258 0. 215 0. 178 25 0. 780 0. 610 0. 478 0. 375 0. 295 0. 233 0. 184 0. 146 0. 116 30 0. 742 0. 552 0. 412 0. 308 0. 231 0. 174 0. 131 0. 099 0. 075 40 0. 672 0. 453 0. 307 0. 208 0. 142 0. 097 0. 067 0. 046 0. 032 50 0. 608 0. 372 0. 228 0. 141 0. 087 0. 054 0. 034 0. 021 0. 013 10 11 12 13 14 15 16 17 18 1 0. 909 0. 901 0. 893 0. 885 0. 877 0. 870 0. 862 0. 855 0. 847 2 0. 826 0. 812 0. 797 0. 783 0. 769 0. 756 0. 743 0. 731 0. 718 3 0. 751 0. 731 0. 712 0. 693 0. 675 0. 658 0. 641 0. 624 0. 609 4 0. 683 0. 659 0. 636 0. 613 0. 592 0. 572 0. 552 0. 534 0. 516 5 0. 621 0. 593 0. 567 0. 543 0. 519 0. 497 0. 476 0. 456 0. 437 6 0. 564 0. 535 0. 507 0. 480 0. 456 0. 432 0. 410 0. 390 0. 370 7 0. 513 0. 482 0. 452 0. 425 0. 400 0. 376 0. 354 0. 333 0. 314 8 0. 467 0. 434 0. 404 0. 376 0. 351 0. 327 0. 305 0. 285 0. 266 9 0. 424 0. 391 0. 361 0. 333 0. 300 0. 284 0. 263 0. 243 0. 225 10 0. 386 0. 352 0. 322 0. 295 0. 270 0. 247 0. 227 0. 208 0. 191 11 0. 350 0. 317 0. 287 0. 261 0. 237 0. 215 0. 195 0. 178 0. 162 12 0. 319 0. 286 0. 257 0. 231 0. 208 0. 187 0. 168 0. 152 0. 137 13 0. 290 0. 258 0. 229 0. 204 0. 182 0. 163 0. 145 0. 130 0. 116 14 0. 263 0. 232 0. 205 0. 181 0. 160 0. 141 0. 125 0. 111 0. 099 15 0. 239 0. 209 0. 183 0. 160 0. 140 0. 123 0. 108 0. 095 0. 084 16 0. 218 0. 188 0. 163 0. 141 0. 123 0. 107 0. 093 0. 081 0. 071 17 0. 198 0. 170 0. 146 0. 125 0. 108 0. 093 0. 080 0. 069 0. 060 18 0. 180 0. 153 0. 130 0. 111 0. 095 0. 081 0. 069 0. 059 0. 051 372
\ ( % ) 10 11 12 13 14 15 16 17 18 19 0. 164 0. 138 0. 116 0. 098 0. 083 0. 070 0. 060 0. 051 0. 043 20 0. 149 0. 124 0. 104 0. 087 0. 073 0. 061 0. 051 0. 043 0. 037 25 0. 092 0. 074 0. 059 0. 047 0. 038 0. 030 0. 024 0. 020 0. 016 30 0. 057 0. 044 0. 033 0. 026 0. 020 0. 015 0. 012 0. 009 0. 007 40 0. 022 0. 015 0. 011 0. 008 0. 005 0. 004 0. 003 0. 002 0. 001 50 0. 009 0. 005 0. 003 0. 002 0. 001 0. 001 0. 001 0 0 19 20 25 30 35 40 50 1 0. 840 0. 833 0. 800 0. 769 0. 741 0. 714 0. 667 2 0. 706 0. 694 0. 640 0. 592 0. 549 0. 510 0. 444 3 0. 593 0. 579 0. 512 0. 455 0. 406 0. 364 0. 296 4 0. 499 0. 482 0. 410 0. 350 0. 301 0. 260 0. 198 5 0. 419 0. 402 0. 320 0. 269 0. 223 0. 186 0. 132 6 0. 352 0. 335 0. 262 0. 207 0. 165 0. 133 0. 088 7 0. 296 0. 279 0. 210 0. 159 0. 122 0. 095 0. 059 8 0. 249 0. 233 0. 168 0. 123 0. 091 0. 068 0. 039 9 0. 209 0. 194 0. 134 0. 094 0. 067 0. 048 0. 026 10 0. 176 0. 162 0. 107 0. 073 0. 050 0. 035 0. 017 11 0. 148 0. 135 0. 086 0. 056 0. 037 0. 025 0. 012 12 0. 124 0. 112 0. 069 0. 043 0. 027 0. 018 0. 008 13 0. 104 0. 093 0. 055 0. 033 0. 020 0. 013 0. 005 14 0. 088 0. 078 0. 044 0. 025 0. 015 0. 009 0. 003 15 0. 074 0. 065 0. 035 0. 020 0. 011 0. 006 0. 002 16 0. 062 0. 054 0. 028 0. 015 0. 008 0. 005 0. 002 17 0. 052 0. 045 0. 023 0. 012 0. 006 0. 003 0. 001 18 0. 044 0. 038 0. 018 0. 009 0. 005 0. 002 0. 001 373
\ ( % ) 19 20 25 30 35 40 50 19 0. 037 0. 031 0. 014 0. 007 0. 003 0. 002 0 20 0. 031 0. 026 0. 012 0. 005 0. 002 0. 001 0 25 0. 013 0. 010 0. 004 0. 001 0. 001 0 0 30 0. 005 0. 004 0. 001 0 0 0 0 40 0. 001 0. 001 0 0 0 0 0 50 0 0 0 0 0 0 0 ( S/ A, i, n) \ ( % ) 1 2 3 4 5 6 7 1 1. 000 1. 000 1. 000 1. 000 1. 000 1. 000 1. 000 2 2. 010 2. 020 2. 030 2. 040 2. 050 2. 060 2. 070 3 3. 030 3. 060 3. 091 3. 122 3. 153 3. 184 3. 215 4 4. 060 4. 122 4. 184 4. 246 4. 310 4. 375 4. 440 5 5. 101 5. 204 5. 309 5. 416 5. 526 5. 637 5. 751 6 6. 152 6. 308 6. 468 6. 633 6. 802 6. 975 7. 153 7 7. 214 7. 434 7. 662 7. 898 8. 142 8. 394 8. 654 8 8. 286 8. 583 8. 892 9. 214 9. 549 9. 897 10. 260 9 9. 369 9. 755 10. 159 10. 583 11. 027 11. 491 11. 978 10 10. 462 10. 950 11. 464 12. 006 12. 578 13. 181 13. 816 11 11. 567 12. 169 12. 808 13. 486 14. 207 14. 972 15. 784 12 12. 683 13. 412 14. 192 15. 026 15. 917 16. 870 17. 888 13 13. 809 14. 680 15. 618 16. 627 17. 713 18. 882 20. 141 14 14. 947 15. 974 17. 086 18. 292 19. 599 21. 015 22. 550 15 16. 097 17. 293 18. 599 20. 024 21. 579 23. 276 25. 129 374
\ ( % ) 1 2 3 4 5 6 7 16 17. 258 18. 639 20. 157 21. 825 23. 657 25. 673 27. 888 17 18. 430 20. 012 21. 762 23. 698 25. 840 28. 213 30. 840 18 19. 615 21. 412 23. 414 25. 645 28. 132 30. 906 33. 999 19 20. 811 22. 841 25. 117 27. 671 30. 539 33. 760 37. 379 20 22. 019 24. 297 26. 870 29. 778 33. 066 36. 786 40. 995 25 28. 243 32. 030 36. 459 41. 646 47. 727 54. 865 63. 249 30 34. 785 40. 588 47. 575 56. 085 66. 439 79. 058 94. 461 40 48. 886 60. 402 75. 401 95. 026 120. 80 154. 76 199. 64 50 64. 463 84. 579 112. 80 152. 67 209. 35 290. 34 406. 53 8 9 10 11 12 13 14 15 1 1. 000 1. 000 1. 000 1. 000 1. 000 1. 000 1. 000 1. 000 2 2. 080 2. 090 2. 100 2. 110 2. 120 2. 130 2. 140 2. 150 3 3. 246 3. 278 3. 310 3. 342 3. 374 3. 407 3. 440 3. 473 4 4. 506 4. 573 4. 641 4. 710 4. 779 4. 850 4. 921 4. 993 5 5. 867 5. 985 6. 105 6. 228 6. 353 6. 480 6. 610 6. 742 6 7. 336 7. 523 7. 716 7. 913 8. 115 8. 323 8. 536 8. 754 7 8. 923 9. 200 9. 487 9. 783 10. 089 10. 405 10. 730 11. 067 8 10. 637 11. 028 11. 436 11. 859 12. 300 12. 757 13. 233 13. 727 9 12. 488 13. 021 13. 579 14. 164 14. 776 15. 416 16. 085 16. 786 10 14. 487 15. 193 15. 937 16. 722 17. 549 18. 420 19. 337 20. 304 11 16. 645 17. 560 18. 531 19. 561 20. 655 21. 814 23. 045 24. 349 12 18. 977 20. 141 21. 384 22. 713 24. 133 25. 650 27. 271 29. 002 13 21. 495 22. 953 24. 523 26. 212 28. 029 29. 985 32. 089 34. 352 14 24. 215 26. 019 27. 975 30. 095 32. 393 34. 883 37. 581 40. 505 15 27. 152 29. 361 31. 772 34. 405 37. 280 40. 417 43. 842 47. 580 375
\ ( % ) 8 9 10 11 12 13 14 15 16 30. 324 33. 003 35. 950 39. 190 42. 753 46. 672 50. 980 55. 717 17 33. 750 36. 974 40. 545 44. 501 48. 884 53. 739 59. 118 65. 075 18 37. 450 41. 301 45. 599 50. 396 55. 750 61. 725 68. 394 75. 836 19 41. 446 46. 018 51. 159 56. 939 63. 440 70. 749 78. 969 88. 212 20 45. 762 51. 160 57. 275 64. 203 72. 052 80. 947 91. 025 102. 44 25 73. 106 84. 701 98. 347 114. 41 133. 33 155. 62 181. 87 212. 79 30 113. 28 136. 31 164. 49 199. 02 241. 33 293. 20 356. 79 434. 75 40 259. 06 337. 89 442. 59 581. 83 767. 09 1 013. 7 1 342. 0 1 779. 1 50 573. 77 815. 08 1 163. 9 1 668. 8 2 400. 0 3 459. 5 4 994. 5 7 217. 7 16 17 18 19 20 25 30 1 1. 000 1. 000 1. 000 1. 000 1. 000 1. 000 1. 000 2 2. 160 2. 170 2. 180 2. 190 2. 200 2. 250 2. 300 3 3. 506 3. 539 3. 572 3. 606 3. 640 3. 813 3. 990 4 5. 066 5. 141 5. 215 5. 291 5. 368 5. 766 6. 187 5 6. 877 7. 014 7. 154 7. 297 7. 442 8. 207 9. 043 6 8. 977 9. 207 9. 442 9. 683 9. 930 11. 259 12. 756 7 11. 414 11. 772 12. 142 12. 523 12. 916 15. 073 17. 583 8 14. 240 14. 773 15. 327 15. 902 16. 499 19. 842 23. 858 9 17. 519 18. 285 19. 086 19. 923 20. 799 25. 802 32. 015 10 21. 321 22. 393 23. 521 24. 701 25. 959 33. 253 42. 619 11 25. 733 27. 200 28. 755 30. 404 32. 150 42. 566 56. 405 12 30. 850 32. 824 34. 931 37. 180 39. 581 54. 208 74. 327 13 36. 786 39. 404 42. 219 45. 244 48. 497 68. 760 97. 625 14 43. 672 47. 103 50. 818 54. 841 59. 196 86. 949 127. 91 15 51. 660 56. 110 60. 965 66. 261 72. 035 109. 69 167. 29 376
\ ( % ) 16 17 18 19 20 25 30 16 60. 925 66. 649 72. 939 79. 850 87. 442 138. 11 218. 47 17 71. 673 78. 979 87. 068 96. 022 105. 93 173. 64 285. 01 18 84. 141 93. 406 103. 74 115. 27 128. 12 218. 05 371. 52 19 98. 603 110. 29 123. 41 138. 17 154. 74 273. 56 483. 97 20 115. 38 130. 03 146. 63 165. 42 186. 69 342. 95 630. 17 25 249. 21 292. 11 342. 60 402. 04 471. 98 1, 054. 8 2 348. 8 30 530. 31 647. 44 790. 95 966. 7 1 181. 9 3 227. 2 8 730. 0 40 2 360. 8 3 134. 5 4 163. 21 5 529. 8 7 343. 9 30 089. 120 393. 50 10 436. 15 090. 21 813. 31 515. 45 497. 280 256. 165 976. ( P / A, i, n ) \ ( % ) 1 2 3 4 5 6 7 8 9 1 0. 990 0. 980 0. 971 0. 962 0. 952 0. 943 0. 935 0. 926 0. 917 2 1. 970 1. 942 1. 913 1. 886 1. 859 1. 833 1. 808 1. 783 1. 759 3 2. 941 2. 884 2. 829 2. 775 2. 723 2. 673 2. 624 2. 577 2. 531 4 3. 902 3. 808 3. 717 3. 630 3. 546 3. 465 3. 387 3. 312 3. 240 5 4. 853 4. 713 4. 580 4. 452 4. 329 4. 212 4. 100 3. 993 3. 890 6 5. 795 5. 601 5. 417 5. 242 5. 076 4. 917 4. 767 4. 623 4. 486 7 6. 728 6. 472 6. 230 6. 002 5. 786 5. 582 5. 389 5. 206 5. 033 8 7. 652 7. 325 7. 020 6. 733 6. 463 6. 210 5. 971 5. 747 5. 535 9 8. 566 8. 162 7. 786 7. 435 7. 108 6. 802 6. 515 6. 247 5. 995 10 9. 471 8. 983 8. 530 8. 111 7. 722 7. 360 7. 024 6. 710 6. 418 11 10. 368 9. 787 9. 253 8. 760 8. 306 7. 887 7. 499 7. 139 6. 805 12 11. 255 10. 575 9. 954 9. 385 8. 863 8. 384 7. 943 7. 536 7. 161 13 12. 134 11. 348 10. 635 9. 986 9. 394 8. 853 8. 358 7. 904 7. 487 377
\ ( % ) 1 2 3 4 5 6 7 8 9 14 13. 004 12. 106 11. 296 10. 563 9. 899 9. 295 8. 745 8. 244 7. 786 15 13. 865 12. 849 11. 938 11. 118 10. 380 9. 712 9. 108 8. 559 8. 061 16 14. 718 13. 578 12. 561 11. 652 10. 838 10. 106 9. 447 8. 851 8. 313 17 15. 562 14. 292 13. 166 12. 166 11. 274 10. 477 9. 763 8. 122 8. 544 18 16. 398 14. 992 13. 754 12. 659 11. 690 10. 828 10. 059 9. 372 8. 756 19 17. 226 15. 678 14. 324 13. 134 12. 085 11. 158 10. 336 9. 604 8. 950 20 18. 046 16. 351 14. 877 13. 590 12. 462 11. 470 10. 594 9. 818 9. 129 25 22. 023 19. 523 17. 413 15. 622 14. 094 12. 783 11. 654 10. 675 9. 823 30 25. 808 22. 396 19. 600 17. 292 15. 372 13. 765 12. 409 11. 258 10. 274 40 32. 835 27. 355 23. 115 19. 793 17. 159 15. 046 13. 332 11. 925 10. 757 50 39. 196 31. 424 25. 730 21. 482 18. 256 15. 762 13. 801 12. 233 10. 962 10 11 12 13 14 15 16 17 18 1 0. 909 0. 901 0. 893 0. 885 0. 877 0. 870 0. 862 0. 855 0. 847 2 1. 736 1. 713 1. 690 1. 668 1. 647 1. 626 1. 605 1. 585 1. 566 3 2. 487 2. 444 2. 402 2. 361 2. 322 2. 283 2. 246 2. 210 2. 174 4 3. 170 3. 102 3. 037 2. 974 2. 914 2. 855 2. 798 2. 743 2. 690 5 3. 791 3. 696 3. 605 3. 517 3. 433 3. 352 3. 274 3. 199 3. 127 6 4. 355 4. 231 4. 111 3. 998 3. 889 3. 784 3. 685 3. 589 3. 498 7 4. 868 4. 712 4. 564 4. 423 4. 288 4. 160 4. 039 3. 922 3. 812 8 5. 335 5. 146 4. 968 4. 799 4. 639 4. 487 4. 344 4. 207 4. 078 9 5. 759 5. 537 5. 328 5. 132 4. 946 4. 472 4. 607 4. 451 4. 303 10 6. 145 5. 889 5. 650 5. 426 5. 216 5. 019 4. 833 4. 659 4. 494 11 6. 495 6. 207 5. 938 5. 687 5. 453 5. 234 5. 029 4. 836 4. 656 12 6. 814 6. 492 6. 194 5. 918 5. 660 5. 421 5. 197 4. 988 4. 793 13 7. 103 6. 750 6. 424 6. 122 5. 842 5. 583 5. 342 5. 118 4. 910 378
\ ( % ) 10 11 12 13 14 15 16 17 18 14 7. 367 6. 982 6. 628 6. 302 6. 002 5. 724 5. 468 5. 229 5. 008 15 7. 606 7. 191 6. 811 6. 462 6. 142 5. 847 5. 575 5. 324 5. 092 16 7. 824 7. 379 6. 974 6. 604 6. 265 5. 954 5. 668 5. 405 5. 162 17 8. 022 7. 549 7. 102 6. 729 6. 373 6. 047 5. 749 5. 475 5. 222 18 8. 201 7. 702 7. 250 6. 840 6. 467 6. 128 5. 818 5. 534 5. 273 19 8. 365 7. 839 7. 366 6. 938 6. 550 6. 198 5. 877 5. 584 5. 316 20 8. 514 7. 963 7. 469 7. 025 6. 623 6. 259 5. 929 5. 628 5. 353 25 9. 077 8. 422 7. 843 7. 330 6. 873 6. 464 6. 097 5. 766 5. 467 30 9. 427 8. 694 8. 055 7. 496 7. 003 6. 566 6. 177 5. 829 5. 517 40 9. 779 8. 951 8. 244 7. 634 7. 105 6. 642 6. 233 5. 871 5. 548 50 9. 915 9. 042 8. 304 7. 675 7. 133 6. 661 6. 246 5. 880 5. 554 19 20 25 30 35 40 50 1 0. 840 0. 833 0. 800 0. 769 0. 741 0. 714 0. 667 2 1. 547 1. 528 1. 440 1. 361 1. 289 1. 224 1. 111 3 2. 140 2. 106 1. 952 1. 816 1. 696 1. 589 1. 407 4 2. 639 2. 589 2. 362 2. 166 1. 997 1. 849 1. 605 5 3. 058 2. 991 2. 689 2. 436 2. 220 2. 035 1. 737 6 3. 410 3. 326 2. 951 2. 643 2. 385 2. 168 1. 824 7 3. 706 3. 605 3. 161 2. 802 2. 508 2. 263 1. 883 8 3. 954 3. 837 3. 329 2. 925 2. 598 2. 331 1. 922 9 4. 163 4. 031 3. 463 3. 019 2. 665 2. 379 1. 948 10 4. 339 4. 192 3. 571 3. 092 2. 715 2. 414 1. 965 11 4. 486 4. 327 3. 656 3. 147 2. 752 2. 438 1. 977 12 4. 611 4. 439 3. 725 3. 190 2. 779 2. 456 1. 985 13 4. 715 4. 533 3. 780 3. 223 2. 799 2. 469 1. 990 379
\ ( % ) 19 20 25 30 35 40 50 14 4. 802 4. 611 3. 824 3. 249 2. 814 2. 478 1. 993 15 4. 876 4. 675 3. 859 3. 268 2. 825 2. 484 1. 995 16 4. 938 4. 730 3. 887 3. 283 2. 834 2. 489 1. 997 17 4. 988 4. 775 3. 910 3. 295 2. 840 2. 492 1. 998 18 5. 033 4. 812 3. 928 3. 304 2. 844 2. 494 1. 999 19 5. 070 4. 843 3. 942 3. 311 2. 848 2. 496 1. 999 20 5. 101 4. 870 3. 954 3. 316 2. 850 2. 497 1. 999 25 5. 195 4. 948 3. 985 3. 329 2. 856 2. 499 2. 000 30 5. 235 4. 979 3. 995 3. 332 2. 857 2. 500 2. 000 40 5. 258 4. 997 3. 999 3. 333 2. 857 2. 500 2. 000 50 5. 262 4. 999 4. 000 3. 333 2. 857 2. 500 2. 000 380
[ 1],,, 1995 [ 2],,, 1995 [ 3],,, 1993 [ 4],,, 1995 [ 5] E ugene F. Brigha : Fundament als of Financial Managemen t, Fift h Edition, T he Dryden P ress, 1989. [ 6 ] Law rence J. Git men : Basic Managerial F inance, Th ird Edit ion, Harper Collins P ublishers, 1992. 381