RENTA Aritmética Anticipada Temporal

C1 = C

C2 = C+d

C3 = C+2d

···

Cn-2 = C+(n-3)d

Cn-1 = C+(n-2)d

Cn = C+(n-1)d

-

La descomponemos como suma de rentas ctes, una de cuntía C y n-1 de cuantía d,

C1

C2

Cn-3

Cn-2

Cn-1

Cn

h

Valor final

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···

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···

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0

1

2

n-3

n-2

n-1

n

h+n

R0

C

C

C

C

C

C

h

C· h/sn | i

|

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···

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···

|

0

1

2

n-3

n-2

n-1

n

h+n

R1

d

d

d

d

d

h

d· h/sn-1 | i

|

|

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···

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···

|

0

1

2

n-3

n-2

n-1

n

h+n

R2

d

d

d

d

h

d· h/sn-2 | i

|

|

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···

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|

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···

|

0

2

n-3

n-2

n-1

n

h+n

··· ··· ···

··· ···

Rn-3

d

d

d

h

d· h/s3 | i

|

|

|

···

|

|

|

|

···

|

0

n-3

n-2

n-1

n

h+n

Rn-2

d

d

h

d· h /s2 | i

|

|

|

···

|

|

|

|

···

|

0

n-2

n-1

n

h+n

Rn-1

d

h

d· h/s1 | i

|

|

|

···

|

|

|

|

···

|

0

n-1

n

h+n

C· h/sn | i  +  d·∑s1,n-1h/sn-s | i = h/( Vn)n | i

VALOR Final PostPagable

-

h/( Vn)n | i = (1+i)h·( Vn) n | i = (1+i)h·[ ( C + d / i ) sn | i - d·n / i ]

-

h/( Vn)n | i = (1+i)h ·S(C,d) n | i = (1+i)h·[ ( C + d / i ) sn | i - d·n / i ] = h/ S(C,d) n | i

VALOR Final PrePagable

-

h/( ··Vn)n | i = (1+i) · h/( Vn) n | i = (1+i)·(1+i)h·( Vn) n | i = (1+i)h+1·[ ( C + d / i ) sn | i - d·n / i ]

-

h/( ··Vn)n | i = (1+i) · h/S(C,d) n | i = (1+i)h+1·[ ( C + d / i ) sn | i - d·n / i ] = h/ ··S(C,d) n | i