:
FV=PV(1+k)n; (1.1)
FV (. future value) , .; PV (. present value) () , ; k ; n , .
(1+k) .1.
, , (. annuity ). :
FVAn = PMTt * (1+k)n-t; (1.2)
FVAn , PMTt - , t; k ; n .
, 1.2 :
FVAn = PMT*FVA1n;k; (1.3)
; FVA1n;k 1 .
FVA1n;k = [(1+k)n1]/k; (1.4)
(FVA1n;k) (.3).
1. 30 1000 . . 10% . 30 ?
FVA30 = PMT FVA120;10 = 1000*164,49 = 164490 (.)
.
2. 5 100 . . 10% . ?
PMT = FVA5/FVA15;10 ( 1.3)
FVA15;10 = 6,105 ( . 2), = 100 / 6,105 = 16,380 . .
, , . :
FV=PV (1+ k 1)n1(1+ k 2)n2(1+ k 3)n3 (1+ k 12)nk; (1.5)
S ; P , ; k 1, k 2 k 12 ; n1, n2 nk - , .
, , :
FV=PV (1+ k)a+b; (1.6)
n=a+b ; ; b .
( , , ), :
FV=PV (1+ j /m)N; (1.7)
j ; m ; N ; N=m*n, n .
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3. 150 . . , 15% . . , .
FV =150(1+0,15/4)2*4=150*1,3425=201,37 (. .)
, m , , , . :
FV=PV (1+j/m)ml(1+aj/m); (1.8)
ml ; .
() . . :
PV(P) , FV(S).
, . :
( ) n , ( ) i , S. 1.1:
PV=FV/(1+k)n PV= FV (1+k)-n (2.1)
(1+n)-n , (.2).
4. 1 , , 10 . . , 25% ? (2.1) :
PV=10 / (1+0,25)1 =8,0 . .
2.
( 2)