1L398,901.543%5,000.00100,000.00NOCUOTAINTERESABONOSALDO0398,901.541100,000.0011,967.0588,032.95310,868.592105,000.009,326.0695,673.94215,194.653110,000.006,455.84103,544.16111,650.494115,000.003,349.51111,650.490.033,323,645.980.0310,0002,500,000NOCUOTAINTERESABONOSALDO033,323,645.9812,500,000999709.3795356521,500,29131,823,35522,490,000954700.6609217211,535,29930,288,05632,480,000908641.6807493731,571,35828,716,69842,470,000861500.9311718541,608,49927,108,19952,460,000813245.959107011,646,75425,461,44562,450,000763843.337880221,686,15723,775,28872,440,000713258.6380166271,726,74122,048,54782,430,000661456.3971571261,768,54420,280,00392,420,000608400.0890718391,811,60018,468,403102,410,000554052.0917439951,855,94816,612,455112,400,000498373.6544963141,901,62614,710,829122,390,000441324.8641312041,948,67512,762,154132,380,000382864.610055141,997,13510,765,018142,370,000322950.5483567942,047,0498,717,969152,360,000261539.0648074982,098,4616,619,508162,350,000198585.2367517232,151,4154,468,093172,340,000134042.7938542752,205,9572,262,136182,330,00067864.07766990292,262,1360.0Una vivienda se esta cancelando con 18 cuotas mensuales que decrecen en $10.000 cada mes, siendo la primera cuota de $2.500.000. Si la tasa de financiacion que se esta cobrando es del 3% mensual. Cul es el valor de contado de la vivienda?

GRADIENTE LINEAL CRECIENTE (PRESENTE)Una deuda se esta cancelando con 4 cuotas mensuales que aumentan cada mes en $5.000. El valor de la primera cuota es $100.000. Si la tasa de interes que se cobra es 3% mensual. Calcular el valor de la deuda

2L3,900,0002.50%20,000.00122,553,5805,140,230.2020,0000.02550,000,000NOCUOTAINTERESABONOSALDONOCUOTAINTERESABONOSALDO0122,553,580013,900,0003,063,840836,160121,717,42015,360,230130,7375,229,4930.023,880,0003,042,935837,064120,880,35525,340,230257,7985,082,4325,229,49333,860,0003,022,009837,991120,042,36435,320,230381,2724,938,95810,311,92543,840,0003,001,059838,941119,203,42345,300,230501,2474,798,98415,250,88353,820,0002,980,086839,914118,363,50955,280,230617,8074,662,42320,049,86763,800,0002,959,088840,912117,522,59665,260,230731,0374,529,19324,712,29073,780,0002,938,065841,935116,680,66175,240,230841,0174,399,21329,241,48383,760,0002,917,017842,983115,837,67885,220,230947,8274,272,40333,640,69693,740,0002,895,942844,058114,993,62095,200,2301,051,5454,148,68637,913,098103,720,0002,874,840845,159114,148,460105,180,2301,152,2444,027,98642,061,784113,700,0002,853,712846,288113,302,172115,160,2301,250,0003,910,23046,089,770123,680,0002,832,554847,446112,454,726125140230.2050,000,000133,660,0002,811,368848,632111,606,094143,640,0002,790,152849,848110,756,247153,620,0002,768,906851,094109,905,153163,600,0002,747,629852,371109,052,782173,580,0002,726,320853,680108,199,101183,560,0002,704,978855,022107,344,079193,540,0002,683,602856,398106,487,681203,520,0002,662,192857,808105,629,873213,500,0002,640,747859,253104,770,620223,480,0002,619,265860,734103,909,885233,460,0002,597,747862,253103,047,633243,440,0002,576,191863,809102,183,823253,420,0002,554,596865,404101,318,419263,400,0002,532,960867,040100,451,379273,380,0002,511,284868,71599,582,664283,360,0002,489,567870,43398,712,231293,340,0002,467,806872,19497,840,036303,320,0002,446,001873,99996,966,037313,300,0002,424,151875,84996,090,188323,280,0002,402,255877,74595,212,443333,260,0002,380,311879,68994,332,754343,240,0002,358,319881,68193,451,073353,220,0002,336,277883,72392,567,350363,200,0002,314,184885,81691,681,534373,180,0002,292,038887,96290,793,572383,160,0002,269,839890,16189,903,411393,140,0002,247,585892,41589,010,996403,120,0002,225,275894,72588,116,271413,100,0002,202,907897,09387,219,178423,080,0002,180,479899,52186,319,658433,060,0002,157,991902,00985,417,649443,040,0002,135,441904,55984,513,090453,020,0002,112,827907,17383,605,918463,000,0002,090,148909,85282,696,066472,980,0002,067,402912,59881,783,467482,960,0002,044,587915,41380,868,054492,940,0002,021,701918,29979,949,755502,920,0001,998,744921,25679,028,499512,900,0001,975,712924,28778,104,212522,880,0001,952,605927,39577,176,817532,860,0001,929,420930,58076,246,238542,840,0001,906,156933,84475,312,393552,820,0001,882,810937,19074,375,203562,800,0001,859,380940,62073,434,583572,780,0001,835,865944,13572,490,448582,760,0001,812,261947,73971,542,709592,740,0001,788,568951,43270,591,277602,720,0001,764,782955,21869,636,059612,700,0001,740,901959,09968,676,960622,680,0001,716,924963,07667,713,884632,660,0001,692,847967,15366,746,732642,640,0001,668,668971,33265,775,400652,620,0001,644,385975,61564,799,785662,600,0001,619,995980,00563,819,780672,580,0001,595,494984,50562,835,274682,560,0001,570,882989,11861,846,156692,540,0001,546,154993,84660,852,310702,520,0001,521,308998,69259,853,618712,500,0001,496,3401,003,66058,849,958722,480,0001,471,2491,008,75157,841,207732,460,0001,446,0301,013,97056,827,237742,440,0001,420,6811,019,31955,807,918752,420,0001,395,1981,024,80254,783,116762,400,0001,369,5781,030,42253,752,694772,380,0001,343,8171,036,18352,716,511782,360,0001,317,9131,042,08751,674,424792,340,0001,291,8611,048,13950,626,285802,320,0001,265,6571,054,34349,571,942812,300,0001,239,2991,060,70148,511,241822,280,0001,212,7811,067,21947,444,022832,260,0001,186,1011,073,89946,370,122842,240,0001,159,2531,080,74745,289,375852,220,0001,132,2341,087,76644,201,610862,200,0001,105,0401,094,96043,106,650872,180,0001,077,6661,102,33442,004,316882,160,0001,050,1081,109,89240,894,424892,140,0001,022,3611,117,63939,776,785902,120,000994,4201,125,58038,651,204912,100,000966,2801,133,72037,517,485922,080,000937,9371,142,06336,375,422932,060,000909,3861,150,61435,224,807942,040,000880,6201,159,38034,065,427952,020,000851,6361,168,36432,897,063962,000,000822,4271,177,57331,719,490971,980,000792,9871,187,01330,532,477981,960,000763,3121,196,68829,335,789991,940,000733,3951,206,60528,129,1841001,920,000703,2301,216,77026,912,4131011,900,000672,8101,227,19025,685,2241021,880,000642,1311,237,86924,447,3541031,860,000611,1841,248,81623,198,5381041,840,000579,9631,260,03721,938,5021051,820,000548,4631,271,53720,666,9641061,800,000516,6741,283,32619,383,6381071,780,000484,5911,295,40918,088,2291081,760,000452,2061,307,79416,780,4351091,740,000419,5111,320,48915,459,9461101,720,000386,4991,333,50114,126,4451111,700,000353,1611,346,83912,779,6061121,680,000319,4901,360,51011,419,0961131,660,000285,4771,374,52310,044,5731141,640,000251,1141,388,8868,655,6881151,620,000216,3921,403,6087,252,0801161,600,000181,3021,418,6985,833,3821171,580,000145,8351,434,1654,399,2161181,560,000109,9801,450,0202,949,1971191,540,00073,7301,466,2701,482,9271201,520,00037,0731,482,927(0)

GRADIENTE LINEAL DECRECIENTE (CUOTA)Una vivienda con valor de $122.553.580,07 se esta cancelando con 120 cuotas mensuales que decrecen en $20.000 cada mes, si la tasa es del 2,5% mensual calcular el valor de la primera cuota?

3L5,800,0003%40,000.00550,000.00NOCUOTAINTERESABONOSALDO05,800,000.001550,000.00174,000.00376,000.005,424,000.002590,000.00162,720.00427,280.004,996,720.003630,000.00149,901.60480,098.404,516,621.604670,000.00135,498.65534,501.353,982,120.255710,000.00119,463.61590,536.393,391,583.866750,000.00101,747.52648,252.482,743,331.377790,000.0082,299.94707,700.062,035,631.318830,000.0061,068.94768,931.061,266,700.259870,000.0038,001.01831,998.99434,701.2610910,000.0013,041.04896,958.96(462,257.70)

GRADIENTE LINEAL CRECIENTE (TIEMPO)Con cuantos pagos mensuales, que aumenten en $40.000 cada mes, se cancela una obligacion de $5.800.000, si se cobra una tasa de interes del 3% mensual y la primera cuota es de $550.000 Cal es el valor de la ultima cuota?

4L3,000,0004.51%10,000.00500,000.00300,000NOCUOTAINTERESABONOSALDONOCUOTAINTERESABONOSALDO0300,0002,700,00001500,000121,887378,1132,321,88712510,000104,818405,1821,916,70523520,00086,526433,4741,483,23134530,00066,958463,0421,020,18945540,00046,055493,945526,24456550,00023,756526,24406

Una propiedad por valor de $22.000.000 se financia a una tasa de interes del 2,5% mensual, por medio de una cuota inciial y 12 cuotas mensuales crecientes cada mes en un 1%. Si la primera cuota es de $2.000.000 Cul es el valor de la cuota inicial?

22,000,0000.010.0252,000,000380,984.34NOCUOTAINTERESABONOSALDO0380,984.3421,619,01612,000,000540475.3914300581,459,52520,159,49122020000503987.276215811,516,01318,643,47832040200466086.9581212051,574,11317,069,36542060602426734.1320742351,633,86815,435,49752081208.02385887.4353760911,695,32113,740,17762102020.1002343504.4207604931,758,51611,981,66172123040.301202299541.5287745061,823,49910,158,16282144270.70421402253954.0594638181,890,3178,267,84692165713.41125616206696.1433450631,959,0176,308,828102187370.54536872157720.7116472862,029,6504,279,179112209244.25082241106979.465804252,102,2652,176,914122231336.6933306354422.84617879592,176,9140.0

GRADIENTE LINEAL CRECIENTE (TASA DE INTERES)Que tasa de interes le reconocen por financiar un electrodomestico que tiene un valor de contado de $3.000.000, por medio de una cuota inicial del 10% y 6 cuotas mensuales crecientes en $10.000, si el valor de la primera cuota es $500.000

5L800,0000.90%62,250.5916,000,000200,0000.01426,415.665,000,000NODEPOSITOINTERESDEP+INTSALDONODEPOSITOINTERESDEP+INTSALDO0800,000800,0000200,000200,0001862,2517,200869,4511,669,4511226,4162,800229,216429,2162924,50115,025939,5262,608,9772252,8316,009258,840688,0563986,75223,4811,010,2333,619,2093279,2479,633288,880976,93641,049,00232,5731,081,5754,700,7854305,66313,677319,3401,296,27551,111,25342,3071,153,5605,854,3455332,07818,148350,2261,646,50261,173,50452,6891,226,1937,080,5376358,49423,051381,5452,028,04771,235,75463,7251,299,4798,380,0167384,91028,393413,3022,441,34981,298,00575,4201,373,4259,753,4418411,32534,179445,5042,886,85391,360,25587,7811,448,03611,201,4779437,74140,416478,1573,365,010101,422,506100,8131,523,31912,724,79710464,15747,110511,2673,876,276111,484,756114,5231,599,28014,324,07611490,57254,268544,8404,421,117121,547,007128,9171,675,92416,000,00012516,98861,896578,8835,000,000

GRADIENTE LINEAL CRECIENTE (FUTURO - GRADIENTE)Si se realizan depositos mensuales comenzando hoy por valor de $800.000 Cual debe ser el incremento constante si la entidad financiera reconoce una tasa del 0,9% mensual para tener acumulados en un ao $16.000.000?

1G5,000,0003.00%563,921.302.70%NOCUOTAINTERESABONOSALDO05,000,0001563,921135,000428,9214,571,0792580,839123,419457,4204,113,6593598,264111,069487,1953,626,4644616,21297,915518,2983,108,1665634,69883,920550,7782,557,3886653,73969,049584,6901,972,6987673,35253,263620,0891,352,6108693,55236,520657,032695,5789714,35918,781695,578(0)Una deuda por valor de $10.000.000 a una tasa del 2,5% mensual, se va a cancelar con 6 cuotas mensuales que crecen $10.000 cada mes. Cul es el valor de la primera cuota?

10,000,0000.0251,791,219.6410,000NOCUOTAINTERESABONOSALDO010,000,00011,791,220250,0001,541,2208,458,78021,801,220211,4701,589,7506,869,03031,811,220171,7261,639,4945,229,53641,821,220130,7381,690,4813,539,05551,831,22088,4761,742,7431,796,31261,841,22044,9081,796,3120.0

GRADIENTE GEOMETRICO CRECIENTE (CUOTA)Se desea financiar una deuda de $5.000.000 con 9 pagos mensuales que aumentan en un 3% cada mes, suponiendo una tasa de interes del 2,7% mensual. Halle el valor del primer pago

2G7,500,00013.87%300,0001.00%NOCUOTAINTERESABONOSALDO07,500,0001300,00075,000225,0007,275,0002341,61072,750268,8607,006,1403388,99170,061318,9306,687,2104442,94466,872376,0726,311,1385504,38163,111441,2695,869,8696574,33858,699515,6395,354,2307653,99953,542600,4564,753,7738744,70847,538697,1704,056,6039847,99940,566807,4333,249,17010965,61632,492933,1252,316,045111,099,54723,1601,076,3871,239,658121,252,05412,3971,239,6580

GRADIENTE GEOMETRICO CRECIENTE (GRADIENTE)Una entidad presta a un cliente $7.500.000 con una tasa de interes del 1% mensual. El deudor tiene un plazo de 12 meses para cancelar la deuda. Si la primera cuota es de $300.000 y vence al final del primer mes. Cal debe ser el porcentaje de reajuste mensual de la cuota para terminar de cancelar la deuda?

3G17,200,0002.50%2,500,0003.00%NODEPOSITOINTERESDEP+INTSALDO017,200,00017,200,0001(2,500,000)516,000(1,984,000)15,216,0002(2,437,500)456,480(1,981,020)13,234,9803(2,376,563)397,049(1,979,513)11,255,4674(2,317,148)337,664(1,979,484)9,275,9825(2,259,220)278,279(1,980,940)7,295,0426(2,202,739)218,851(1,983,888)5,311,1547(2,147,671)159,335(1,988,336)3,322,8188(2,093,979)99,685(1,994,294)1,328,5249(2,041,630)39,856(2,001,774)(673,250)

GRADIENTE GEOMETRICO DECRECIENTE (TIEMPO)Durante cuantos meses podre hacer retiros de fin de mes de tal manera que cada retiro sea el 2,5% menor que el retiro anterior. Si se sabe que el valor del primer retiro es de $2.500.000 y el valor del deposito inicial fue de $17.200.000 y la entidad financiera reconoce el 3% mensual

4G24,174,2642.50%2,000,0002.00%NOCUOTAINTERESABONOSALDO024,174,26412,000,000483,4851,516,51522,657,74922,050,000453,1551,596,84521,060,90432,101,250421,2181,680,03219,380,87242,153,781387,6171,766,16417,614,70852,207,626352,2941,855,33215,759,37762,262,816315,1881,947,62913,811,74872,319,387276,2352,043,15211,768,59682,377,372235,3722,142,0009,626,59792,436,806192,5322,244,2747,382,323102,497,726147,6462,350,0795,032,243112,560,169100,6452,459,5242,572,719122,624,17351,4542,572,7190.0

GRADIENTE GEOMETRICO CRECIENTE (PRESENTE)Hallar el valor de contado de una deuda, que se cancela con un primer pago de $2.000.000 durante el primer mes y 12 cuotas que crecen mensualmente en un 2,5%, la tasa que esta cobrando la entidad financiera es del 2% mensual.