RENTA Aritmética Diferida 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,

Valor actual

k

C1

C2

Cn-3

Cn-2

Cn-1

Cn

|

···

|

|

|

···

|

|

|

|

0

k+0

k+1

k+2

k+n-3

k+n-2

k+n-1

k+n

R0

C· k/an | i

k

C

C

C

C

C

C

|

···

|

|

|

···

|

|

|

|

0

k+0

k+1

k+2

k+n-3

k+n-2

k+n-1

k+n

R1

d· k+1/an-1 | i

k+1

d

d

d

d

d

|

···

|

|

|

···

|

|

|

|

0

k+0

k+1

k+2

k+n-3

k+n-2

k+n-1

k+n

R2

d· k+2/an-2 | i

k+2

d

d

d

d

|

···

|

|

|

···

|

|

|

|

0

k+0

k+2

k+n-3

k+n-2

k+n-1

k+n

··· ···

··· ··· ···

Rn-3

d· k+n-3/a3 | i

k+n-3

d

d

d

|

···

|

|

|

···

|

|

|

|

0

k+0

k+n-3

k+n-2

k+n-1

k+n

Rn-2

d· k+n-2 /a2 | i

k+n-2

d

d

|

···

|

|

|

···

|

|

|

|

0

k+0

k+n-2

k+n-1

k+n

Rn-1

d· k+n-1 /a1 | i

k+n-1

d

|

···

|

|

|

···

|

|

|

|

0

k+0

k+n-1

k+n

k/(V0)n | i = C· k/an | i + d·∑s1,n-1k+s/an-s | i

VALOR Actual PostPagable

-

k/( V0)n | i = (1+i)-k( V0) n | i = (1+i)-k [( C + d / i + d·n ) an | i - d·n / i]

-

k/( V0)n | i = (1+i)-kA(C,d) n | i = (1+i)-k [( C + d / i + d·n ) an | i - d·n / i] = k/A(C,d) n | i

VALOR Actual PrePagable

-

k/( ··V0)n | i = (1+i) k/( V0) n | i = (1+i) (1+i)-k( V0) n | i = (1+i)-k+1 [( C + d / i + d·n ) an | i - d·n / i]

-

k/( ··V0)n | i = (1+i) k/A(C,d) n | i = (1+i)-k+1 [( C + d / i + d·n ) an | i - d·n / i] = k/ ··A(C,d) n | i