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1. .
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() .
| FV = PV*(1+i)n | (1.4) |
FV (future value);
PV (present value);
i ;
n .
:
- . , (, , ). : .
. 1 . , 10% 5 . . 5 ?
FV = 1 .*(1+10%)5 = 1,61 .
. 1000 . 24% 1 . (.. %) . (ip), (FV), () (i).
, : ip= i/2 = 24% /2 =12%
: FV =1000(1+0,12)2 = 1254,4 .
: = FV PV = 1254,4 1000 = 254,4 .
: i= (FVPV)/PV=(1254,41000)/1000=0,2544=25%
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, , . , , .
. , , , 12%?
72-. , , , : 72 / %
72 / 12% = 6 .
, 3 18%.
.
, .. , , () - (1,2,3 ..).
(payment) k. ( ).
.
.
( ). :
| FV = | (1+i)n -1 | *PMT | (1.5) |
| i |
( ). :
| FV =[ | (1+i)n+1 -1 | -1] | *PMT | (1.6) |
| i |
. , 1000 $ 12% 5 . ( ), 5 5 ?
, , 5 , :
| FV = | (1+12%)5 -1 | *1000$ | =6353 $ | |
| 12% |
, , ?
| FV = [ | (1+12%)5+1 -1 | -1] | *1000$ | = 7115 $ |
| 12% |
, , , .
.
, () , () . .. , 1 . . . () , 5 . - .
, , ( ) .
( ):
| = | = | _____i___ | *FV | (1.7) |
| (1+i)n - 1 |
( ):
| = | = | ______i______ | *FV | (1.8) |
| (1+i)n+1 (1+i) |
2- 3- . 2- FV, 3- PV.
. 5 1000$. , . 15% . ? , 5- 1000$?
1. :
| = | _____15%___ | *1000$ | = 148 $ |
| (1+15%)5 - 1 |
- :
| = | _______15%________ | *1000$ | = 129 $ |
| (1+15%)5+1 (1+15%) |
, .
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. 10000$ 5 . , 15%, ( ) . ?
1. :
| = | _____1,25%____ | *10000$ | = 113 $ |
| (1+1,25%)5*12 - 1 |
2. :
| = | ________1,25%__________ | *10000$ | = 111,5 $ |
| (1+1,25%)5*12+1 (1+1,25%) |
111,5 $.
.
, . :
PV = FV /(1+i)n (1.9)
4- 1- . 1- .
. 12000$. 4 . 10% , 4 12000$.
PV = 12000$ /(1+10%)4 = 8196 $
.
5- (PV) , .. , , () - (1,2,3 ..) (i).
, 5- 2- , , 2- FV.
( ) ( ).
:
| PV= | 1 (1+i) n | *PMT | (1.10) |
| I |
:
| PV=[ | 1 (1+i) (n 1) | +1] | *PMT | (1.11) |
| i |
. , , 100$ 4- , 10% ?
1. :
| PV= | 1 (1+10%) 4 | *100 | = 316,9 $ |
| 10% |
2. :
| PV = [ | 1 (1+10%) (4 1) | +1] | *100 | = 348,6$ |
| i |
.
6- (), (n) (PV) .
. 6- 5- . , : .
( ):
| = | PV*i___ | (1.12) |
| 1 (1+i) n |
( ):
| = | PV*i_____ | (1.13) |
| (1+i) (1+i) (n 1) |
. 15000$ 5 12% , . , (15000$) ?
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1. :
| = | 15000$*12%___ | = 4161$ |
| 1 (1+12%) 5 |
2. :
| = | 15000$*12%_____ | = 3715$ |
| (1+12%) (1+12%) (5 1) |
1. , .
2. ?
3. , ?
4. ? ?
5. , .
6. , ?
7. ?
8. ? .
1.1. ?
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1.2. :
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1.1. :
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1.2. () ?
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1.3. ?
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1.4. :
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1.7. ?
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1.8. , ?
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1.9. :
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1.10. - :
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1.1.
800 . ., 10 12%.
1.2.
12% 10 800 . .
1.3.
12% 10 800 . .
1.4.
800 . ., 12% . , 10 ?
1.5.
, 10 , 80 . . 12%?
1.6.
, 10 12% , 80 . .?
