MATEMATICA FINANCIERA
UNIDAD 1: FASE 1 VALORAR EL DINERO EN EL TIEMPO
PRESENTADO POR: MARIA ELENA MARTINEZ COD MISAEL SIERRA COD: ARMANDO CALLEJAS COD: 15725149 ATILIO MANUEL HERNANDEZ CÓD: 7222608 TUTOR RENE CARLOS PAREDES !RUPO 102007_20
UNIVERSIDAD UNIVERS IDAD NACIONAL NACION AL A"IERTA A"IERTA # A DISTANCIA $UNAD% MARZO&2017
INTRODUCCION
1
MATEMATICA FINANCIERA
C'( )* +)*,'-*./( +) -+3+(+ -*,*' ,3.*'3 +3*--'))*- )*3 .'++(./*3 (+.+3*-/*3 *-* -+*)/*- ++-././'3 +) -+* + )* *+/.* /(*(./+-* .'( .'(.+'3 ; -)*3 + /(+-<3 3/)+= /(+-<3 .'+3'= *3*3 + /(+-<3= +(-+ '-'3> L*3 *+/.*3 /(*(./+-*3 3'( (*+(*)+3 (*+(*)+3 *-* '*- )* +'- +./3/(= .*(' 3+ -++(+ -++(+ ?*.+- (* /(@+-3/( ' -';+.'= '- *) '/@' +3 .'(@+(/+(+= + 3+ .'('.* )* /'-*(./* +) .'(.+' +) @*)'- +) /(+-' * -*@<3 +) /+'= .'' +)++(' (*+(*) + )*3 *+/.*3 /(*(./+-*3= *3B .'' +) -/(.//' + +/@*)+(./* ; +) -/(.//' + @/3/( +.'(/.*= + 3+ *)/.*( +( +) /*-** +.'(/.'= *-* ++.' + -*3)**- )'3 )'3 + .** *) -+3+(+ ' *) -'>
Actividades a desarrollar
2
MATEMATICA FINANCIERA
1.
D+3*--'))*- T*,)*3 + /(+-<3 3/)+ ; T*,)*3 + /(+-<3 .'+3' + +( -+3+3* * )'3 3//+(+3 /(+--'*(+3
A> A)/.*(' )* *3* + /(+-<3 *(*) 3/)+ +) 12=5 + ( .-</' + G 2>500>000>000 * 12 +3+3 + )+ -+3* )* +(/* A= .*) +3 +) @*)'- + )'3 /(+-+3+3 + +,+ **- )* .'*B* ENRECOL S>A>S *) <-/(' + )'3 12 +3+3
"> A)/.*(' )* *3* + /(+-<3 ++./@* *(*) +) 12=5 + ( .-</' + G 2>500>000>000 * 12 +3+3 + )+ -+3* )* +(/* A= .*) +3 +) @*)'- + )'3 /(+-+3+3 + +,+ **- )* .'*B* ENRECOL S>A>S *) <-/(' + )'3 12 +3+3
3
MATEMATICA FINANCIERA
C> A)/.*(' )* *3* + /(+-<3 *(*) 3/)+ +) 1=7 + ( .-</' + G 2>500>000>000 * 24 +3+3 + )+ -+3* )* +(/* "= .*) +3 +) @*)'- + )'3 /(+-+3+3 + +,+ **- )* .'*B* ENRECOL S>A>S *) <-/(' + )'3 24 +3+3
D. ¿Aplicando la tasa de interés efectiva anual del 13,7% de un crédito de $ 2.500.000.000 a 24 eses !ue le presta la entidad ", cual es el valor
4
MATEMATICA FINANCIERA
de los intereses !ue de#e paar la copa&a '()'*+ -.A.- al térino de los 24 eses
E> A)/.*(' )* *3* + /(+-<3 *(*) 3/)+ +) 11=9 + ( .-</' + G 2>500>000>000 * 6 +3+3 + )+ -+3* )* +(/* C= .*) +3 +) @*)'- + )'3 /(+-+3+3 + +,+ **- )* .'*B* ENRECOL S>A>S *) <-/(' + )'3 6 +3+3 CAPITAL PRINCIPAL
G 2>500>000>000=00
5
MATEMATICA FINANCIERA
TASA DE INTERES TIEMPO $MESES% CAPITA INICIA!"#
MES
1 2 4 5 6 7 8 9 10 11 12 1 14 15 16 17 18 19 20 21 22 2 24
G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G
11=90 6 INTERESES $ENERADOS
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G G
24>791>650=00 24>791>650=00
CAPITA %INA
G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G
INTERESES ACUMUADOS
G
24>791>650=00
G
49>58>00=00
G
74>74>950=00
G
99>166>600=00
G
12>958>250=00
G
148>749>900=00
G
17>541>550=00
G
198>>200=00
G
22>124>850=00
G
247>916>500=00
G
272>708>150=00
G
297>499>800=00
G
22>291>450=00
G
47>08>100=00
G
71>874>750=00
G
96>666>400=00
G
421>458>050=00
G
446>249>700=00
G
471>041>50=00
G
495>8>000=00
G
520>624>650=00
G
545>416>00=00
G G
570>207>950=00 594>999>600=00
6
MATEMATICA FINANCIERA
25 26 27 28 29 0 1 2 4 5 6 FINAL EN CUENTAS TOTAL POR CANCELAR
2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
G
24>791>650=00
2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00
G
619>791>250=00
G
644>582>900=00
G
669>74>550=00
G
694>166>200=00
G
718>957>850=00
G
74>749>500=00
G
768>541>150=00
G
79>2>800=00
G
818>124>450=00
G
842>916>100=00
G
867>707>750=00
G
892>499>400=00
G
892>499>400=00
G >92>499>400=00
/. ¿Aplicando la tasa de interés efectiva anual del 11,% de un crédito de $ 2.500.000.000 a 3 eses !ue le presta la entidad *, cual es el valor de los intereses !ue de#e paar la copa&a '()'*+ -.A.- al térino de los 3 eses
CAPITAL PRINCIPAL TASA DE INTERES TIEMPO (MESES)
MES
1 2
CAPITAL INICIAL($) $ 2.500.000.000,0 0 $ 2.523.535.000,0
$ 2.500.000.000,0 0 11,90% 36 INTERESES GENERADOS
CAPITAL FINAL
$ 23.535.000,00 $ 23.756.558,49
$ 2.523.535.000,00 $ 2.547.291.558,49
INTERESES ACUMULAD OS
7
MATEMATICA FINANCIERA
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17 18
0 $ 2.547.291.558,4 9 $ 2.571.271.761,2 2 $ 2.595.477.713,5 8 $ 2.619.911.540,7 8 $ 2.644.575.388,0 2 $ 2.669.471.420,7 3 $ 2.694.601.824,6 8 $ 2.719.968.806,2 6 $ 2.745.574.592,6 0 $ 2.771.421.431,8 1 $ 2.797.511.593,1 7 $ 2.823.847.367,3 1 $ 2.850.431.066,4 3 $ 2.877.265.024,4 9 $ 2.904.351.597,4 3 $ 2.931.693.163,3
$ 23.980.202,73
$ 2.571.271.761,22
$ 24.205.952,36
$ 2.595.477.713,58
$ 24.433.827,20
$ 2.619.911.540,78
$ 24.663.847,24
$ 2.644.575.388,02
$ 24.896.032,70
$ 2.669.471.420,73
$ 25.130.403,95
$ 2.694.601.824,68
$ 25.366.981,58
$ 2.719.968.806,26
$ 25.605.786,34
$ 2.745.574.592,60
$ 25.846.839,21
$ 2.771.421.431,81
$ 26.090.161,36
$ 2.797.511.593,17
$ 26.335.774,14
$ 2.823.847.367,31
$ 26.583.699,12
$ 2.850.431.066,43
$ 26.833.958,06
$ 2.877.265.024,49
$ 27.086.572,94
$ 2.904.351.597,43
$ 27.341.565,94 $ 27.598.959,44
$ 2.931.693.163,37 $ 2.959.292.122,81
8
MATEMATICA FINANCIERA
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33 34
7 $ 2.959.292.122,8 1 $ 2.987.150.898,8 5 $ 3.015.271.937,4 1 $ 3.043.657.707,4 3 $ 3.072.310.701,0 9 $ 3.101.233.434,0 3 $ 3.130.428.445,5 8 $ 3.159.898.298,9 6 $ 3.189.645.581,5 5 $ 3.219.672.905,0 5 $ 3.249.982.905,7 8 $ 3.280.578.244,8 6 $ 3.311.461.608,4 5 $ 3.342.635.708,0 4 $ 3.374.103.280,5 9 $ 3.405.867.088,8
$ 27.858.776,04
$ 2.987.150.898,85
$ 28.121.038,56
$ 3.015.271.937,41
$ 28.385.770,02
$ 3.043.657.707,43
$ 28.652.993,66
$ 3.072.310.701,09
$ 28.922.732,94
$ 3.101.233.434,03
$ 29.195.011,55
$ 3.130.428.445,58
$ 29.469.853,39
$ 3.159.898.298,96
$ 29.747.282,59
$ 3.189.645.581,55
$ 30.027.323,50
$ 3.219.672.905,05
$ 30.310.000,73
$ 3.249.982.905,78
$ 30.595.339,08
$ 3.280.578.244,86
$ 30.883.363,60
$ 3.311.461.608,45
$ 31.174.099,58
$ 3.342.635.708,04
$ 31.467.572,56
$ 3.374.103.280,59
$ 31.763.808,28 $ 32.062.832,77
$ 3.405.867.088,87 $ 3.437.929.921,65
9
MATEMATICA FINANCIERA
35
36 TOTAL POR CANCELA R
7 $ 3.437.929.921,6 5 $ 3.470.294.593,9 3
$ 32.364.672,28
$ 3.470.294.593,93
$ 32.669.353,31
$ 3.502.963.947,24
$ 3.502.963.947,24
. ¿Aplicando la tasa de interés anual siple del 14,2% de un crédito de $ 2.500.000.000 a 4 eses !ue le presta la entidad D, cual es el valor de los intereses !ue de#e paar la copa&a '()'*+ -.A.- al térino de los 4 eses G CAPITAL PRINCIPAL 2>500>000>000=00 TASA DE INTERES 14=20 TIEMPO $MESES% 48
MES
1 2 4 5 6 7 8 9 10 11 12 1 14
CAPITA INICIA!"#
INTERESES $ENERADOS
CAPITA %INA
INTERESES ACUMUADOS
G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G
G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G
G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G
G 29>500>000=00 G 59>000>000=00 G 88>500>000=00 G 118>000>000=00 G 147>500>000=00 G 177>000>000=00 G 206>500>000=00 G 26>000>000=00 G 265>500>000=00 G 295>000>000=00 G 24>500>000=00 G 54>000>000=00 G 8>500>000=00 G
10
MATEMATICA FINANCIERA
15 16 17 18 19 20 21 22 2 24 25 26 27 28 29 0 1 2 4 5 6 7 8 9 40
2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00
29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00
2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00
41>000>000=00 G 442>500>000=00 G 472>000>000=00 G 501>500>000=00 G 51>000>000=00 G 560>500>000=00 G 590>000>000=00 G 619>500>000=00 G 649>000>000=00 G 678>500>000=00 G 708>000>000=00 G 77>500>000=00 G 767>000>000=00 G 796>500>000=00 G 826>000>000=00 G 855>500>000=00 G 885>000>000=00 G 914>500>000=00 G 944>000>000=00 G 97>500>000=00 G 1>00>000>000=00 G 1>02>500>000=00 G 1>062>000>000=00 G 1>091>500>000=00 G 1>121>000>000=00 G 1>150>500>000=00 G 1>180>000>000=00
11
MATEMATICA FINANCIERA
41 42 4 44 45 46 47 48 FINAL EN CUENTAS TOTAL POR CANCELA R
G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00
G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00 G 29>500>000=00
G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00
G 1>209>500>000=00 G 1>29>000>000=00 G 1>268>500>000=00 G 1>298>000>000=00 G 1>27>500>000=00 G 1>57>000>000=00 G 1>86>500>000=00 G 1>416>000>000=00 G 1>416>000>000=00 G >916>000>000=00
H. ¿Aplicando la tasa de interés efectiva anual del 14,2% de un crédito de
$ 2.500.000.000 a 4 eses !ue le presta la entidad D, cual es el valor de los intereses !ue de#e paar la copa&a '()'*+ -.A.- al térino de los 4 eses
CAPITAL PRINCIPAL TASA DE INTERES TIEMPO (MESES)
MES
1
2
3
4
CAPITAL INICIAL($) $ 2.500.000.000,0 0 $ 2.527.817.500,0 0 $ 2.555.944.525,3 2 $ 2.584.384.520,0 6
$ 2.500.000.000,0 0 14,20% 48 INTERESES GENERADOS $ 27.817.500,00 $ 28.127.025,32 $ 28.439.994,73 $ 28.756.446,55
INTERESES ACUMULA CAPITAL FINAL DOS $ 2.527.817.500,0 0 $ 2.555.944.525,3 2 $ 2.584.384.520,0 6 $ 2.613.140.966,6 1
12
MATEMATICA FINANCIERA
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
$ 2.613.140.966,6 1 $ 2.642.217.386,1 5 $ 2.671.617.339,0 0 $ 2.701.344.425,1 3 $ 2.731.402.284,5 5 $ 2.761.794.597,7 7 $ 2.792.525.086,2 6 $ 2.823.597.512,9 0 $ 2.855.015.682,4 2 $ 2.886.783.441,9 2 $ 2.918.904.681,2 8 $ 2.951.383.333,6 7 $ 2.984.223.376,0 2 $ 3.017.428.829,5 3 $ 3.051.003.760,1 1 $ 3.084.952.278,9 5
$ 29.076.419,54 $ 29.399.952,86 $ 29.727.086,13 $ 30.057.859,42 $ 30.392.313,22 $ 30.730.488,49 $ 31.072.426,63 $ 31.418.169,53 $ 31.767.759,50 $ 32.121.239,36 $ 32.478.652,39 $ 32.840.042,35 $ 33.205.453,50 $ 33.574.930,59 $ 33.948.518,84 $ 34.326.264,01
$ 2.642.217.386,1 5 $ 2.671.617.339,0 0 $ 2.701.344.425,1 3 $ 2.731.402.284,5 5 $ 2.761.794.597,7 7 $ 2.792.525.086,2 6 $ 2.823.597.512,9 0 $ 2.855.015.682,4 2 $ 2.886.783.441,9 2 $ 2.918.904.681,2 8 $ 2.951.383.333,6 7 $ 2.984.223.376,0 2 $ 3.017.428.829,5 3 $ 3.051.003.760,1 1 $ 3.084.952.278,9 5 $ 3.119.278.542,9 6
13
MATEMATICA FINANCIERA
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
$ 3.119.278.542,9 6 $ 3.153.986.755,3 1 $ 3.189.081.165,9 3 $ 3.224.566.072,0 7 $ 3.260.445.818,7 5 $ 3.296.724.799,3 7 $ 3.333.407.456,2 2 $ 3.370.498.280,9 8 $ 3.408.001.815,3 5 $ 3.445.922.651,5 5 $ 3.484.265.432,9 0 $ 3.523.034.854,3 7 $ 3.562.235.663,1 9 $ 3.601.872.659,4 2 $ 3.641.950.696,5 0 $ 3.682.474.681,9 0
$ 34.708.212,35 $ 35.094.410,63 $ 35.484.906,13 $ 35.879.746,68 $ 36.278.980,63 $ 36.682.656,84 $ 37.090.824,77 $ 37.503.534,37 $ 37.920.836,20 $ 38.342.781,34 $ 38.769.421,47 $ 39.200.808,82 $ 39.636.996,22 $ 40.078.037,08 $ 40.523.985,40 $ 40.974.895,79
$ 3.153.986.755,3 1 $ 3.189.081.165,9 3 $ 3.224.566.072,0 7 $ 3.260.445.818,7 5 $ 3.296.724.799,3 7 $ 3.333.407.456,2 2 $ 3.370.498.280,9 8 $ 3.408.001.815,3 5 $ 3.445.922.651,5 5 $ 3.484.265.432,9 0 $ 3.523.034.854,3 7 $ 3.562.235.663,1 9 $ 3.601.872.659,4 2 $ 3.641.950.696,5 0 $ 3.682.474.681,9 0 $ 3.723.449.577,6 9
14
MATEMATICA FINANCIERA
37
38
39
40
41
42
43
44
45
46
47
48 TOTAL POR CANCELA R
$ 3.723.449.577,6 9 $ 3.764.880.401,1 4 $ 3.806.772.225,3 6 $ 3.849.130.179,9 1 $ 3.891.959.451,4 2 $ 3.935.265.284,2 4 $ 3.979.052.981,0 6 $ 4.023.327.903,5 8 $ 4.068.095.473,1 6 $ 4.113.361.171,4 9 $ 4.159.130.541,2 5 $ 4.205.409.186,7 8
$ 41.430.823,45 $ 41.891.824,22 $ 42.357.954,55 $ 42.829.271,51 $ 43.305.832,82 $ 43.787.696,82 $ 44.274.922,52 $ 44.767.569,58 $ 45.265.698,33 $ 45.769.369,76 $ 46.278.645,53 $ 46.793.588,02
$ 3.764.880.401,1 4 $ 3.806.772.225,3 6 $ 3.849.130.179,9 1 $ 3.891.959.451,4 2 $ 3.935.265.284,2 4 $ 3.979.052.981,0 6 $ 4.023.327.903,5 8 $ 4.068.095.473,1 6 $ 4.113.361.171,4 9 $ 4.159.130.541,2 5 $ 4.205.409.186,7 8 $ 4.252.202.774,8 0 $ 4.252.202.774,8 0
. ¿Aplicando la tasa de interés anual siple del 14,3% de un crédito de $ 2.500.000.000 a 0 eses !ue le presta la entidad ', cual es el valor de los intereses !ue de#e paar la copa&a '()'*+ -.A.- al térino de los 0 eses TASA DE INTERES
1=0
15
MATEMATICA FINANCIERA
TIEMPO $MESES%
MES
1 2 4 5 6 7 8 9 10 11 12 1 14 15 16 17 18 19 20 21 22 2 24
60
CAPITA INICIA!"#
INTERESES $ENERADOS
INTERESES CAPITA %INA ACUMUADOS
G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00
G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50
G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00
G 27>708>2=50 G 55>416>665=00 G 8>124>997=50 G 110>8>0=00 G 18>541>662=50 G 166>249>995=00 G 19>958>27=50 G 221>666>660=00 G 249>74>992=50 G 277>08>25=00 G 04>791>657=50 G 2>499>990=00 G 60>208>22=50 G 87>916>655=00 G 415>624>987=50 G 44>>20=00 G 471>041>652=50 G 498>749>985=00 G 526>458>17=50 G 554>166>650=00 G 581>874>982=50 G 609>58>15=00 G 67>291>647=50 G 664>999>980=00
16
MATEMATICA FINANCIERA
25 26 27 28 29 0 1 2 4 5 6 7 8 9 40 41 42 4 44 45 46 47 48 49 50 51
G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G
G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G
G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G
G 692>708>12=50 G 720>416>645=00 G 748>124>977=50 G 775>8>10=00 G 80>541>642=50 G 81>249>975=00 G 858>958>07=50 G 886>666>640=00 G 914>74>972=50 G 942>08>05=00 G 969>791>67=50 G 997>499>970=00 G 1>025>208>02=50 G 1>052>916>65=00 G 1>080>624>967=50 G 1>108>>00=00 G 1>16>041>62=50 G 1>16>749>965=00 G 1>191>458>297=50 G 1>219>166>60=00 G 1>246>874>962=50 G 1>274>58>295=00 G 1>02>291>627=50 G 1>29>999>960=00 G 1>57>708>292=50 G 1>85>416>625=00 G
17
MATEMATICA FINANCIERA
52 5 54 55 56 57 58 59 60 FINAL EN CUENTAS TOTAL POR CANCELA R
2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00
27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50 G 27>708>2=50
2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00 G 2>500>000>000=00
1>41>124>957=50 G 1>440>8>290=00 G 1>468>541>622=50 G 1>496>249>955=00 G 1>52>958>287=50 G 1>551>666>620=00 G 1>579>74>952=50 G 1>607>08>285=00 G 1>64>791>617=50 G 1>662>499>950=00 G 1>662>499>950=00 G 4>162>499>950=00
. ¿Aplicando la tasa de interés efectiva anual del 14,3% de un crédito de $ 2.500.000.000 a 0 eses !ue le presta la entidad ', cual es el valor de los intereses !ue de#e paar la copa&a '()'*+ -.A.- al térino de los 0 eses
CAPITAL PRINCIPAL TASA DE INTERES TIEMPO (MESES)
MES
CAPITAL INICIAL($)
1
$ 2.500.000.000,00
2
$ 2.526.150.000,00
3
$ 2.552.573.529,00
$ 2.500.000.000 ,00 13,30% 60
INTERESES GENERADOS
CAPITAL FINAL $ $ 2.526.150.000, 26.150.000,00 00 $ $ 2.552.573.529, 26.423.529,00 00 $ $ 2.579.273.448, 26.699.919,11 11
INTERESE S ACUMULA DOS
18
MATEMATICA FINANCIERA
4
$ 2.579.273.448,11
$ 26.979.200,27
5
$ 2.606.252.648,38
$ 27.261.402,70
6
$ 2.633.514.051,08
$ 27.546.556,97
7
$ 2.661.060.608,06
$ 27.834.693,96
8
$ 2.688.895.302,02
$ 28.125.844,86
9
$ 2.717.021.146,88
$ 28.420.041,20
10
$ 2.745.441.188,07
$ 28.717.314,83
11
$ 2.774.158.502,90
$ 29.017.697,94
12
$ 2.803.176.200,84
$ 29.321.223,06
13
$ 2.832.497.423,90
$ 29.627.923,05
14
$ 2.862.125.346,96
$ 29.937.831,13
15
$ 2.892.063.178,08
$ 30.250.980,84
16
$ 2.922.314.158,93
$ 30.567.406,10
17
$ 2.952.881.565,03
$ 30.887.141,17
18
$ 2.983.768.706,20
$ 31.210.220,67
19
$ 3.014.978.926,87
$ 31.536.679,58
$ 2.606.252.648, 38 $ 2.633.514.051, 08 $ 2.661.060.608, 06 $ 2.688.895.302, 02 $ 2.717.021.146, 88 $ 2.745.441.188, 07 $ 2.774.158.502, 90 $ 2.803.176.200, 84 $ 2.832.497.423, 90 $ 2.862.125.346, 96 $ 2.892.063.178, 08 $ 2.922.314.158, 93 $ 2.952.881.565, 03 $ 2.983.768.706, 20 $ 3.014.978.926, 87 $ 3.046.515.606, 44
19
MATEMATICA FINANCIERA
20
$ 3.046.515.606,44
$ 31.866.553,24
21
$ 3.078.382.159,68
$ 32.199.877,39
22
$ 3.110.582.037,08
$ 32.536.688,11
23
$ 3.143.118.725,18
$ 32.877.021,87
24
$ 3.175.995.747,05
$ 33.220.915,51
25
$ 3.209.216.662,56
$ 33.568.406,29
26
$ 3.242.785.068,85
$ 33.919.531,82
27
$ 3.276.704.600,67
$ 34.274.330,12
28
$ 3.310.978.930,80
$ 34.632.839,62
29
$ 3.345.611.770,41
$ 34.995.099,12
30
$ 3.380.606.869,53
$ 35.361.147,86
31
$ 3.415.968.017,39
$ 35.731.025,46
32
$ 3.451.699.042,85
$ 36.104.771,99
33
$ 3.487.803.814,84
$ 36.482.427,90
34
$ 3.524.286.242,74
$ 36.864.034,10
35
$ 3.561.150.276,84
$ 37.249.631,90
$ 3.078.382.159, 68 $ 3.110.582.037, 08 $ 3.143.118.725, 18 $ 3.175.995.747, 05 $ 3.209.216.662, 56 $ 3.242.785.068, 85 $ 3.276.704.600, 67 $ 3.310.978.930, 80 $ 3.345.611.770, 41 $ 3.380.606.869, 53 $ 3.415.968.017, 39 $ 3.451.699.042, 85 $ 3.487.803.814, 84 $ 3.524.286.242, 74 $ 3.561.150.276, 84 $ 3.598.399.908, 73
20
MATEMATICA FINANCIERA
36
$ 3.598.399.908,73
$ 37.639.263,05
37
$ 3.636.039.171,78
$ 38.032.969,74
38
$ 3.674.072.141,52
$ 38.430.794,60
39
$ 3.712.502.936,12
$ 38.832.780,71
40
$ 3.751.335.716,83
$ 39.238.971,60
41
$ 3.790.574.688,43
$ 39.649.411,24
42
$ 3.830.224.099,67
$ 40.064.144,08
43
$ 3.870.288.243,75
$ 40.483.215,03
44
$ 3.910.771.458,78
$ 40.906.669,46
45
$ 3.951.678.128,24
$ 41.334.553,22
46
$ 3.993.012.681,46
$ 41.766.912,65
47
$ 4.034.779.594,11
$ 42.203.794,55
48
$ 4.076.983.388,66
$ 42.645.246,25
49
$ 4.119.628.634,91
$ 43.091.315,52
50
$ 4.162.719.950,43
$ 43.542.050,68
51
$ 4.206.262.001,11
$ 43.997.500,53
$ 3.636.039.171, 78 $ 3.674.072.141, 52 $ 3.712.502.936, 12 $ 3.751.335.716, 83 $ 3.790.574.688, 43 $ 3.830.224.099, 67 $ 3.870.288.243, 75 $ 3.910.771.458, 78 $ 3.951.678.128, 24 $ 3.993.012.681, 46 $ 4.034.779.594, 11 $ 4.076.983.388, 66 $ 4.119.628.634, 91 $ 4.162.719.950, 43 $ 4.206.262.001, 11 $ 4.250.259.501, 64
21
MATEMATICA FINANCIERA
52
$ 4.250.259.501,64
$ 44.457.714,39
53
$ 4.294.717.216,03
$ 44.922.742,08
54
$ 4.339.639.958,11
$ 45.392.633,96
55
$ 4.385.032.592,07
$ 45.867.440,91
56
$ 4.430.900.032,98
$ 46.347.214,35
57
$ 4.477.247.247,33
$ 46.832.006,21
58
$ 4.524.079.253,54
$ 47.321.868,99
59
$ 4.571.401.122,53
$ 47.816.855,74
$ 4.619.217.978,27
$ 48.317.020,05
60 TOTAL POR CANCEL AR
2.
$ 4.294.717.216, 03 $ 4.339.639.958, 11 $ 4.385.032.592, 07 $ 4.430.900.032, 98 $ 4.477.247.247, 33 $ 4.524.079.253, 54 $ 4.571.401.122, 53 $ 4.619.217.978, 27 $ 4.667.534.998, 32 $ 4.667.534.998, 32
R+*)/*- ( C&adro co'(arativo de alter)ativas de *i)a)ciaci+) + .'(+(* )'3 3//+(+3 +)++('3
22
MATEMATICA FINANCIERA
,.
R+*)/*- ( %l&-o de *o)dos *-* .** (' + )'3 '.?' $8% +3.+(*-/'3 -';+.*'3
Tabla de evaluación de proyectos de inversión Esce)ari o
%l&-os )etos Aos 1 al /
I)versi+)
1
2
$ E!"# 2.500.000.00 &' 1 0
3
4
5
$
E3.+(*-/' 2.500.000.00 1 2 0,00
2
PN
TIR
$ 835.730.000,0 0 $ 919.011.905,9 0 $ 1.025.863.308, 00 $ 28,78 138.426.132 % $ 1.173.362.482, 20 $ 1.380.329.122, 70 $ 5.334.296.818, 80 $ $ 875.044.200,0 30,17 61.983.515,0 0 % 0 $
Tasa de Relaci+ desc&e) ) C to
0,94
31,50 %
0,98
31,40 %
23
MATEMATICA FINANCIERA
3
4
5
1
2
$ E3.+(*-/' 2.500.000.00 0,00
3
4
5
E3.+(*-/' $ 4 2.500.000.00 1 0,00 2
3
4
5
969.459.744,6 0 $ 1.072.711.720, 40 $ 1.189.141.402, 60 $ 1.327.467.540, 70 $ 5.433.824.608, 30 $ 879.456.000,0 0 $ 977.772.196,5 0 $ 1.088.295.578, 20 $ 30,71 5.469.919,00 % $ 1.208.304.593, 10 $ 1.348.464.383, 20 $ 5.502.292.751, 00 $ $ 28,75 870.722.500,0 63.582.974,0 % 0 0 $ 948.879.568,1 0 $ 1.036.495.333, 50 $ 1.133.211.684, 40 $ 1.249.834.622, 00 $
1
0,97
30,60 %
30,00 %
24
MATEMATICA FINANCIERA
1
2
$ E3.+(*-/' 2.500.000.00 5 0,00
3
4
5
1
2
$ E3.+(*-/' 2.500.000.00 6 0,00
3
4
5
E3.+(*-/' $ 7 2.500.000.00 1 0,00 2
3 4
5.239.143.708, 00 $ 889.209.100,0 0 $ 951.801.982,9 0 $ 1.023.090.560, $ 60 28,49 25.846.232,0 % $ 0 1.104.135.810, 60 $ 1.205.925.782, 90 $ 5.174.163.237, 00 $ 969.570.000,0 0 $ 1.041.912.125, 80 $ 1.120.667.433, $ 50 32,86 93.202.244,0 % $ 0 1.204.326.002, 30 $ 1.305.901.312, 80 $ 5.642.376.874, 40 $ $ 33,58 965.331.200,0 79.103.187,0 % 0 0 $ 1.042.342.824, 90 $ 1.136.522.329, 30 $
0,99
29%
1,04
31%
1,03
32%
25
MATEMATICA FINANCIERA
5
1
2
$ E3.+(*-/' 2.500.000.00 8 0,00
3
4
5
1.245.780.697, 80 $ 1.382.896.884, 30 $ 5.772.873.936, 30 $ 965.268.000,0 0 $ 1.046.495.098, 80 $ 1.136.570.553, $ 40 71,15 3.257.442.85 % $ 9,00 7.132.704.252, 20 $ 7.645.635.108, 70 $ 17.926.673.01 3,10
2,3
34%
CONCUSIONES
D+3<3 + -+*)/*- +3+ -*,*' .')*,'-*/@' ?+'3 '/' .'-+(+- )*3 +/.*3 + )* -/+-* (/* +) .-3'> A) +3*--'))*- +3'3 ++-././'3 ('3 -+*-*'3 +) +3/*(+ 3+ -+*-* *-* 3 -+,* (*./'(*) ; *-* ?*.+- -*(3+-+(./* + 33 3*,+-+3 *) +('-(' +( +) + 3+ +3++*> M*(+*- )*3 /3/(*3 ?+--*/+(*3 /)/**3 *-* )* )//*./( + )'3 /(+-+3+3 +( 3/)+ ; .'+3'= *-* +))' +3 (+.+3*-/' ?*.+- /@+-3'3 *))+-+3 *-* +3*--'))*- +3-+*3> E3 /'-*(+ +(+- +( .+(* ; 3*,+- )//*- )*3 *3*3 + /(+-<3 + *.+-' *) /' + /(+-<3 '-+ + +3' ++(+ + )'3 .'3'3 /(*(./+-'3 (' 3+ 3,*( *(' .*(' + /(@+-3/( 3+ -**>
26
MATEMATICA FINANCIERA
REFERENCIAS "I"LIO!RFICAS
•
•
C*,+*= L K C*3-/))(= J $2012%> M*+/.*3 /(*(./+-*3> "*--*(/))*= C'): U(/@+-3/* +) N'-+= R+.+-*' + ?:&&,/,)/'+.*@/-*)>(*>+>.':2048&)'/( 3+--'@++'-K*33*(+0*0K-)?:&&,/,)/'+.*@/-*)>(*>+>.':2051&)'/ (>*3/-+.-+K,()+,KAN710226K)*(+3K3/++3)/@+ M+*= J $2010%> E@*)*./( /(*(./+-* + -';+.'3> "'': E.'+ +/./'(+3= R+.+-*' + ?:&&,/,)/'+.*@/-*)>(*>+>.':2048&)'/( 3+--'@++'-K*33*(+0*0K-)?:&&,/,)/'+.*@/-*)>(*>+>.':2051&)'/ (>*3/-+.-+K,()+,KAN478467K)*(+3K3/++3)/@+
27
MATEMATICA FINANCIERA
•
P*-++3 S*@+= R> $ 28=11=2016%> I(+-+3 ; *3*3 + /(+-+3> QP/(* +,> R+.+-*' +: ?:&&?)>?*()+>(+&10596&9128
28
