Sansanee Thebpanya

1
????????????????????

• ?????????????????
• ??????????????

2

• Time lines ??????????????????????????????

0
1
2
3
i
CF0
CF1
CF3
CF2
??????????????????????? t0 ????????? t1
????????????? 1 ????????????? 2
3
Time line ?????????? 100 ??? ?????????????? 2
0
1
2 ??
i
100
4
Time line ?????? ordinary annuity ??????? 100 ???
???????? 3 ??
0
1
2
3
i
100
100
100
5
Time line ?????????????????????????? -50 ??? ???
t 0, 100, 75, ??? 50 ??? ? ???????????? 1 ??? 3
0
1
2
3
i
100
50
75
-50
6
?????????????????????? 100 ??? ??????? 3 ??? i
10
0
1
2
3
10
FV ?
100
????? FVs (????????????????? time line) ????????
??????????? (compounding)
7
???????????? 1
FV1 PV INT1 PV PV (i) PV(1 i)
100(1.10) 110.00 ???
???????????? 2
FV2 PV(1 i)2 100(1.10)2 121.00 ???
8
???????????? 3
FV3 PV(1 i)3 100(1.10)3 133.10 ???
??????????,
FVn PV(1 i)n.
9
???????????????? (PV) ??????? 100
????????????????????? 3 ??? i 10
????? PVs ??????????? (discounting)
???????????????????????????
0
1
2
3
10
100
PV ?
10
Solve FVn PV(1 i )n for PV
3
1
?
?
?
PV

100

?
?
?
1.10
?
?


100
0.7513


75.13 ???
11
??????????????????????????????????????????????????
????????????
0
1
2
?
20
2
-1
FV PV(1 i)n 2 1(1
0.20)n (1.2)n 2/1 2 nLN(1.2) LN(2)
n LN(2)/LN(1.2) n
0.693/0.182 3.8
12
??????????????????????????? 100 ???????????
125.97 ???????? 3 ??????????
100(1 i )3 125.97. (1 i)3
125.97/100 1.2597 1 i
(1.2597)1/3 1.08 i 8.

13
????????????????? ordinary annuity ??? annuity due
Ordinary Annuity
0
1
2
3
i
PMT
PMT
PMT
Annuity Due
0
1
2
3
i
PMT
PMT
PMT
PV
FV
14
??????????????? (FV) ?????????? 3 ?? ????? 100
??? (ordinary annuity) ????????????? 10
0
1
2
3
10
100
100
100
110 121 FV 331
15
???????????????? (PV) ??? ordinary annuity
0
1
2
3
10
100
100
100
90.91
82.64
75.13
248.69 PV
16
?? FV ??? PV ??????????????????????? (annuity due)
0
1
2
3
10
100
100
100
17
?? FV?????????? (annuity due) ????? 100
???????? 3 ?? ??? 10
1
2
3
0
10
100
100
100
110.0 121.0 133.1 FV
364.1
18
????? PV?????????? (annuity due) ????? 100
???????? 3 ?? ??? 10
0
1
2
3
10
100
100
100
90.91
82.64
273.55 PV
19
?? PV ?????????????????????????????????????
4
0
1
2
3
10
100
300
300
-50
90.91
247.93
225.39
-34.15
530.08 PV
20
??????????????????????????????????????????????????
????? ?????? I ?????????????? ????????????
???????! ?????????????????????
??????????????????? ?????????????? ?????????
?????????? ???????????????????????????????????????
????
21
0
1
2
3
10
100
133.10
?????????? FV3 100(1.10)3 133.10 ???
0
1
2
3
0
1
2
3
4
5
6
5
134.01
100
??????????????? FV6 100(1.05)6 134.01 ???