URJC _Universidad Rey Juan Carlos_ _ Grado de Administración y Dirección de Empresas _ Matemáticas Financieras _ 4 Discount

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Discounting at a simple interest rate
The process of calculating C0 from Cn is called discounting 
at a simple interest rate (i) 
0, 0 0n nD C C i C n= − =  
( )
0
1
nCC
i n
=
+ 
The discounted amount is proportional to C0
and “n”
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Discount at a simple interest rate
Financial Mathematics
( )
0 
1
nCC
i n
= 
+ 
( )0 1nC C i n= + 
Discount at a simple 
interest 
 Simple interest law
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Discount factor at a simple interest
Relationship between simple interest rate and simple discount rate
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( )0 1nC C d n= − 
Discount at a simple 
discount rate
0
1 ·
nCC
i n
=
+
Discount at a simple 
interest rate
( )
( )
1
1
n
n
C
i d C d n
i n
  −  =
+ 
( )( )1 1 1i d d n i n  −  +  =
1
1
i
d
i n
d
i
d n

= + 
 
 =
 − 
Compound discount
Matemáticas Financieras
( )nn dCC −= 10
( )
d
C
CC
C
ssD
s
ss
s
=
−
=
+
+
+
+ 1
1
1
1,
d is effective discount rate
d represents the cost of anticipating each monetary unit from the 
nominal
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Note: a temporary correspondence must exist between n and d, as both 
must be expressed using the same units (time)
Compound discount
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Equivalent discount rates
In compound discount the equivalent interest rates are not related 
in a proportional way
( ) ( )1 1
m
md d− = −
Equivalent discount rates
Two types of discount rates are said to be equivalent or 
indifferent using whichever chosen : they will produce the 
same discounted value of the same future value for the 
same period of time
( )
( )
1
1 1
1 1 m
m
m
m
d d
d d
 = − −
 
= − −
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Relationship between compund interest rate and compound discount 
rate
( )0 1
n
nC C d= −
COMPOUND DISCOUNT
( )0 1
n
nC C i
−
= +
COMPOUND INTEREST 
RATE
( ) ( )1 1
n n
n ni d C d C i
−
  − = +
( )( )1 1 1i d d i − + =
1
1
i
d
i
d
i
d

= +
 
 =
 −
Financial Mathematics