Note Formulae

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I NTRODUCTI ON TO FI NANCE
FORMULAE FORMULAE
Some I mpor t ant For mul ae Some I mpor t ant For mul ae
1) Fut ure Value of a Single Cash Flow I nvest ed for n Periods
FV= P* FF(r,n) FV Fact or, FF(r,n)= (1 + r)
n
2) Present Value of a Single Cash Flow Received n Periods from Now 2) Present Value of a Single Cash Flow Received n Periods from Now
PV= F* PF(r,n) PV Fact or,
( )
n
r 1
1
n) PF(r,
+
=
3) Fut ure Value of a St ream of Cash Flows as of n Periods from Now
( ) ( ) ( )
n 1 n
2 n
2
1 n
1
C r 1 * C ... r 1 * C r 1 * C FV + + + + + + + =
÷
÷ ÷
4) Present Value of a St ream of Cash Flows
( ) ( )
PV
C
1 r
C
1 r
...
C
1 r
1 2
2
n
n
=
+
+
+
+ +
+
2
Some I mpor t ant For mul ae Some I mpor t ant For mul ae
5) Fut ure Value of an Annuit y Paying $C at t he End of Each of n Periods
FV = C* FAF(r,n) FV Annuit y Fact or,
( ) | | 1
n
r 1 *
1
n) FAF(r ÷ + =
6) Present Value of an Annuit y
( ) | | 1 r 1
r
n) FAF(r, +
(
(


1 1
PV = C* PAF(r,n) PV Annuit y Fact or,
7) Present Value of an Annuit y growing at rat e g:
( )
(
¸
(

¸

+
÷ =
n
r 1
1
1 *
r
1
n) PAF(r,
) y g g g
PV= C* PAF(r,n,g)
( )
( )
(
(
¸
(


¸

+
+
÷
÷
=
n
n
r 1
1
1 *
r
1
) n, PAF(r,
g
g
g
3
( )
(
¸

¸
Some I mpor t ant For mul ae Some I mpor t ant For mul ae
8) Present Value of a Perpet uit y
r
C
PV =
9) Present Value of a Const ant Growt h Perpet uit y
PV
C
1
=
r g ÷
4

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