2113

2113	ǘǔǙǔǝǞǑǜǝǞǎǚ ǚǍǜnjǓǚǎnjǙǔǫ ǔ Ǚnjǟǖǔ ǜǠ

ǠǑǐǑǜnjǗǨǙǚǑ ǏǚǝǟǐnjǜǝǞǎǑǙǙǚǑ njǎǞǚǙǚǘǙǚǑ ǚǍǜnjǓǚǎnjǞǑǗǨǙǚǑ ǟǣǜǑǒǐǑǙǔǑ ǎǧǝǤǑǏǚ ǛǜǚǠǑǝǝǔǚǙnjǗǨǙǚǏǚ ǚǍǜnjǓǚǎnjǙǔǫ

«ǙnjǢǔǚǙnjǗǨǙǧǕ ǔǝǝǗǑǐǚǎnjǞǑǗǨǝǖǔǕ ǞǑǡǙǚǗǚǏǔǣǑǝǖǔǕ ǟǙǔǎǑǜǝǔǞǑǞ «ǘǔǝǴǝ»

ǖǬȀDZǰǼǬ ǻǼǺǸȇȄǷDZǹǹǺǯǺ ǸDZǹDZǰDzǸDZǹǾǬ

ǝǾǼǬȁǺǮǬǹǴDZ

ǟȃDZǭǹǺDZ ǻǺǽǺǭǴDZ

ǐǺǻǿȅDZǹǺ ǟȃDZǭǹǺ-ǸDZǾǺǰǴȃDZǽǶǴǸ ǺǭȆDZǰǴǹDZǹǴDZǸ ǻǺ ǺǭǼǬdzǺǮǬǹǴȊ

ǮǺǭǷǬǽǾǴ ǶǺǸǸDZǼȂǴǴ Ǵ ǻǺ ǺǭǼǬdzǺǮǬǹǴȊ Ǯ ǺǭǷǬǽǾǴ ǸǬǼǶDZǾǴǹǯǬ

ǮǶǬȃDZǽǾǮDZ ǿȃDZǭǹǺǯǺ ǻǺǽǺǭǴȋ ǰǷȋ ǽǾǿǰDZǹǾǺǮ ǮȇǽȄǴȁ ǿȃDZǭǹȇȁ dzǬǮDZǰDZǹǴǵ, ǺǭǿȃǬȊȅǴȁǽȋ ǻǺ ǹǬǻǼǬǮǷDZǹǴȊ 100700.62 – ǞǺǼǯǺǮǺDZ ǰDZǷǺ Ǵ ǻǺ ǽǻDZȂǴǬǷȈǹǺǽǾȋǸ 080301 – ǖǺǸǸDZǼȂǴȋ

(ǾǺǼǯǺǮǺDZ ǰDZǷǺ), 080111 – ǘǬǼǶDZǾǴǹǯ Ǵ 032401 – ǜDZǶǷǬǸǬ

ǘǺǽǶǮǬ 2014

ɍȾɄ 368

ɋ83

Ɋɟɰɟɧɡɟɧɬɵ :

ɤɚɧɞ. ɷɤɨɧ. ɧɚɭɤ, ɩɪɨɮ. ɋ.ȼ. ɋɬɟɩɚɧɨɜɚ (ɊȽɌɗɍ); ɤɚɧɞ. ɷɤɨɧ. ɧɚɭɤ, ɩɪɨɮ. ɂ.ɉ. ɂɥɶɢɱɟɜ

Ⱥ ɜ ɬ ɨ ɪ ɵ:

Ⱥ.ɘ. Ⱥɧɢɫɢɦɨɜ, ɘ.ɘ. Ʉɨɫɬɸɯɢɧ – ɪɚɡɞɟɥɵ 4–6; Ⱥ.ɋ. Ɉɛɭɯɨɜɚ, Ɉ.Ɉ. ɋɤɪɹɛɢɧ – ɪɚɡɞɟɥɵ 1–3

ɋɬɪɚɯɨɜɚɧɢɟ : ɭɱɟɛ. ɩɨɫɨɛɢɟ / Ⱥ.ɘ. Ⱥɧɢɫɢɦɨɜ [ɢ ɞɪ]. – Ɇ. :

ɋ83 ɂɡɞ.Ⱦɨɦ Ɇɂɋɢɋ, 2014. – 182 ɫ. ISBN 978-5-87623-784-2

Ɋɚɫɫɦɨɬɪɟɧɵ ɨɫɧɨɜɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɥɢɱɧɨɝɨ ɫɬɪɚɯɨɜɚɧɢɹ, ɫɬɪɚɯɨɜɚɧɢɹ ɢɦɭɳɟɫɬɜɚ, ɫɬɪɚɯɨɜɚɧɢɹ ɨɬɜɟɬɫɬɜɟɧɧɨɫɬɢ, ɜɨɩɪɨɫɵ ɫɨɫɬɪɚɯɨɜɚɧɢɹ ɢ ɩɟɪɟɫɬɪɚɯɨɜɚɧɢɹ, ɫɨɡɞɚɧɢɹ ɫɬɪɚɯɨɜɵɯ ɪɟɡɟɪɜɨɜ ɢ ɨɩɪɟɞɟɥɟɧɢɹ ɮɢɧɚɧɫɨɜɨɫɬɚɬɢɫɬɢɱɟɫɤɢɯ ɩɨɤɚɡɚɬɟɥɟɣ ɞɟɹɬɟɥɶɧɨɫɬɢ ɫɬɪɚɯɨɜɨɣ ɨɪɝɚɧɢɡɚɰɢɢ. ɇɚ ɨɫɧɨɜɟ ɫɬɪɚɯɨɜɨɣ ɦɚɬɟɦɚɬɢɤɢ ɩɪɢɜɟɞɟɧɚ ɦɟɬɨɞɢɤɚ ɪɚɫɱɟɬɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɩɨɤɚɡɚɬɟɥɟɣ ɢ ɟɟ ɩɪɢɦɟɧɟɧɢɟ ɩɪɢ ɪɟɲɟɧɢɢ ɬɢɩɨɜɵɯ ɡɚɞɚɱ, ɦɚɤɫɢɦɚɥɶɧɨ ɩɪɢɛɥɢɠɟɧɧɵɯ ɤ ɪɟɚɥɶɧɨɫɬɢ. Ⱦɥɹ ɥɭɱɲɟɝɨ ɭɫɜɨɟɧɢɹ ɦɚɬɟɪɢɚɥɚ ɜ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ ɫɨɞɟɪɠɢɬɫɹ ɢɥɥɸɫɬɪɚɬɢɜɧɵɣ, ɬɚɛɥɢɱɧɵɣ, ɬɟɫɬɨɜɵɣ ɦɚɬɟɪɢɚɥ, ɚ ɬɚɤɠɟ ɤɪɨɫɫɜɨɪɞɵ, ɫɩɨɫɨɛɫɬɜɭɸɳɢɟ ɡɚɤɪɟɩɥɟɧɢɸ ɡɧɚɧɢɣ ɫɬɪɚɯɨɜɨɣ ɬɟɪɦɢɧɨɥɨɝɢɢ.

Ⱦɥɹ ɫɬɭɞɟɧɬɨɜ ɜɵɫɲɢɯ ɭɱɟɛɧɵɯ ɡɚɜɟɞɟɧɢɣ, ɨɛɭɱɚɸɳɢɯɫɹ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ 100700.62 – Ɍɨɪɝɨɜɨɟ ɞɟɥɨ ɢ ɩɨ ɫɩɟɰɢɚɥɶɧɨɫɬɹɦ 080301 – Ʉɨɦɦɟɪɰɢɹ (ɬɨɪɝɨɜɨɟ ɞɟɥɨ), 080111 – Ɇɚɪɤɟɬɢɧɝ ɢ 032401 – Ɋɟɤɥɚɦɚ.

ɍȾɄ 368

ISBN 978-5-87623-784-2

♥ Ʉɨɥɥɟɤɬɢɜ ɚɜɬɨɪɨɜ, 2014

2

ɈȽɅȺȼɅȿɇɂȿ
ȼɜɟɞɟɧɢɟ .....................................................................................................................	4
1. ɅɂɑɇɈȿ ɋɌɊȺɏɈȼȺɇɂȿ..............................................................................	5
1.1. Ɍɟɨɪɟɬɢɤɨ-ɦɟɬɨɞɢɱɟɫɤɢɟ ɨɫɧɨɜɵ..................................................................	5
1.2. Ɍɢɩɨɜɵɟ ɡɚɞɚɱɢ...............................................................................................	9
1.3. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ.......................................................	12
1.4. Ɍɟɫɬ................................................................................................................	14
1.5. Ʉɪɨɫɫɜɨɪɞ......................................................................................................	19
2. ɋɌɊȺɏɈȼȺɇɂȿ ɂɆɍɓȿɋɌȼȺ...................................................................	21
2.1. Ɍɟɨɪɟɬɢɤɨ-ɦɟɬɨɞɢɱɟɫɤɢɟ ɨɫɧɨɜɵ................................................................	21
2.2. Ɍɢɩɨɜɵɟ ɡɚɞɚɱɢ.............................................................................................	25
2.3. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ.......................................................	30
2.4. Ɍɟɫɬ................................................................................................................	34
2.5. Ʉɪɨɫɫɜɨɪɞ......................................................................................................	38
3. ɋɌɊȺɏɈȼȺɇɂȿ ɈɌȼȿɌɋɌȼȿɇɇɈɋɌɂ........................................................	39
3.1. Ɍɟɨɪɟɬɢɤɨ-ɦɟɬɨɞɢɱɟɫɤɢɟ ɨɫɧɨɜɵ................................................................	39
3.2. Ɍɢɩɨɜɵɟ ɡɚɞɚɱɢ.............................................................................................	41
3.3. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ.......................................................	43
3.4. Ɍɟɫɬ................................................................................................................	45
3.5. Ʉɪɨɫɫɜɨɪɞ......................................................................................................	49
4. ɉȿɊȿɋɌɊȺɏɈȼȺɇɂȿ ɂɋɈɋɌɊȺɏɈȼȺɇɂȿ...............................................	51
4.1. Ɍɟɨɪɟɬɢɤɨ-ɦɟɬɨɞɢɱɟɫɤɢɟ ɨɫɧɨɜɵ................................................................	51
4.2. Ɍɢɩɨɜɵɟ ɡɚɞɚɱɢ.............................................................................................	57
4.3. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ.......................................................	68
4.4. Ɍɟɫɬ................................................................................................................	71
4.5. Ʉɪɨɫɫɜɨɪɞɵ...................................................................................................	75
5. ɋɌɊȺɏɈȼɕȿ ɊȿɁȿɊȼɕ................................................................................	79
5.1. Ɍɟɨɪɟɬɢɤɨ-ɦɟɬɨɞɢɱɟɫɤɢɟ ɨɫɧɨɜɵ................................................................	79
5.2. Ɍɢɩɨɜɵɟ ɡɚɞɚɱɢ.............................................................................................	89
5.3. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ.......................................................	99
5.4. Ɍɟɫɬ..............................................................................................................	103
6. ɎɂɇȺɇɋɈȼɈ-ɋɌȺɌɂɋɌɂɑȿɋɄɂȿɉɈɄȺɁȺɌȿɅɂ
ɋɌɊȺɏɈȼɈɃȾȿəɌȿɅɖɇɈɋɌɂ.....................................................................	106
6.1. Ɍɟɨɪɟɬɢɤɨ-ɦɟɬɨɞɢɱɟɫɤɢɟ ɨɫɧɨɜɵ..............................................................	106
6.2. Ɍɢɩɨɜɵɟ ɡɚɞɚɱɢ...........................................................................................	135
6.3. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ.....................................................	145
6.4. Ɍɟɫɬ..............................................................................................................	148
6.5. Ʉɪɨɫɫɜɨɪɞ....................................................................................................	152
7. ɄɊɈɋɋȼɈɊȾɕ ɄɈȼɋȿɆɍ ɄɍɊɋɍ............................................................	153
ɋɅɈȼȺɊɖ ɌȿɊɆɂɇɈȼ...................................................................................	158
ȻɂȻɅɂɈȽɊȺɎɂɑȿɋɄɂɃ ɋɉɂɋɈɄ ...............................................................	180

3

ȼȼȿȾȿɇɂȿ

ɋɬɪɚɯɨɜɚɧɢɟ ɹɜɥɹɟɬɫɹ ɫɬɪɚɬɟɝɢɱɟɫɤɢ ɜɚɠɧɵɦ ɷɥɟɦɟɧɬɨɦ ɪɵɧɨɱɧɨɣ ɷɤɨɧɨɦɢɤɢ ɥɸɛɨɣ ɫɬɪɚɧɵ. ɋɬɪɚɯɨɜɨɣ ɪɵɧɨɤ ɜ Ɋɨɫɫɢɣɫɤɨɣ Ɏɟɞɟɪɚɰɢɢ ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɧɚɯɨɞɢɬɫɹ ɜ ɫɬɚɞɢɢ ɷɜɨɥɸɰɢɨɧɧɨɝɨ ɪɚɡɜɢɬɢɹ. ɇɚɩɪɢɦɟɪ, ȼɫɟɪɨɫɫɢɣɫɤɢɦ ɫɨɸɡɨɦ ɫɬɪɚɯɨɜɳɢɤɨɜ ɪɚɡɪɚɛɨɬɚɧɵ ɪɟɤɨɦɟɧɞɚɰɢɢ ɞɥɹ ɧɨɜɨɣ ɫɬɪɚɬɟɝɢɢ ɪɚɡɜɢɬɢɹ ɪɨɫɫɢɣɫɤɨɝɨ ɫɬɪɚɯɨɜɨɝɨ ɪɵɧɤɚ, ɤɨɬɨɪɚɹ ɪɟɚɥɢɡɨɜɚɧɚ ɜ 2013 ɝɨɞɭ. Ʉɥɸɱɟɜɵɦɢ ɧɚɩɪɚɜɥɟɧɢɹɦɢ ɫɬɪɚɬɟɝɢɢ ɪɚɡɜɢɬɢɹ ɪɨɫɫɢɣɫɤɨɝɨ ɫɬɪɚɯɨɜɚɧɢɹ ɹɜɥɹɸɬɫɹ ɜɨɩɪɨɫɵ ɪɚɡɜɢɬɢɹ ɫɬɪɚɯɨɜɚɧɢɹ ɠɢɡɧɢ, ɦɟɞɢɰɢɧɫɤɨɝɨ ɫɬɪɚɯɨɜɚɧɢɹ, ɫɨɜɟɪɲɟɧɫɬɜɨɜɚɧɢɹ ɧɨɪɦɚɬɢɜɧɨɣ ɛɚɡɵ, ɩɪɢɧɰɢɩɨɜ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɢ ɧɚɞɡɨɪɚ ɜ ɫɬɪɚɯɨɜɚɧɢɢ, ɜɨɩɪɨɫɵ ɩɨɜɵɲɟɧɢɹ ɧɚɞɟɠɧɨɫɬɢ ɢ ɭɫɬɨɣɱɢɜɨɫɬɢ ɫɬɪɚɯɨɜɳɢɤɨɜ, ɩɪɨɡɪɚɱɧɨɫɬɢ ɛɢɡɧɟɫɚ, ɚ ɬɚɤɠɟ ɫɨɡɞɚɧɢɹ ɝɚɪɚɧɬɢɣɧɵɯ ɮɨɧɞɨɜ ɜ ɫɨɰɢɚɥɶɧɨ ɡɧɚɱɢɦɵɯ ɢ ɨɫɨɛɨ ɨɬɜɟɬɫɬɜɟɧɧɵɯ ɜɢɞɚɯ ɫɬɪɚɯɨɜɚɧɢɹ. Ʉɪɨɦɟ ɩɟɪɟɱɢɫɥɟɧɧɵɯ ɧɚɩɪɚɜɥɟɧɢɣ, ɧɟɥɶɡɹ ɧɟ ɨɬɦɟɬɢɬɶ ɟɳɟ ɨɞɧɨ ɧɚɩɪɚɜɥɟɧɢɟ (ɜɚɠɧɟɣɲɭɸ ɫɨɫɬɚɜɥɹɸɳɭɸ ɫɬɪɚɯɨɜɨɣ ɞɟɹɬɟɥɶɧɨɫɬɢ) – ɚɤɬɭɚɪɧɚɹ ɞɟɹɬɟɥɶɧɨɫɬɶ. ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ Ƚɨɫɭɞɚɪɫɬɜɟɧɧɨɣ Ⱦɭɦɨɣ ɩɪɢɧɹɬ Ɏɟɞɟɪɚɥɶɧɵɣ ɡɚɤɨɧ ɨɬ 02.11.2013 ʋ 293-ɎɁ «Ɉɛ ɚɤɬɭɚɪɧɨɣ ɞɟɹɬɟɥɶɧɨɫɬɢ ɜ Ɋɨɫɫɢɣɫɤɨɣ Ɏɟɞɟɪɚɰɢɢ», ɤɨɬɨɪɵɣ ɨɤɚɡɵɜɚɟɬ ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɜɥɢɹɧɢɟ ɧɚ ɜɫɟ ɨɛɥɚɫɬɢ ɪɨɫɫɢɣɫɤɨɣ ɷɤɨɧɨɦɢɤɢ. ɗɬɨ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɩɪɟɞɩɨɥɚɝɚɟɬ ɧɚɥɢɱɢɟ ɫɩɟɰɢɚɥɢɫɬɨɜ ɜɵɫɨɤɨɣ ɤɜɚɥɢɮɢɤɚɰɢɢ, ɡɧɚɸɳɢɯ ɬɟɨɪɢɸ ɢ ɩɪɚɤɬɢɤɭ ɜ ɨɛɥɚɫɬɢ ɫɬɪɚɯɨɜɨɝɨ ɞɟɥɚ.

ɐɟɥɶ ɞɚɧɧɨɝɨ ɩɨɫɨɛɢɹ ɫɨɫɬɨɢɬ ɜ ɨɤɚɡɚɧɢɢ ɩɨɦɨɳɢ ɜ ɩɪɨɰɟɫɫɟ ɢɡɭɱɟɧɢɹ ɬɟɨɪɟɬɢɤɨ-ɦɟɬɨɞɢɱɟɫɤɢɯ ɨɫɧɨɜ ɫɬɪɚɯɨɜɚɧɢɹ. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɨɫɬɚɜɥɟɧɧɨɣ ɰɟɥɶɸ ɛɵɥɢ ɩɪɟɞɨɩɪɟɞɟɥɟɧɵ ɫɨɞɟɪɠɚɧɢɟ ɢ ɥɨɝɢɤɚ ɢɡɥɨɠɟɧɢɹ ɦɚɬɟɪɢɚɥɚ. ȼ ɩɨɫɨɛɢɢ ɪɚɫɫɦɨɬɪɟɧɵ ɨɫɧɨɜɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɥɢɱɧɨɝɨ ɫɬɪɚɯɨɜɚɧɢɹ, ɫɬɪɚɯɨɜɚɧɢɹ ɢɦɭɳɟɫɬɜɚ, ɫɬɪɚɯɨɜɚɧɢɹ ɨɬɜɟɬɫɬɜɟɧɧɨɫɬɢ, ɜɨɩɪɨɫɵ ɫɨɫɬɪɚɯɨɜɚɧɢɹ ɢ ɩɟɪɟɫɬɪɚɯɨɜɚɧɢɹ, ɜɨɩɪɨɫɵ ɫɨɡɞɚɧɢɹ ɫɬɪɚɯɨɜɵɯ ɪɟɡɟɪɜɨɜ ɢ ɨɩɪɟɞɟɥɟɧɢɹ ɮɢɧɚɧɫɨɜɨɫɬɚɬɢɫɬɢɱɟɫɤɢɯ ɩɨɤɚɡɚɬɟɥɟɣ ɞɟɹɬɟɥɶɧɨɫɬɢ ɫɬɪɚɯɨɜɨɣ ɨɪɝɚɧɢɡɚɰɢɢ.

4

1.ɅɂɑɇɈȿ ɋɌɊȺɏɈȼȺɇɂȿ

1.1.Ɍɟɨɪɟɬɢɤɨ-ɦɟɬɨɞɢɱɟɫɤɢɟ ɨɫɧɨɜɵ

Ʌɢɱɧɨɟ ɫɬɪɚɯɨɜɚɧɢɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɜɚɠɧɵɣ ɮɢɧɚɧɫɨɜɵɣ ɦɟɯɚɧɢɡɦ ɨɛɟɫɩɟɱɟɧɢɹ ɛɥɚɝɨɫɨɫɬɨɹɧɢɹ ɧɚɫɟɥɟɧɢɹ. ɉɨɞ ɥɢɱɧɵɦ ɫɬɪɚɯɨɜɚɧɢɟɦ ɜ ɊɎ ɩɨɧɢɦɚɟɬɫɹ ɨɬɪɚɫɥɶ ɫɬɪɚɯɨɜɚɧɢɹ, ɨɛɴɟɤɬɚɦɢ ɤɨɬɨɪɨɣ ɹɜɥɹɸɬɫɹ ɠɢɡɧɶ ɱɟɥɨɜɟɤɚ, ɡɞɨɪɨɜɶɟ, ɟɝɨ ɬɪɭɞɨɫɩɨɫɨɛɧɨɫɬɶ, ɬ.ɟ. ɠɢɡɧɟɧɧɵɟ ɢɧɬɟɪɟɫɵ, ɧɟ ɢɦɟɸɳɢɟ ɩɪɹɦɨɣ ɞɟɧɟɠɧɨɣ ɨɰɟɧɤɢ ɢ ɫɜɹɡɚɧɧɵɟ ɫ ɧɚɧɟɫɟɧɢɟɦ ɥɢɱɧɨɫɬɧɨɝɨ ɭɳɟɪɛɚ.

Ɉɛɴɟɤɬɚɦɢ ɥɢɱɧɨɝɨ ɫɬɪɚɯɨɜɚɧɢɹ ɦɨɝɭɬ ɛɵɬɶ ɢɦɭɳɟɫɬɜɟɧɧɵɟ ɢɧɬɟɪɟɫɵ, ɫɜɹɡɚɧɧɵɟ ɫ:

–ɞɨɠɢɬɢɟɦ ɝɪɚɠɞɚɧ ɞɨ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɜɨɡɪɚɫɬɚ ɢɥɢ ɫɪɨɤɚ, ɫɨ ɫɦɟɪɬɶɸ, ɫ ɧɚɫɬɭɩɥɟɧɢɟɦ ɫɨɛɵɬɢɣ ɜ ɠɢɡɧɢ ɝɪɚɠɞɚɧ (ɫɬɪɚɯɨɜɚɧɢɟ ɠɢɡɧɢ);

–ɩɪɢɱɢɧɟɧɢɟɦ ɜɪɟɞɚ ɠɢɡɧɢ, ɡɞɨɪɨɜɶɸ ɝɪɚɠɞɚɧ, ɨɤɚɡɚɧɢɟɦ ɢɦ ɦɟɞɢɰɢɧɫɤɢɯ ɭɫɥɭɝ (ɫɬɪɚɯɨɜɚɧɢɟ ɨɬ ɧɟɫɱɚɫɬɧɵɯ ɫɥɭɱɚɟɜ ɢ ɛɨɥɟɡɧɟɣ, ɦɟɞɢɰɢɧɫɤɨɟ ɫɬɪɚɯɨɜɚɧɢɟ).

ɉɪɢ ɨɫɭɳɟɫɬɜɥɟɧɢɢ ɥɢɱɧɨɝɨ ɫɬɪɚɯɨɜɚɧɢɹ ɫɬɪɚɯɨɜɚɹ ɜɵɩɥɚɬɚ (ɫɬɪɚɯɨɜɚɹ ɫɭɦɦɚ) ɩɪɨɢɡɜɨɞɢɬɫɹ ɫɬɪɚɯɨɜɚɬɟɥɸ ɢɥɢ ɥɢɰɭ, ɢɦɟɸɳɢɦ ɩɪɚɜɨ ɧɚ ɩɨɥɭɱɟɧɢɟ ɫɬɪɚɯɨɜɨɣ ɜɵɩɥɚɬɵ (ɫɬɪɚɯɨɜɨɣ ɫɭɦɦɵ) ɩɨ ɞɨɝɨɜɨɪɭ ɫɬɪɚɯɨɜɚɧɢɹ, ɧɟɡɚɜɢɫɢɦɨ ɨɬ ɫɭɦɦ, ɩɪɢɱɢɬɚɸɳɢɯɫɹ ɢɦ ɩɨ ɞɪɭɝɢɦ ɞɨɝɨɜɨɪɚɦ ɫɬɪɚɯɨɜɚɧɢɹ, ɚ ɬɚɤɠɟ ɩɨ ɨɛɹɡɚɬɟɥɶɧɨɦɭ ɫɨɰɢɚɥɶɧɨɦɭ ɫɬɪɚɯɨɜɚɧɢɸ, ɫɨɰɢɚɥɶɧɨɦɭ ɨɛɟɫɩɟɱɟɧɢɸɢ ɜ ɩɨɪɹɞɤɟ ɜɨɡɦɟɳɟɧɢɹɜɪɟɞɚ.

Ⱦɨɝɨɜɨɪ ɥɢɱɧɨɝɨ ɫɬɪɚɯɨɜɚɧɢɹ – ɝɪɚɠɞɚɧɫɤɨ-ɩɪɚɜɨɜɚɹ ɫɞɟɥɤɚ, ɩɨ ɤɨɬɨɪɨɣ ɫɬɪɚɯɨɜɳɢɤ ɨɛɹɡɭɟɬɫɹ ɩɨɫɪɟɞɫɬɜɨɦ ɩɨɥɭɱɟɧɢɹ ɢɦ ɫɬɪɚɯɨɜɵɯ ɜɡɧɨɫɨɜ ɜ ɫɥɭɱɚɟ ɧɚɫɬɭɩɥɟɧɢɹ ɫɬɪɚɯɨɜɨɝɨ ɫɨɛɵɬɢɹ ɜɨɡɦɟɫɬɢɬɶ ɜ ɭɤɚɡɚɧɧɵɟ ɫɪɨɤɢ ɧɚɧɟɫɟɧɧɵɣ ɭɳɟɪɛ ɢɥɢ ɩɪɨɢɡɜɟɫɬɢ ɜɵɩɥɚɬɭ ɫɬɪɚɯɨɜɨɝɨ ɤɚɩɢɬɚɥɚ, ɪɟɧɬɵ ɢɥɢ ɚɧɧɭɢɬɟɬɚ: ɫɬɪɚɯɨɜɚɬɟɥɸ, ɡɚɫɬɪɚɯɨɜɚɧɧɨɦɭ ɢɥɢ ɜɵɝɨɞɨɩɪɟɨɛɪɟɬɚɬɟɥɸ (ɩɪɢɧɚɫɬɭɩɥɟɧɢɢ ɫɦɟɪɬɢ).

ɋɭɳɟɫɬɜɭɟɬ ɬɪɢ ɫɢɫɬɟɦɵ ɫɬɪɚɯɨɜɚɧɢɹ ɠɢɡɧɢ (ɪɢɫ. 1.1):

1)ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɟ ɫɨɰɢɚɥɶɧɨɟ ɫɬɪɚɯɨɜɚɧɢɟ;

2)ɤɨɥɥɟɤɬɢɜɧɨɟ ɫɬɪɚɯɨɜɚɧɢɟ;

3)ɢɧɞɢɜɢɞɭɚɥɶɧɨɟ (ɥɢɱɧɨɟ) ɫɬɪɚɯɨɜɚɧɢɟ ɝɪɚɠɞɚɧ.

ȼ ɭɫɥɨɜɢɹɯ ɥɢɰɟɧɡɢɪɨɜɚɧɢɹ ɫɬɪɚɯɨɜɨɣ ɞɟɹɬɟɥɶɧɨɫɬɢ ɧɚ ɬɟɪɪɢɬɨɪɢɢ ɊɎ ɭɤɚɡɚɧɵ ɬɪɢ ɩɨɞɨɬɪɚɫɥɢ ɥɢɱɧɨɝɨ ɫɬɪɚɯɨɜɚɧɢɹ:

1)ɫɬɪɚɯɨɜɚɧɢɟ ɠɢɡɧɢ;

2)ɫɬɪɚɯɨɜɚɧɢɟ ɨɬ ɧɟɫɱɚɫɬɧɵɯ ɫɥɭɱɚɟɜ;

3)ɦɟɞɢɰɢɧɫɤɨɟ ɫɬɪɚɯɨɜɚɧɢɟ.

5

6

			Ƚɨɫɭɞɚɪɫɬɜɟɧɧɨɟ
			ɫɨɰɢɚɥɶɧɨɟ ɫɬɪɚɯɨɜɚɧɢɟ
ɐɟɥɶ			Ƚɚɪɚɧɬɢɪɨɜɚɧɢɟ
			ɩɪɨɠɢɬɨɱɧɨɝɨ ɦɢɧɢɦɭɦɚ
Ɏɨɪɦɚ			Ɉɛɹɡɚɬɟɥɶɧɨɟ
ɉɪɢɧɰɢɩ			ɉɪɢɧɰɢɩ ɫɨɥɢɞɚɪɧɨɫɬɢ
ɜɨɡɦɟɳɟɧɢɹ
Ɏɨɪɦɚ ɢ ɪɚɡɦɟɪ			Ɂɚɤɪɟɩɥɹɸɬ ɡɚɤɨɧɨɦ
ɫɬɪɚɯɨɜɨɝɨ
ɩɨɤɪɵɬɢɹ

Ʉɨɥɥɟɤɬɢɜɧɨɟ ɫɬɪɚɯɨɜɚɧɢɟ

Ƚɚɪɚɧɬɢɪɨɜɚɧɢɟ ɩɪɢɜɵɱɧɨɝɨ ɭɪɨɜɧɹ ɠɢɡɧɢ

Ɉɛɹɡɚɬɟɥɶɧɨɟ ɢ ɞɨɛɪɨɜɨɥɶɧɨɟ

ɉɪɢɧɰɢɩ ɫɭɛɫɢɞɢɚɪɧɨɫɬɢ

Ɉɩɪɟɞɟɥɹɸɬɫɹ ɜ ɤɨɥɥɟɤɬɢɜɧɨɦ ɞɨɝɨɜɨɪɟ ɢɥɢ ɍɫɬɚɜɨɦ ɤɨɥɥɟɤɬɢɜɧɨɝɨ ɫɬɪɚɯɨɜɚɧɢɹ

Ʌɢɱɧɨɟ ɫɬɪɚɯɨɜɚɧɢɟ

Ƚɚɪɚɧɬɢɪɨɜɚɧɢɟɞɨɫɬɢɝɧɭɬɨɝɨ ɭɪɨɜɧɹ ɛɥɚɝɨɫɨɫɬɨɹɧɢɹ ɢ ɟɝɨ ɭɜɟɥɢɱɟɧɢɟ

Ⱦɨɛɪɨɜɨɥɶɧɨɟ

ɉɪɢɧɰɢɩ ɷɤɜɢɜɚɥɟɧɬɧɨɫɬɢ

Ɉɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɜɵɛɨɪɭ ɫɬɪɚɯɨɜɚɬɟɥɹ ɢ ɡɚɤɪɟɩɥɹɸɬɫɹ ɭɫɥɨɜɢɹɦɢ ɜ ɫɬɪɚɯɨɜɨɦ ɞɨɝɨɜɨɪɟ

Ɋɢɫ. 1.1. ɋɢɫɬɟɦɵ ɫɬɪɚɯɨɜɚɧɢɹ ɠɢɡɧɢ

ȼɟɥɢɱɢɧɚ ɬɚɪɢɮɧɵɯ ɫɬɚɜɨɤ ɜ ɫɬɪɚɯɨɜɚɧɢɢ ɠɢɡɧɢ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɫɜɟɞɟɧɢɣ ɢ ɩɪɢɟɦɨɜ ɞɟɦɨɝɪɚɮɢɢ. ɇɚ ɨɫɧɨɜɟ ɫɬɚɬɢɫɬɢɱɟɫɤɢɯ ɞɚɧɧɵɯ ɩɨ ɫɦɟɪɬɧɨɫɬɢ ɧɚɫɟɥɟɧɢɹ (ɞɟɦɨɝɪɚɮɢɱɟɫɤɚɹ ɫɬɚɬɢɫɬɢɤɚ) ɢɫɱɢɫɥɹɟɬɫɹ ɜɟɪɨɹɬɧɨɫɬɶ ɞɨɠɢɬɢɹ ɥɢɰɚ ɞɨ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɜɨɡɪɚɫɬɚ, ɧɚ ɨɫɧɨɜɟ ɤɨɬɨɪɵɯ ɡɚɬɟɦ ɫɬɪɨɢɬɫɹɬɚɛɥɢɰɚ ɫɦɟɪɬɧɨɫɬɢ(ɬɚɛɥ. 1.1).

			Ɍɚɛɥɢɰɚ 1.1
	ɍɱɟɛɧɚɹ ɬɚɛɥɢɰɚ ɫɦɟɪɬɧɨɫɬɢ
ȼɨɡɪɚɫɬ ɯ, ɥɟɬ	ɑɢɫɥɨ	ȼɨɡɪɚɫɬ ɯ, ɥɟɬ	ɑɢɫɥɨ
	ɞɨɠɢɜɚɸɳɢɯ ɞɨ		ɞɨɠɢɜɚɸɳɢɯ ɞɨ
	ɜɨɡɪɚɫɬɚ ɯ, Lx, ɱɟɥ		ɜɨɡɪɚɫɬɚ ɯ, Lx, ɱɟɥ
18	97 028	42	91 473
19	96 918	43	91 046
20	96 773	44	90 588
21	96 607	45	90 096
22	96 422	46	89 560
23	96 223	47	89 012
24	96 018	48	88 424
25	95 807	49	87 799
26	95 586	50	87 064
27	95 357	51	86 174
28	95 218	52	85 229
29	95 169	53	84 237
30	94 989	54	83 199
31	94 786	55	82 041
32	94 588	56	80 953
33	94 384	57	79 809
34	94 187	58	78 605
35	93 847	59	77 339
36	93 563	60	75 999
37	93 225	61	74 439
38	92 922	62	72 749
39	92 596	63	70 917
40	92 246	64	68 936
41	91 872	65	66 702

Ɏɨɪɦɭɥɵ ɞɥɹ ɚɤɬɭɚɪɧɵɯ ɪɚɫɱɟɬɨɜ ɩɨ ɥɢɱɧɨɦɭ ɫɬɪɚɯɨɜɚɧɢɸ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɬɚɛɥ. 1.2.

7

Ɍɚɛɥɢɰɚ 1.2

Ɏɨɪɦɭɥɵ ɞɥɹ ɚɤɬɭɚɪɧɵɯ ɪɚɫɱɟɬɨɜ

ɉɨɤɚɡɚɬɟɥɶ

Ɏɨɪɦɭɥɚɞɥɹɪɚɫɱɟɬɚ

ɍɫɥɨɜɧɨɟɨɛɨɡɧɚɱɟɧɢɟ

Ⱦɢɫɤɨɧɬɢɪɭɸɳɢɣ

V n !1 (1 i)n

i – ɩɪɨɰɟɧɬɧɚɹɫɬɚɜɤɚ, ɞɨɥɢ

ɦɧɨɠɢɬɟɥɶVn

ɟɞɢɧɢɰɵ

ȼɟɪɨɹɬɧɨɫɬɶɭɦɟɪɟɬɶ

qx

=

dx

dx – ɱɢɫɥɨɭɦɟɪɲɢɯɩɪɢɩɟ-

ɜɬɟɱɟɧɢɟɩɪɟɞɫɬɨɹ-

ɪɟɯɨɞɟɨɬɜɨɡɪɚɫɬɚɯɤɜɨɡɪɚɫ-

lx

ɳɟɝɨɝɨɞɚqx

ɬɭɯ+ 1;

lx – ɱɢɫɥɨɥɢɰ, ɞɨɠɢɜɚɸɳɢɯ

ɞɨɜɨɡɪɚɫɬɚɯɥɟɬ

ɋɭɦɦɚɩɟɪɜɨɧɚɱɚɥɶ-

K !

Kt

Kt – ɫɭɦɦɚɫɬɪɚɯɨɜɨɝɨɮɨɧɞɚ,

ɧɨɝɨɜɡɧɨɫɚK

ɧɟɨɛɯɨɞɢɦɨɝɨɞɥɹɜɵɩɥɚɬɵ

(1 i)n

ɫɬɪɚɯɨɜɨɝɨɜɨɡɦɟɳɟɧɢɹɤ

ɤɨɧɰɭt-ɝɨɞɚ

ȼɟɪɨɹɬɧɨɫɬɶɞɨɠɢɬɢɹ

P

! lx n

ɥɢɰɚɜɜɨɡɪɚɫɬɟɯɥɟɬ

x

lx

ɞɨɜɨɡɪɚɫɬɚ(ɯ+ n) ɥɟɬ

Px

ɇɟɬɬɨ-ɫɬɚɜɤɚɌɧ

Ɍɧ

= Ɍɨ + Ɍɪ

Ɍɨ – ɧɟɬɬɨ-ɫɬɚɜɤɚɨɫɧɨɜɧɚɹ

Ɍɪ – ɝɚɪɚɧɬɢɪɨɜɚɧɧɚɹɧɚɞɛɚɜ-

ɤɚ(ɪɢɫɤɨɜɚɹ)

Ȼɪɭɬɬɨ-ɫɬɚɜɤɚɌɛ

Ɍɛ=

Ɍ

ɧ

100

f – ɞɨɥɹɧɚɝɪɭɡɤɢɫɬɪɭɤɬɭɪɟ

ɬɚɪɢɮɚ, %

100 f

Ƚɚɪɚɧɬɢɪɨɜɚɧɧɚɹ

¬2

Ɋ– ɜɟɪɨɹɬɧɨɫɬɶɧɚɫɬɭɩɥɟɧɢɹ

ɧɚɞɛɚɜɤɚ(ɪɢɫɤɨɜɚɹ)

1 P

R

­

ɪɢɫɤɚ;

­

Tp

­

R – ɫɪɟɞɧɢɣɪɚɡɛɪɨɫɫɬɪɚɯɨ-

Tp To A

B

®

Ʉɞ ¸Ɋ

ɜɨɣɨɛɟɫɩɟɱɟɧɧɨɫɬɢ;

ȼ – ɫɪɟɞɧɹɹɜɟɥɢɱɢɧɚɫɬɪɚ-

ɯɨɜɨɝɨɨɛɟɫɩɟɱɟɧɢɹ;

Kɞ – ɤɨɥɢɱɟɫɬɜɨɞɨɝɨɜɨɪɨɜ;

Ⱥ– ɤɨɷɮɮɢɰɢɟɧɬ, ɡɚɜɢɫɹɳɢɣ

ɨɬɝɚɪɚɧɬɢɢɛɟɡɨɩɚɫɧɨɫɬɢ

Ƚɨɞɨɜɚɹɬɚɪɢɮɧɚɹ

T ! Tɛ

ɚ– ɤɨɷɮɮɢɰɢɟɧɬɪɚɫɫɪɨɱɤɢ

ɫɬɚɜɤɚ(ɧɚɞɨɠɢɬɢɟ) Ɍɝ

ɝ

ɚ

(ɢɫɱɢɫɥɹɟɬɫɹɫɢɫɩɨɥɶɡɨɜɚɧɢ-

ɟɦɬɚɛɥɢɰɵɫɦɟɪɬɧɨɫɬɢ)

ȿɞɢɧɨɜɪɟɦɟɧɧɚɹɧɟɬ-

n ȿx

!

lx n

V n

n – ɱɢɫɥɨɥɟɬɫɬɪɚɯɨɜɚɧɢɹ;

ɬɨ-ɫɬɚɜɤɚɫɨ100 ɞɟ-

x – ɜɨɡɪɚɫɬ, ɥɟɬ;

ɧɟɠɧɵɯɟɞɢɧɢɰɫɬɪɚ-

lx

lx – ɱɢɫɥɨɞɨɠɢɜɚɸɳɢɯɞɨ

ɯɨɜɨɣɫɭɦɦɵɧɚɞɨɠɢ-

ɜɨɡɪɚɫɬɚɯ, ɱɟɥ.

ɬɢɟnEx ɞɨɜɨɡɪɚɫɬɚɯ

lx + n – ɱɢɫɥɨɞɨɠɢɜɚɸɳɢɯɞɨ

ɜɨɡɪɚɫɬɚx + n, ɱɟɥ.

ȿɞɢɧɨɜɪɟɦɟɧɧɚɹɧɟɬ-

n Ax !

dx – ɱɢɫɥɨɭɦɟɪɲɢɯɩɪɢɩɟ-

ɬɨ-ɫɬɚɜɤɚɫɬɪɚɯɨɜɨɣ

d V d

V 2 d

V3

ɪɟɯɨɞɟɨɬɜɨɡɪɚɫɬɚɯɤɜɨɡɪɚɫ-

ɫɭɦɦɵɧɚɫɥɭɱɚɣ

ɬɭɯ+ 1

!

x

x 1

x n 1

100

lx

ɫɦɟɪɬɢɞɥɹɜɨɡɪɚɫɬɚɯ

ɜɬɟɱɟɧɢɢn ɥɟɬnAx, %

8

1.2. Ɍɢɩɨɜɵɟ ɡɚɞɚɱɢ

Ɂɚɞɚɱɚ 1.2.1

ɋɨɝɥɚɫɧɨ ɩɪɢɜɟɞɟɧɧɨɣ ɬɚɛɥɢɰɟ ɫɦɟɪɬɧɨɫɬɢ (ɬɚɛɥ. 1.1) ɞɨ ɜɨɡɪɚɫɬɚ 50 ɥɟɬ ɞɨɠɢɜɚɟɬ 87 064 ɱɟɥɨɜɟɤ, ɞɨ ɜɨɡɪɚɫɬɚ 51 ɝɨɞɚ ɞɨɠɢɜɚɟɬ 86174 ɱɟɥɨɜɟɤ. Ɉɩɪɟɞɟɥɢɬɶ ɜɟɪɨɹɬɧɨɫɬɶ ɫɦɟɪɬɢ ɜ ɜɨɡɪɚɫɬɟ 50 ɥɟɬ, ɜɟɪɨɹɬɧɨɫɬɶ ɞɨɠɢɬɢɹ ɥɢɰɚ ɜ ɜɨɡɪɚɫɬɟ 50 ɥɟɬ ɞɨ ɜɨɡɪɚɫɬɚ 51.

Ɋɟɲɟɧɢɟ

1. Ɉɩɪɟɞɟɥɢɦ ɜɟɪɨɹɬɧɨɫɬɶ ɫɦɟɪɬɢ ɥɢɰɚ ɜ ɜɨɡɪɚɫɬɟ 50 ɥɟɬ:

q		d50	(87064 86174) 0,010.
50		l50	87064

2. ȼɟɪɨɹɬɧɨɫɬɶ ɞɨɠɢɬɢɹ ɥɢɰɚ ɜ ɜɨɡɪɚɫɬɟ 50 ɥɟɬ ɞɨ ɜɨɡɪɚɫɬɚ 51 ɝɨɞɚ ɫɨɫɬɚɜɢɬ

86174 Ɋɯ ! 87064 ! 0,989 .

Ɉɬɜɟɬ: 1) 0,01; 2) 0,989.

Ɂɚɞɚɱɚ 1.2.2

Ɋɚɫɫɱɢɬɚɬɶ ɩɟɪɜɨɧɚɱɚɥɶɧɭɸ ɫɭɦɦɭ ɫɬɪɚɯɨɜɨɝɨ ɮɨɧɞɚ ɧɚ ɞɨɠɢɬɢɟ ɩɨ ɞɨɝɨɜɨɪɭ ɫɬɪɚɯɨɜɚɧɢɹ ɱɟɥɨɜɟɤɚ ɜ ɜɨɡɪɚɫɬɟ 45 ɥɟɬ ɧɚ ɫɪɨɤ 10 ɥɟɬ ɫɨ ɫɬɪɚɯɨɜɨɣ ɫɭɦɦɨɣ 100 ɪɭɛ.

Ɋɟɲɟɧɢɟ

1.Ɉɩɪɟɞɟɥɢɦ ɤɨɥɢɱɟɫɬɜɨ ɜɵɩɥɚɬ ɫɬɪɚɯɨɜɵɯ ɫɭɦɦ ɱɟɪɟɡ 10 ɥɟɬ. ɂɡ ɬɚɛɥ. 1.1 ɜɢɞɧɨ, ɱɬɨ ɞɨ 55 ɥɟɬ ɞɨɠɢɜɚɸɬ 82 041 ɱɟɥ. Ɂɧɚɱɢɬ, ɜɵɩɥɚɬ ɛɭɞɟɬ 82 041 ɲɬ.

2.ɋɬɪɚɯɨɜɨɣ ɮɨɧɞ ɱɟɪɟɡ 10 ɥɟɬ ɫɨ ɫɬɪɚɯɨɜɨɣ ɫɭɦɦɨɣ 100 ɪɭɛ. ɫɨɫɬɚɜɢɬ

82 041 ǜ 100 = 8 204 100 ɪɭɛ.

3. ɉɟɪɜɨɧɚɱɚɥɶɧɚɹ ɫɭɦɦɚ ɫɬɪɚɯɨɜɨɝɨ ɮɨɧɞɚ ɫ ɩɨɦɨɳɶɸ ɞɢɫɤɨɧɬɢɪɭɸɳɟɝɨ ɦɧɨɠɢɬɟɥɹ (V10 ! 0,0346 ) ɫɨɫɬɚɜɢɬ

8 204 100 ǜ 0,0346 = 283 861 ɪɭɛ.

9

ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɱɬɨɛɵ ɱɟɪɟɡ 10 ɥɟɬ ɢɦɟɬɶ ɫɪɟɞɫɬɜɚ ɞɥɹ ɜɵɩɥɚɬɵ ɫɬɪɚɯɨɜɵɯ ɫɭɦɦ ɩɨ ɞɨɠɢɬɢɸ, ɫɬɪɚɯɨɜɳɢɤ ɜ ɧɚɱɚɥɟ ɫɬɪɚɯɨɜɚɧɢɹ ɞɨɥɠɟɧ ɢɦɟɬɶ ɫɬɪɚɯɨɜɨɣ ɮɨɧɞ ɜ ɪɚɡɦɟɪɟ 283 861 ɪɭɛ. ɗɬɭ ɫɭɦɦɭ ɧɚɞɨ ɟɞɢɧɨɜɪɟɦɟɧɧɨ ɫɨɛɪɚɬɶ ɫɨ ɫɬɪɚɯɨɜɚɬɟɥɟɣ.

Ɉɬɜɟɬ: 283 861 ɪɭɛ.

Ɂɚɞɚɱɚ 1.2.3

Ɇɭɠɱɢɧɚ ɜ ɜɨɡɪɚɫɬɟ 20 ɥɟɬ ɡɚɤɥɸɱɢɥ ɞɨɝɨɜɨɪ ɫɬɪɚɯɨɜɚɧɢɹ ɧɚ ɫɥɭɱɚɣ ɫɦɟɪɬɢ ɧɚ ɫɪɨɤ 5 ɥɟɬ ɧɚ ɫɭɦɦɭ 40 000 ɪɭɛ. ɩɪɢ ɧɨɪɦɟ ɞɨɯɨɞɧɨɫɬɢ 3 % ɝɨɞɨɜɵɯ. Ɉɩɪɟɞɟɥɢɬɶ ɧɟɬɬɨ-ɫɬɚɜɤɭ ɧɚ ɫɥɭɱɚɣ ɫɦɟɪɬɢ.

Ɋɟɲɟɧɢɟ

1. Ɉɩɪɟɞɟɥɢɦ ɤɨɥɢɱɟɫɬɜɨ ɭɦɢɪɚɸɳɢɯ ɡɚ ɤɚɠɞɵɣ ɝɨɞ ɠɢɡɧɢ ɦɭɠɱɢɧɵ:

d21 = l20 – l21 = 96 773 – 96 607 = 166;

d22 = l21 – l22 = 96 607 – 96 422 = 185;

d23 = l22 – l23 = 96 422 – 96 223 = 199;

d24 = l23 – l24 = 96 223 – 96 018 = 205;

d25 = l24 – l25 = 96 018 – 95 807 = 211.

2. Ɋɚɫɫɱɢɬɚɟɦ ɞɢɫɤɨɧɬɢɪɭɟɦɵɣ ɦɧɨɠɢɬɟɥɶ ɡɚ ɤɚɠɞɵɣ ɝɨɞ, ɩɪɨɠɢɬɵɣ ɦɭɠɱɢɧɨɣ:

	1-ɣ ɝɨɞ V1 !		1		! 0,97 ;
			(1 0,03)
	2-ɣ ɝɨɞ V 2	!		1		! 0,943 ;
			(1 0,03)2
	3-ɣ ɝɨɞ V 3	!	1			! 0,915 ;
			(1 0,03)3
	4-ɣ ɝɨɞ V 4	!		1		! 0,888 ;
			(1 0,03)4
	5-ɣ ɝɨɞ V 5	!	1			! 0,863 .
			(1 0,03)5

3. Ɉɩɪɟɞɟɥɢɦ ɧɟɬɬɨ-ɫɬɚɜɤɭ ɧɚ ɫɥɭɱɚɣ ɫɦɟɪɬɢ:

10