, . , , . {CF}. 2 :
1. () 1 .
2. . 1 .
:
1. ( )
2. ( )
, ..
:
CF1(1+r)6
FVpre=∑nk=1 CFk(1+r)n-k+1
FVpre=∑nk=1 CFk(1+r)n-k(1+r)=(1+r)∑nk=1CFk(1+r)n-k=(1+r)FVpst
FVpre=(1+r)FVpst
FVpre
:
CF1/(1+r)5
PVpre=∑nk=1 CFk
(1+r)k-1
PVpre=∑nk=1 CFk*(1+r) =(1+r) ∑nk=1 CFk =(1+r)PVpst
(1+r)k-1(1+r)k
FVpre=(1+r)FVpst
( )
.
. .
CF1 = CF2 = CF3 CFn =
: 1. ( )2. ( )
, , .
. .
0 1 2 3 n n-1
CF = const =
FVpst = CF (1 + r)n-k FVpst = A (1 + r)n-k
FVpst = A (1 + r)n-k = A FM3 (r; n)
FM3 , ( ).
FM3 (r; n) = (1 + r)n-k
FM3 (r; n) = (1 + r)n-1 + (1 + r)n-2 + + (1 + r) +1
(1 + r).
FM3 (r; n) (1 + r) = (1 + r)n + (1 + r)n-1 + + (1 + r)2 + (1 + r)
.
FM3 (r; n) r = (1 + r)n 1
FM3 (r; n) = ((1 + r)n 1)/ r
FVpst = A (((1 + r)n 1)/ r)
.
0 1 2 3 n
CF = const =
FVpre = (1 + r) FVpst
FVprea = (1 + r) FVpsta
FVprea = (1 + r) A FM3(r; n)
FVprea = (1 + r) A (((1 + r)n 1)/ r)
. , , .. n→∞ , .
|
|
PVpsta=A*FM4(r,n), FM4(r,n)- , , n , % r.
n→∞
lim FM4(r,n)= lim(1-(1/(1+ r) n))/ r=1/ r
PVpsta∞= A/r
PVprea=(1+r)*PVpsta
PVprea∞= (1+r)* A/r
PVprea∞= PVpsta∞+A/r