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2.1. . (, , ) (date of maturity, due date). (principal) , , . .
( 1 ) , , . (simple interest) :
I ;
V ;
FV , . . ;
i ( );
n .
( ), i . Pv×i. I = PV×ni. , ,
FV = V + I = V + PV×ni = V(1 + ni).
, (1 + ni) . . 1. , k . (1 + kni) / (1 + ni) .
. 1
, 700 . ., 4 , 20% (i = 0,2). I = 700 × 4 × 0,2 = 560 . .; FV = 700 + 560 = 1260 . . . , , . (1 + 2 × 4 × 0,2) / (1 + 4 × 0,2) = 1,444 .
2.2. . , , , , . , . . , . n
,
t , , (time basis). : = 360 (12 30 ) 365, 366 . = 360, (ordinary interest), (365, 366 ) (exact interest). . , 30 . . . . 1 .
, .
1. . , , . 365/365 ACT/ACT.
2. . , (Banker's Rule), , 365/360 /360 , . , , 360, , , . , t = 364, n = 364/360 = 1,01111. , i = 20%, 1,20222.
3. . , , . 360/360.
, .
, , , ( , , 30,58), , .
1. 1 . 20 05 18% . ? . : 258, 255.
1. (365/365) :
2. (365/360) :
3. (360/360) :
1. 1 . ջ 2013 Y 2013 Z% . ? .
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2.3. . (, ..), , : I = I1+I2 = PV×n1×i + PV×n2×i, n1 n2 , .
2.4. . . , :
it t, nt ,
2. : 16%, 1%. 2,5 . :
2. : ջ %, Y %. Z.
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2.5. . , , , ( , ..).
Rj j , nj ( ) . - , . , ( ). :
K , a tj . ∑Rjtj /100 (interest number), ( ) (interest divisor).
3. : 5 12 . ., 10 4 . . 20 8 . . . 18% .
365: 18 = 20,27778. .
| (.)
| (Rj)
(.)
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05.02
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10.07
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20.10
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31.12
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| | | | 38,28
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31.12 16 .., 1,888 .., 17,888 ..
3. : ջ 7 . ., Y 2 . . Z 9 . . . 16% .
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2.6. . , : FV, , V. , , . V FV , FV , .. , . , FV , , (discount) . , , , .
"" , , . , , . ( , , .)
PV, , , (present value), FV, . . , , , .
, . : , FV, , i? :
,
n = t/K .
V FV, n . 1/(1 + ni) , , . , .
4. 180 310 . . 16% . , 365 ? :
FV V , V FV.
4. ջ Y . . Z% . , 365 ?
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2.7. . , , . :
( n=t/K, K ):
5. , , 100 . ., 120 . . , 25% (/)? :
5. , , ջ . ., Y . . , Z% (/)?
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2.8. . , . :
6. 110 . . 120 . 90 . . (/360). , . . :
6. ջ . . Y . Z . . (/360). .
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3.1. . - - , , , (compound interest). . , . , (running period). , , .
, ( ). . , PV×i, PV + PV×i = PV×(1+i). PV×(1+i) + PV×(1+i)i = PV×(1+i)2 .. n- :
FV = PV(1+i)n.
:
. :
, , , PV, (1+i). . . 2.
.2
(1 + i)n (compound interest factor) . n . ( , ..). ACT/ ACT. , 1 . ., 5 15,5% , FV FV = 1 000 000 (1+0,155)5 = 2055464,22 . , i n. , . . . , -, ( ) 24 . 350 40 . ., .. 1,667×109 ! , 6,3% .
3.2. . . , . , . , , , . , (. . 3).
.3
n1, n2. , I = I1 + I2,
7. 1 2013 . 1 2015 . 10 . . ( 14% ACT/ACT) . ( ..):
1 2013 (244 ): ;
2014 .: ;
, 1 1 2015 . (121 ):
2 996 . .
:
10 000 ×(1,142 - 1) = 2 996 . . .
7. ջ 2013 . Y 2015 . 10 . . ( Z% ACT/ACT) .
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3.3. . , , ..
,
i1,i2,ik ; n1,n2,,nk , "" .
8. 5 , 12% 0,5% 0,75% . :
q = (1 + 0,125)2 ×(1 + 0.1275)3 = 1,81407.
8. 7 , ջ % Y% Z% . .
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3.4. . , (. 4).
.4
, . , , , ( s ):
:
(1 + nis) > (1 + i)n ,
:
(1 + nis) < (1 + i)n,
, , .
, n > 1 . is = i = 12%, = 365.
|
|
30
| 180
| 1
| 5
| 10
| 100
|
1 + in
| 1,01644
| 1,05918
| 1,12
| 1,6
| 2,2
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|
(1 + i)n
| 1,00936
| 1,05748
| 1,12
| 1,76234
| 3,10584
| 83522,3
|
.
, (.. ) . , (annuity). , , . . , . , , (immediate annuity). , , (ordinary annuity). .
4.1. . , 1000 . . , 10% ? - ( payment).
i, n, , FV.
:
, : .
, 1000- 3 310 .
(FV), (PMT), , , , , . , :
9. 10 500 . , , 10% , :
9. ջ Y . , , Z% , .
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4.2. . . , ( ), 10% , 1000 ? . 1000 . :
, : .
(PMT), , , , :
10. ( ), 2 . . 25 15% , :
10. ( ), ջ . . Y Z% , .
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: 2016-12-18; !; : 2352 |
:
:
, .
==> ...
1752 - | 1533 -
© 2015-2024 lektsii.org - -
: 0.132 .