1515.Determine el nmero de pagos necesarios para amortizar totalmente la compra acrdito de un automvil que cuesta $198 000 y se vende con un enganche de 40% y elresto a pagar en mensualidades vencidas de $5 592.33 con inters de 12% convertiblemensualmente.DATOSM = $ 198,000.00Enganche 40%=$ 79,200.00C=198.000-79200=$ 118,800.00n =?i =12%/12= 1%/100 =0.01mensualR =$ 5,592.33SOLUCIONDe C = R 1-(1+i)-niC*i -1= -(1+i)-n R (1+i)-n =1-C*iR -n log(1+i)= log (1-C*i)Rlog(1-C*i) log(1-118,800(0,01))n = - R = - 5592.33log(1 + i)log(1,01) = - log(0,787566184) = - (-0,103712939) = 24log(1,01)0.004321374TABLA DE AMORTIZACIONFECHAPAGOINTERES AMORTIZACION SALDO0118,800.0015,592.331,188.004,404.33114,395.6725,592.331,143.964,448.37109,947.3035,592.331,099.474,492.86105,454.4445,592.331,054.544,537.79100,916.6555,592.331,009.174,583.1696,333.4965,592.33963.334,629.0091,704.5075,592.33917.044,675.2987,029.2185,592.33870.294,722.0482,307.1795,592.33823.074,769.2677,537.91105,592.33775.384,816.9572,720.96115,592.33727.214,865.1267,855.84125,592.33678.564,913.7762,942.07135,592.33629.424,962.9157,979.16145,592.33579.795,012.5452,966.62155,592.33529.675,062.6647,903.96165,592.33479.045,113.2942,790.67175,592.33427.915,164.4237,626.25185,592.33376.265,216.0332,410.22195,592.33324.105,268.2327,141.99205,592.33271.425,320.9121,821.08215,592.33218.215,374.1216,446.96225,592.33164.475,427.8611,019.10235,592.33110.195,482.145,536.96245,592.3355.375,536.96(0.00)TOTAL134,215.9215415.88118800.00RTA. EL NUMERO DE PAGOS NECESARIOS PARA AMORTIZAR TOTALMENTE LA DEUDA ES DE 24 PAGOS

1616. En una operacin de crdito se salda una deuda de $15 000 mediante pagos trimestralesvencidos e iguales por $3 002.68 durante ao y medio. Cul es la tasa deinters nominal anual con capitalizacin trimestral que se pag? Cules eran los derechosdel acreedor despus del tercer pago?DATOSM = $ 15,000.00n =6 trimestresi =?tasa de interes nominal R =$ 3,002.68SOLUCION15,000.00 = 3.002,681-(1+i)-6i1-(1+i)-6 = 15,000.00 = 4.9955i3,002.68(1+i)8-1 = $ 3,550.00i420.00Ensayando valores de i: Si i = 0,0541-(1+0,054)-6 = 5.011404220.054i = 0,055(1+0,055)-6 = 4.99550310.055

Entonces i se encuentra entre 0.054 y 0.055 interpolando.

5.011404224.995537324.9955031

0.054i0.055

= 4.99553732 - 5.01140422 = i- 0,0544.9955031 - 5.011404220,055-0,054

= 0.0158669 = i- 0,0540.015901120.001 - 0.99784795 = i- 0,054(0.001)i = 0,54=0.000997848i = 0,54+0,000997848i = 0.055verificado

1-(1,055)^-6 = 0.55

la tasa efectiva mensual es de aproximanadamente 0,0157 yb la tasa efectiva anual es de:(1,015656490)12-1 = 4,9955

TABLA DE AMORTIZACIONFECHAPAGOINTERES AMORTIZACION SALDO015000.0013,002.68825.002177.6812822.3223,002.68705.232297.4510524.8733,002.68578.872423.818101.0643,002.68445.562557.125543.9353,002.68304.922697.792846.1463,002.68156.542846.140.00TOTAL18,016.083016.1115000.00

RTA. La tasa de inters nominal anual con capitalizacin trimestral que se pag es aproximdamente de: 33% (0,055x6trimestresx100)

RTA. Derechos del acreedor despus del tercer pago =8.101,06