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? ? 1 ? 2


? ? ? 1 ? 2 ? 3 ? 4


? ? ?



=/ ARR= / X 100%





0


1

2

3

4

5


n



P principal


F(future value)


? 1 ? 2


1100

2200200

?
? 1 ? ------:

I ? P?i ? n
F ? P ? P ? i ? n ? P ? (1 ? i ? n)

?

. ? F=P(1+i)n

I ? F ? P ? P[ 1 ? i ? 1]
n

2
1 2 3 100000 100000 100000 6000 6000 6000 106000 112000 118000 100000 106000 112360 6000 6360 6742 106000 112360 119102

4
5

100000
100000

6000
6000

124000
130000

119102
126248

7146
7575

126248
133823






? 1100

10%3
P=100

F=
I=10%


1 =100+100?0.1=100+10=110 =110+110 ? 0.1=110+11=121 =121+121 ? 0.1=121+12.1=133.1 100+100 ? 0.1=100 ? 1+0.1=100 ? 1.1 110+110 ? 0.1=100 ? 1+0.12 =100 ? 1.21 121+121 ? 0.1=100 ? 1+0.13=100 ? 1.331

?
? ? ? ? ? ? ? 1 P1i 2 P1i1i= P1i2 3 P1i2 1i=P1i3 nP1in


1

?





1(Future Value) F=P1+in (PF) (F/P,i,n)

100008%

F/P, i, n )
1 2 3 4 5 6% 1.0600 1.1236 1.1910 1.2625 1.3382 7% 1.0700 1.1449 1.2250 1.3108 1.4026 8% 1.0800 1.1664 1.2597 1.3605 1.4693

(F/P, 8%, 5)= 14693

2 i
P=F /1+in = F (1+i)-n (FP) (P/F,i,n)

3 10010%
P= F=100

I=10% 0 1 2 3

P=FP/FIn =100P/F10%3=1000.751 =75.1

12% 4 ` 1+12%-5 =(P/F,12,5) 0.5674 P4 0.5674 = 2.2696




? 5 15

? 3
? A

? ? ? ?

1 2 3


:





A

A

A

0

1

2

3




A

A

A

0

1

2

3




A

A

0

1

2

3

4




A

A

A

0

1

2

3



(1) ,

A 1 2

A A

A n-1 n

A

A (1+i)0
A (1+i)1 A (1+i)2 A (1+i)n-2 A (1+i)n-1



F=A1+i)0+A1+i)1+ +A1+i)n-2 +A1+i)n-1
(1+i) :
(1+i)F=A(1+i)+A(1+i)2 + +A(1+i)n-1+A(1+i)n

: i F=A(1+i)n -A

F=A

(1 ? i ) n ? 1 i

:

(1 ? i ) n ? 1 ? i) n ? 1 (1 i

F=A

1

i 1in F/AinA


5100

10%3


100 100 100 FA=?

I=10%
0 1 2 3

100
1001+10% 1001+10%
2

FA=100+1001+10%+1001+10% =1001+1.1+1.21 =1003.31 =331
10%

2


(1 ? i ) n ? 1 F = A[ ] (A) i (F/A,i,n)
A

5100 8%5


F =A(F/A,8%,5 )1005.866586.6
A



F=AF/AIn
A=F / F/AIn 1/F/AIn

4 51000 5 10% 5 1000 A=F/F/AIn =1000/F/A10%5 =1000/6.1051 =163.7975

2)
A 1 A (1+i)-1 A (1+i)-2 A (1+i)-(n-2) A (1+i)-(n-1) A (1+i)-n 2 A A A n-1 n A



p=A(1+i)-1+A(1+i)-2+ +A(1+i)-(n-1)+A(1+i)-n
(1+i) : (1+i)p=A+A(1+i)-1 + +A(1+i)-(n-2)+A(1+i)-(n-1) :
? (1 ? i ) ? n 1

i p=A-A(1+i)-n

p=A

i

: p=A

?n 1 ? (1 ? i )

?n 1 ? (1 ? i )

i

1

i

1in p/Ain


3100 10%

P=


100 100 100

I=10% 1001+0.1 1001+0.1 1001+0.1
-1 -2 -3

0

1

2

3

P=1001+0.1 -1+1001+0.1 -2+1001+0.1 -3 =100*[1+0.1 -1+ 1+0.1 -2+1+0.1 -3] =100*0.9091+0.8264+0.7513 =100*2.4868 =248.68

10%

100 31330 10

3


A 1 A 2 A A A n-1 n A (1+i)1 A (1+i)2 A (1+i)n-2 A (1+i)n-1 A (1+i)n



F=A(1+i)1+A(1+i)2+ +A(1+i)n

A(1 ? i )[1 ? (1 ? i ) n ] F= 1 ? (1 ? i )
? i ) n ?1 ? 1 (1 =A[ -1] i





1+i F=(1+i)[A+A(1+i)1+A(1+i)2++A(1+i)n]
(1 ? i ) n ? 1 =A 1+i i



[
(1 ? i ) n ? 1 i

(1 ? i ) n i

?1

?1

-1]

[F/Ain+1-1]

11

(1 ? i ) n ? 1 1+i i

F/Ain1+i 1+i

: A A AA A
1 2 n-1 n

A (1+i)0
A (1+i)-1 A (1+i)-2 A (1+i)-(n-2) A (1+i)-(n-1)



p=A+A(1+i)-1+A(1+i)-2++A(1+i)-(n-1)




? (1 ? i) ? n ? (1 ? i) ?(n?1) 1 1 p=A [ +1] ?1 =A 1 ? (1 ? i) i

(1+i)

(1+i)p= A(1+i)+A+A(1+i)-1+ +A(1+i)-(n C2)
i p=A(1+i)-A(1+i)-(n-1)
1 ? (1 ? i ) n p=A (1+i) i
?

[

1 ? (1 ? i) i

? ( n ?1)

+1]

1 ? (1 ? i) i

?n

1+i

[p/Ain1 +1]p/Ain1+i 11 1+i

300i=10%10

5400i=10%

4


m A m+1 A A m+n A

1

2



1 2

p=Ap/Ain p/sim
p=A[p/Aim+n-p/Aim]

167-9300 i=8%,9




5

1 ? (1 ? i ) p=A i
?n

?n

n1+i

1 p=A i



300i=10%



1. S P N






1 2
?

3


1. 2. 3. 4.

1 ? ? 2 ? ? ? 3 ? ?

(1)


a.


b.


c.
()

d.

(2)


a.. b. c.


d.



2.
(NCF) ,,

; , .
? = - ? = - ? = - - = + ? = + +


? 1M ? (1)12 5002() 100( ) ? (2)16 ? (3)300 60080 16030% ?

? ? =1000 - 16/6=164 ? NCF0 = - 500 ? NCF1 = - 500 ? NCF2 = - 100 ? NCF3 = 300 - ( 80 + 164 ) (1 - 30%) + 164 = 203.2 ? NCF4 - 7 =600 - ( 160 + 164) ( 1 30%) + 164 = 357.2 ? NCF8 = 357.2 + 100 + 16 = 473.2


5,000 1,000 5 3,000640 60 54% 33%



=+= 640+960 = 1,600 = - -

= 3,000 - 1,600 C 60 = 1,340
=1,34033% = 442.2


1. ϡ ϣ

2
(1) , (2) (3)





K?

? Gi K j
j ?1

n

Gjj

Kjj

---
1.34500 5% (1)
1)P=FP/Fin=34500P/F5% 3 =29801.1()

2.5 2500i =5%, (1) (2)?

1P=A(P/A,i,n)=2500(P/A,5%,5) =2500X4.330=10825 () 2F=A(F/A,i,n)=2500(F/A,5%,5) =2500X5.526=13815 ()

3.3100

i=10%,
P=A(P/A,10%,3)(1+10%) =100X2.487X1.1 =273.57() OR P=A(P/A,10%,3-1,+1) =1002.7355=273.55()

4. 1000910% P=1000[ (P/A,10%,9)- (P/A,10%,3)]=3272.1() P=1000 (P/A,10%,6)(P/F,10%,3) =1000X4.355X0.751=3271()

? 20 2.5 5% ? PA APA/Ain

? ? ?

=25000 PA/A5%20 =2500012.4622 =311555


? 112 100 10% ? 1


? ? ? ? ? ? ? ? 10090.982.645 =100 =100XP/Fin =100x (P/F10%,1) =100X0.90909=90.9() = 100XP/Fin =100x (P/F10%,2) =100X0.82645=82.645()



? 1200 300 55 200300 800 40% ? =1200-200/5=200

? ? ? ? ? ? ?



800 300 200 300 120 180 380

0

1

2

3

4

5




-1200 -300
380 380 380 380 380



200 300



-1500

380

380

380

380

880

1.100 10% 30 30 ( ) A. C. B. D.

2.800063 ( ) A. B.

C.

D.

3.80063 ( )

A.
C.

B.
D.

4.
A. C. B. D.




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