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Notes on TVM
1 . Present va lue / future value of lump sum amount :
PV 
FV
1 r
2 . Present va lue of perpetuity
PV 
C
(1 r )
(1  r) PV  C 

:
C
(1 r )
C
(1  r)
2


C
(1 r )
C
(1 r )
2
3
     

(1)

(2)  (1)  (1  r)
Now (2) - (1)
PV  r  C
 PV 
C
r
1
3 . Present va
lue of Annuity

PVA(n, r)  Perpetuity (r) - Perpetuity (r) starting

C
r

1
(1 r )

C

1
r 

n

after nth period
C
r

1

n

(1 r ) 
2

4. Present value of growing perpetuity
PV 
C
1 r
PV(1  r)
(1 g)


C (1 g)
(1 r)
C
(1 g)

2

C (1 g)
(1 r)
C
(1 r)

3
2
     
C (1 g)
2
(1 r )
 
(1)
(2)  (1) 
Now (2) - (1)
PV(r - g)
(1  g)

C
(1  g)
 PV 
C
rg
3
1 r
1 g
5 . Present va lue of growing
annuity
:
PVA(n, r, g)  Perpetuity (r) growing
- growing
perpetuity (r) @g starting

C
r-g

(1 g )
(1 r )

C 

1
r-g 

@g
after nth period

n
n

(1 g )
(1 r )
n
n
C
rg




4
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