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6.7.1.

. , , , , .

( , ) . . , . : , .

( ), ( ). , (Ordinary Annuity); (Annuity Due), , , ; , .

: , , , . : ( ) .

, ; . ; CF1 = CF2 = ... = CFn = . - . 6.12. , , , 0 ( , , ; ).

, . , , .

( ), ( anno). .

, . ( ) , . , . 6.6.

(. . ) , , : () , () () r.

, 6.8 , CFk = = const, n.

,

(6.31) . ,

FM3(r, n) = (1 + r)n-1 + (1 + r)n-2 + ... + (1 + r) + 1.            (6.32)

(6.32) (1 + r),

FA/3(r,n) = (1 + r) = (1+ r)n + (1 + r)n-1 + ... +(1 + r)2 + (1 + r).            (6.33)

(6.33) (6.32),

FM3(r,n)(1+ r) - FM3(r,n) = (1 + r)n - 1.
. . FM3(r, n)r = (1 + r)n - 1.

(6.31).

FM3(r, n), , . , (, ) . , , . FM3(r, n) . , FM3 (r, n) . r n (. 3).

(6.30) , FM3(r, n) , . FM3(r, n) .

, (6.30) . , (n = 1) FM3(r, n) = 1 = . r = 0, .. , (6.30) = n; , .

    3 , : (1) 100 . . ; (2) 350 . . . , 20% ?

    n = 3 A = 100 . . 20% (, ). , , . 6.8.

    = A FM3(20%,3) =100 3,640 = 364 . .

    , , (1) .

(. . ) , , : () , () () r.

. 6.10 , CFk = = const. . 6.6, (1 + r), . .

= (1 + r) = A FM3(r, n)(1 + r).            (6.34)

    10 . . 20% . 3 ?

    , . (6.34) S:

    S = 10 FM3(20%,3) (1 + 0,2) = 10 3,640 1,2 = 43,68 . .

(Present Value of Ordinary Annuity) (. e. ) , , : () , () () r.

. 6.9 , CFk = = const, n.

,

(6.36) . ,

(6.37) (1 + r), :

(6.38) (6.37),

(6.36).

FM4(r, n), , . , , (. . , ), (, ), . FM4 (r, n) , r n, . (. 3).

, , . FM4(0, n) = n, r = 0 . , : r = 0.

FM4 (r, n) , r, n ( ).

(Present Value of Annuity Due) (. e. ) , , : () , () () r.

. 6.11 , CFk = = const, . , (1 + r), . .

. , , . , . , .

, , . .

    100 . . 5 ( 20 . .). 5 30 . . , 12% ?

    . 5- :

    F5 = P(1 + r)5 = 100 (1 + 0,12)5 = 176.23 . .

    , , , 20 . . , . , . :

  • c A=20, n = 5, r = 20% 30 . .;
  • = 20, n = 4, r = 20% 20 30 . .

    (6.30)

    S = 20 FM3(12%,5) + 30 = 20 6,353 + 30 = 157,06 . .

    (6.34)

    S = 20 FM3(12%,4) 1,2 + 20 + 30 = 20 4,779 1,12 + 50 = 157,06 . .

    , . , 5- (107,06 . .), (20 . .) (30 . .). , , 157,06 . . .

 

 

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