Rambler's Top100




2.2 ???????? ??????? ?????
Версия для печати
Опубликовал: Administrator  
19.07.2008
??? ????? ??????? ?????: ? ??? ?????? ???? ?????? R? ???, ???????????? ?? n???, ??????? ?????????? ?????? i. ?? ??????? ??????? ??????????? ??????? ????????.
?????? 2.
?????????? 5-?????? ????? ? ??????? ???????? 1000 ???., ?????????? ?????? i=10%.

??????? ???????? ???????? ????. ? ????? 1-?? ???? ? ???? ???????? 1000 ???. ? ????? 2-?? ???? ??? ????? ?????????? ?? 1100 ???. ?? ???? ??????????? 10%. ?????? ? ????????? ????????? ???????? ? 1000 ???. ?? ????? ??? 2100. ? ????? 3-?? ???? ??? ????? ?????????? ?? 2310 ???. ?? ???? ??????????? 10%. ?????? ? ????????? ????????? ???????? ?? ????? ?????? ??? 3310 ???. ? ?.?. ?????????? ????? ????? ????? 6105,1 ???. ??????????? ???????? ????? ??????, ??????????? ? ??????? 0 ?????????? ????? 6105,1. ???????? 6105,1/1,15=3791
???? ??????? ????????? ? ????? ?????????? ??????????, ?? ????? ?????????? ?????????????. ??????????????? ????? ? ??????? ?????????????. ? ?????????? ??????????????? ?????? ????? ?????.
?????? ???????? ???????? ??????? ????? {R,n,i} ? ????? ????.

??????? ?????? – ????? ??????????? ???????? ???? ?????. ?????
A=R/(1+i)+R/(1+i)2+…+R/(1+i)n=R[(1+i) 1+…+(1+i)n].
? ?????????? ??????? ????? ????? n?????? ?????????????? ?????????? ? ?????? ?????? (1+i)1 ? ???????????? (1+i)1. ??? ????????, ????? n?????? ?????????????? ?????????? ? ?????? ?????? b1 ? ???????????? q????? b1(qn1)/(q1) ??? (bnqb1)/(q1). ?????????????, ????? ? ?????????? ??????? ???? [1(1+i)n]/i. ? ?????? ??????????? ???????? ????? ???? A=R[1(1+i)n]/i.
???????? [1(1+i)n]/i ???????????? a(n,i) ? ?????????? ????????????? ?????????? ?????. ? ?????? ????? ??????????? ????? A=R*a(n,i).
???? ??????????? ???????? ?????, ????? ????? ????? ???????? ?? ????????, ??????? ??? ?????????? ????????? ????? S: S=A(1+i)n, ??? S=R*a(n,i)(1+i)n=R[(1+i)n1]/i.
???????? [(1+i)n1]/i???????????? s(n,i) ? ?????????? ????????????? ????????? ?????. ? ?????? ????? ??????????? ????? S=R*s(n,i).
???????? a(n,i), s(n,i) ??????? ????????? ???????????? s(n,i)=a(n,i)*(1+i)n ??? s(n,i)=a(n,i)* M(n,i).
??????????? ????????? s(n,i) ??????????, ?? ??????? ??? ?????????? ???????? ????? ?????? ?? ???????? ???????. ??????????? ????? ????? ? ??????????? ?????????? ?????: ?? ??????????, ?? ??????? ??? ??????????? ???????? ????? ?????? ?? ???????? ???????. ????? ???? ?????? ?????????? ?????? ???????
«??????????? ???????? ?????»: ???? ? ?????? 0 ???????? ? ???? ??????????? ???????? ????? ??? i ????????? ???????, ?? ? ????? n-?? ???? ??? ???????? ?? ?????????? ???????? ????? S. ????, ????? ??????? ??? ???????? ??????? ?????
?=R* a(n,i), S=R*s(n,i).
??? ??????? ????????? ????? ????? ? ??? ??????? ?. ??? ???? ???? ???????????? ???????????? ??????? ??? ?(n,i) ? s(n,i) .
???? ????????? ????????? ?????? ????????????? ?????????? ? ????????? ??????? ?????. ??????? ???????? ?????? ????????? ?????????????? ? ??????????? 3 ? 4.

 

??????????? ?????????? ??????? ????? a(n,i)=[1(1+i)n]/i

 

3

4

5

6

7

8

9

! ?

11

3

2,829

1,775

2,723

2,673

2,624

2,577

2,531

2,487

2,444

4

3,717

3,630

3,546

3,465

3,387

3,312

3,240

3,170

3,102

5

4,&??

4,452

4,329

4,212

4,100

3,993

3,890

3,791

3,696

6

5,417

5,242

5,076

4.917

4,767

4,623

4,486

4,355

4,231

7

6,230

6,002

5,786

5,582

5,389

5,206

5,033

4,868

4.71?

8

7,020

6,733

B,463

6,210

5.971

5,747

5,535

5,335

5.146

9 .

7,786

7,435

7,108

6,802

6,515

6.247

5,995

5,759

5,537

to

8,530

8,110

7,722

7,360

7,024

6,710

6,418

6,145

5,889

??????????? ????????? ??????? ????? s(n,i)=[(1+i)n1]/i

 

3

4

5

6

7

8

9

10

11

3

3,091

3,122

3,153

3,184

3,215

3,246

3,278

3,310

3,342

4

4,184

4,246

4,310

4,375

4.440

4,506

4,573

4.641

4,710

5

5,309

5,416

5,526

5,637

5,751

5,867

5.985

6,105

6,228

6

6,468

6,633

6,802

6,975

7,153

7,336

7.523

7,716

7,913

7

7.662

7,898

8(H2

8,394

8,654

8,923

9.200

9,487

9,783

8

8.892

9,214

9,549

9,897

10,260

10,637

11,028

11,436

11,859

9

10.159

10,583

11,027

11,491

11,978

12,488

13.021

13,579

14,164

10

11,464

13,006

12.578

13,181

13,816

14,4*7

15,193

15137

16,722

?????????? ????????????? ?????????? ? ????????? ??????? ?? ???????.
?????? 3.
????? ??????????? ? ?????????? ???????? ??????? ????? ? R=1000, n=8, i=8%.
??????? ?? ???????? a(8,8)=5,747, s(8,8)=10,637. ??????, ??????????? ???????? ????? ????? 5747, ?????????? 10,637. ??? ???????? ????????? ? ??????? ????????????????? ??????????, ??????? ?(8,8)=1,851.
????????: 5747*1,851=10638.