Matematica financiera-interes compuesto.

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Capítulo 03: Interés Compuesto

Jennyffer Alexandra Coronado Sarmiento

Administración Financiera

Fundamentos de Matemática Financiera

Tutor: Román Andrés Agudelo Chavarro

Corporación Universitaria Minuto de Dios

Bogotá D.C.

2016

PROBLEMAS

1- Dado el 30 % nominal trimestral, calcular una tasa nominal mensual equivalente

NTV = NMV 30%

[(1+1/5)^5/m-1] *m = J

[1+0.075)^4/12-1]*12

[(1+0.075)^0.333333-1]*12

0.024399*12 = 0.292798

0.292798*100 = 29.2798% NMV

2- Dado el 27% nominal trimestre anticipado, calcular la tasa nominal bimestre vencida.

NTA 27%= NBV

[(1 - J / 5 )^ -5/m-1] * m = J

[(1-0.27/4)^(-4/6)-1]*6

[(1-0.0675)^ -0.666666-1]*6

0.047693154*6 = 0.286159

0.286159*100 = 28.6159% NBV

6- Dado el 36% nominal mensual, hallar una tasa nominal semestre anticipada

NMV 36% = NSA

[[(1+ j / 5 )^(5/-m)-1]*(-1)]*2

[[(1+0.03)^-6(-1)]-(-1)]*2

0.162515*2 = 0.325031

0.325031*100 = 32.5031 % NSA

8- Hallar la tasa nominal convertible semestralmente equivalente al 12% CM

CM 12% = NSV

[(1+ J / 2)^5/m-1]*m = J

[(1+0.12/12)^12/2-1]*2

[(1+0.01)^6-1]*2

0.061520*2 = 0.123040

0.123040*100 = 12.3040%NSV

9- Encontrar una tasa TV equivalente al 24% SV

SV 24% = NTV

[(1+0.24/2)^2/4-1]*4

[(1+0.12]^0.5-1]*4

0.058300524*4 = 0.233202

0.233202*100 = 23.3202% NTV

12- Hallar una tasa nominal semestral equivalente al 24% TV

24% TV = NSV

[(1+0.24/4)^4/2-1]*2

[(1+0.06)^2-1]*2

0.1236*2 = 0.2472

0.2472*100 = 24.72% NSV

13- Dado el 30% anual anticipado, hallar una tasa anual vencida que sea equivalente

30% AN = EAV

[(1-0.30)^(-1/1)-1]

[(0.7)^-1]

1.428571-1

0.428571*100 = 42.8571% EAV

16- Hallar la tasa efectiva anual anticipada, equivalente al 4% efectiva bimestral

EAV 4% = EAA

[(1+0.04)^(6/-1)-1]

[(0.790314525-1)*-1)]

-0.209685*(-1)

0.209685*100 = 20.9685% EAA

28- Encontrar una tasa efectiva anual equivalente al 30% nominal semestral anticipada

EAV 30% = NSA

[(1-0.30/2)^-2/1]-1

[(1-0.15)^-2]-1

(1.384083045)-1

0.384083*100 = 38.4083% NSA

 32- Encontrar la tasa efectiva anual anticipada equivalente al 32% anual capitalizable bimestre anticipado

EAA 32% = NBA = EAA

[(1-0.32/6)^(-6/-1)-1]*(-1)

[(1-0.053333)^6-1]*(-1)

-0.280249*(-1)

0.280249*100 = 28.0249% EAA

33- Hallar la tasa convertible anualmente equivalente al 12% TV

NTV 12% = NAV

[(1+0.12/4)^4/1]-1

[(1+0.03)^4]-1

1.12550881-1

0.125509*100 = 12.5509% NAV

34- Encontrar la tasa nominal semestre anticipado equivalente al 24% MV

NMV 24% = NSA

[[(1+0.24/12)^(12/-2)-1]*(-1)]*2

[[[(1+0.02)^-6(-1)]*(-1)]*2

[(-0.112028617)*(-1)]*2

0.112028617*2 = 0.224057

0.224057*100 = 22.4057% NSA

39- Calcular la tasa nominal mes anticipado equivalente al 40% TA

NTA 40% = NMA

[[(1-0.40/4)^(-4/-12)-1]*(-1)]*12

[[(1-0.1)^0.333333(-1)]*(-1)]*12

[(-0.034510615)*(-1)]*12

0.034510615*12

0.414127*100 = 41.4127% NMA

40- Hallar la tasa efectiva anual equivalente al 41.4127% nominal mes anticipado

NMA 41.4127% = EAV

[(1-0.414127/12)^(-12/1)-1]

[(1-0.034510)^-(12)-1]

1.524157289-1

0.524158*100 = 52.4158% EAV

45- Dada la tasa del 21% anual capitalizable mes anticipado, halle:

- Nominal bimestre anticipado

[[(1-0.21/12)^(-12/-6)-1]*(-1)]*6

[[(1-0.0175)-1]*(-1)]*6

[(-0.03469375)*(-1)]*6

0.03469375*6 = 0.208163

0.208163*100 = 20.8163% NBA

-Nominal trimestre vencido

[(1-0.21/12)^(-12/4)-1]*4

[(1-0.0175)^-3-1]*4

(0.054392535)*4

0.217570*100 = 21.7570% NTV

-Efectiva semestre anticipado

[[(1-021/12)^(-12/-2)-1]*(1)]

[(1-0.0175)^6(-1)]*(-1)]

[(-0.100512)*(-1)]

0.100512*100 = 10.0512% ESA

- Efectiva mensual vencido

[(1-0.21/12)^(-12/12)*-1]

[(1-0.0175)^-1]*-1

(1.017812)-1

0.017812*100 = 1.7812% EMV

46- Dada la tasa del 2% mensual, halle:

-Efectiva bimestral vencida

[(1+0.02)^(12/6)-1] = i

[(1+0.02)^(2)]-1 = i

(1.0404) -1 = i

0.0404*100 = 4.040% EBV

-Efectiva trimestral anticipada

[(1+0.02)^(12/-4)-1]*(-1)]

[[(1+0.02)^(-3)-1]*(-1)]

[(0.942322334)-1]*-1

(-0.057677665)*-1

0.057678*100 = 5.7678% ETA

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