1) se constituye cdt 180 das C = 650.000 I = 26% NT Rete = 7%

Renta antes de tx , Renta desp tx , Valor que entregaron al vencimiento

Suponiendo i = 18 % determinar tasa real obtenida a) renta antes tx

26/4 = 6.5 =

0.065% S =

650000(1+0.2864663506)1/2 (1 + i ) = (1 +

0.065)4 S =737.246.25 28.64663506 renta ant tx

C) valor al vencimiento

650000 737246.25= 87246.25 87246.25 * 0.07 = $ 6107.2375

B) 731139.0125 = 650000(1+i)6

(731139.0125/650000)1/6 1 = 0.019798651 = 1.97985191

(1 + 0-0197986191)12= (1+ i)

I = 0.26524081 = 26.52 rent antes de tx

tasa real

c) 0.02652408416 0.18/1 + 0.18= 0.07223801 =

7.22380014

2) un inversionista desea obtener

rentabilidad = 8% inflacin = 18%

it = ir +if + ir*if

it = 0 .08+0.18+0.08*0.18 it = 27.44 % tasa de inversion

3) un articulo se fabrica en EEUU y se vende en Colombia 50.000 cuanto valdr el articulo en Colombia y EEUU al final de un ao

Cambio actual us $ 1=1200

Inflacin EEUU 3% Devaluacin peso 18%

Colombia 2000 EEUU

50.000 us $ 25

60770 25.75

Inflacin EEUU 3%

25(1+0.003) = 25.75 valor EEUU 25.75 (1+0.18) =30.385

30385*2000 = 60770 valor Colombia

4) un articulo se fabrica e Colombia y cuesta 68000 cuando el cambio es

1=2000suponiendo ipp del sector en Colombia 22%devalucion frente al peso 18%

34 68000

35.15 82960

S = 68000((1+0.22) S =2000(1+0.18) S = 82960 S = 2360

82960/2360 = 35.15254237 us $

5) 2 inversionistas origen alemn 1 residente en Alemania y otro en colombia cada

uno aporta el 50%.

C = 300.000 S = 400.000 Hallar tasas totales y reales

Tasa prome infla 22% Colombia Alemania 2% devaluacin peso frente dlar

1 ao 18% 2 ao 20% 3 ao 17% Devaluacin marco frente dlar 1 y 2 aos 2%....... 3 aos revaluacin 3%

Marco

150.000 2.23 134.539.1 1300 = 174.887.892.4

200.000 2.25 177.777.77 2153.7 = 382.386.00

S= C(1+i)n 200.000=150.000(1+i)3 ..i= (200.000/150.000)1/3-1 = 10.06% ea

Ir = 0.01006-0.02/1+0.02 = 7.90% ea

150.000/2.23=67.264.5739 uS$ . . . . . 67.264.5739*1300= $87.443.946.07

2.23 (10.02)2*(1-0.03) = 200.000/2.2504 = 88.896.56

Cambio $ u$ 1300(1+0.18)(1+0.20)(1+0.17) = 2153.73

U$ 88.869.56*2153.73 = 191401059.70

191401059.70 = 87443946.07 (1+i)2 191401059.70 / 87443946.07 - 1. . . . It = 29.85%

Ir = 0.2984-0.22/1+0.22 = ir 6.43% ea

8) pais A moneda abc un par de zapatos vale 24.000 if 22% Cambio actual us$ 1 = abc 1000

Inflacin 6.5%

A 1000 X 24000 ABC 24 us

29280 25.56 us

Precio de salida A Precio de salida X S = C(1+i)n

S= 24000(1+0.22) S= 24(1+0.06) S = 29.280 S = 25.44

Devaluacin TC = 29.280/25.44 = 1.150.94

S = C(1+ dev)n 1150.94 = 1000(1+dev)1 . . . . . 1150.94/1000 = 1+ dev dev =0.1509 = 15.09%

9) un inversionista desea todas las inversiones le den el rentab 8% if 17%

Ir = it if/1+if . 0.08 0 it 0.17/1 + 0.17 = 0.08 = it 0.17/1.17 (0.08*1.17) = it 0.17 . . . . 0.0936 + 0.17=it . .. it = 0.2636 . . . 26.36%

10)un ahorador consigna 300.000 el 1 marzo 200.000 el 20 de junio

Cuando retire el 30 agosto si la coperativa pago 27% ea marzo abril y 25 resto

Calcular pesos y upac 300.000(1+0.27)59/360 = 311.984.8687

311984.8687(1+0.25)50/360 =

321.805.3465 S = 521.805.3465 (1+0.25) =

545.285.208

b) 300.000/6650 = 45.112781% 45.112781(1+0.27)59/360 = 46.915%

46915(1+0.25)50/360 =48.3917%

200.000/7.149095 = 28.037.3 48.3917 +28.0373 = 76.42909 unid upac

76.42909(1+0.25)71/360 = 79.867 upac

11) se estima correccin monetaria 1 ao 18% y 2 ao 17%

Calcular vlr antes de tx que entregaron a un inver q invie 800.000a dos aos

Calcular rent antes de tx upac 1 =14000 800.000(1+0.22)(1+0.21)= 1.180.960

1180960/14000 = 84.3542 . . . . .800.000/14000 = 57.1428 84.3542 = 57.1428(1 + i)2

1.2149-1 = i i = 21.4988% Ip = i ( 1 rotacion) . . . . ip 0.2149(1-0.07 = 20% S= 800.000(1+0.20)2 = 1.152.000

12) hallar tasa efectiva annual

DTF + 6 p ipc + 7p labor + 8p . dtf =15%TA ipc = 10 % labor =5.14 ns

a) DTF + 6 p . 15+6 = 21 TA d =21/4=5.25 TA de period Ip = d/1 d = 0.0525/1-0.0525 = 0.055408 . Ip 5.5408% et (1+i)1=(1+0.055408)4 . . . . I = 1.055408-1 . I 24.07 % EA

b) IPC +7p IPC =10% . . . . . it = 0.10+0.07+0.07*0.10 = 17.7%

c ) Labor + 8 p labor 5.14 ns . . . . .5.14+8 =13.14 . . . .ip = 13.14/2 = 6.57 ep

(1+i) = (1 +0.0657)2 I = 13.5716% EA

13 ) suponiendo IPC 8.5 CM = 12% DTF 15% TA TCC = 15.5

%TA TBS (CF) 180 dias = 19.27% EA TBS (bancos 360 dias) = 19.19 EA

a) DTF +8.6 = IPC + X . . . . 0.15 +0.086 = 0.085 +X

0.236 = 0.085 + X ia = ( 1-ja/m)-m -1 .. ia = ( 1-0.236/4)

-4 -1= ia = 0.27538 = 27% 0.2753=0.085+ x + 0.085*X . .

. 0.2753=0.085+X(1+0.085) 0.2753=0.085+X(1.085) . . . .0.2753/1.085 = X . . . X =

17.53% EA

b) 19.27%ea + 6% EA= 15%TA + X 25.57%EA

4((1+0.2527)1/4-1)-1)/(1+0.2527)1/4 = ja = 0.2190 TA

0.2190=0.15+X. X 0.069.6.9 % TA

14 ) idev +10 = IPC + X idev + (prime + 200 pb) = DTF +X

idev + (libor + 500 pb) = DTF +X

idev = 25% IPC = 9% prime rate 8.25% DTF 14.5% TA labor 5%

I = 0.25 +0.10 + 0.25*0.10= 0.09 + X + 0.09*X I= 0.375 EA = 0.09(X+0.09X)

0.375 = 0.09 +X(1+0.099) . . . . .0.375-0.09/1+0.09= X 0.285/1.09 = 0.26147 X = 26.147% EA

Ja= 4((1+0.25)1/4-1)-1)/(1+0.25)1/4 = ja = 0.2170 TA

Ja= 4((1+0.1025)1/4-1)-1)/(1+0.1025)1/4 = ja = 0.09636TA

b ) idev + (prime + 200 pb)= DTF +X

25% + 10.25 = 14.5 + X

0.2170 + 0.09636+0.2170(0.09636)=0.145+X

0.334270 = 0.145+(x + 0.145X) 0.334270 = 0.145+ X ( 1+0.145)

0.334270-0.145/1+0.145 = X X = 0.18927/1.145 = 16.53% TA

c ) idev + (libor + 500 pb)= DTF +X

Ja= 4((1+0.25)

1/4-1)-1)/(1+0.25)1/4 = ja = 0.217033563 TA

Ja= 4((1+0.10)1/4-1)-1)/(1+0.10)1/4 = ja = 0.09418364 TA

25% 10% = 14.5 + X

0.2170..56.+0.09418364+0.217033563*0.09418364

0.331655214 = 0.145 + X( 1+0.145) 0.331655214 -0.145/1+0.145 = X . X = 0.186658214/1.145 = 16.30 15 ) cual es la rentabilidad ea comprador acep t 180 dias si se conserva hasta su

maduracin bolsa 86.225

S= C (1+i)n = pr = pc (1+i)180/360 . 100= 86.225(1+ i)0.5 (100/36.225)1/0.5=(1+i) ..1.345035-1 =I . 0.345035 =I I= 34.50%

ic=ir-comisicion ic= 34.5035-0.5 .. ic = 34.0035%

pr = pc(1+i)n . 100 = pc(1+0.3400)0.5 .100/1.15959 = pc .pc 86.387%

18 ) un exporta recibe ab tasa emisicion 28 %ns comiciones compra y venta 0.4 y 0.6

N 0 180 dias J= 28% ns 0.4 compra 0.6 venta

a ) (1+i) = ( 1+0.28/2)2 .. i = (1.14)2-1 ..i = 29.96% EA . TR = 29.96 % EA d ) pr 100(1+0.2996)-180/360 .. 87.7192982% b ) tc= tr cm.c .tc & 0.2996 0.04 tc 29.56 % EA pc = 100(1+0.2956)-180/360 pc 87.854604% c ) tasa vendedor tv = tr+comv .. tv = 0.2996 +0.006= 30.56 pv 100(1+0.03056)-180/360 .. pv 87.51%

22 ) seor xx ab 10 millones v. faltando 87 dias compra yy ti = 32% cc0.4% cv 0.375%

a ) TR = 32% + 0.4% . Tr32.4% EA b ) Pr =100(1+0.324)-87/360 . PR = 93.44 % .. pr 10.000.000(93.44) = 9.344.234 c ) tasa de cesion tv = tr + comv tv = 32.4% + 0.375% = 32.775% d ) pv = 100(1+0.32775)= 93.378499% . 0.933784(10.000.000) = 9.337849.966 e ) pc= 32.4%-0.4%= 32% EA . 100(1+0.32)-87/360=93.51069826% pc 0.9351069826(10.000.000)=9.351.069.82

f ) retef 10.000.000-9.344234.3 = 655.765.7 ..RF 655.765.7(0.07) =45.903.62 g ) p pagar yy pc +rf . =9.351.069.62+45.903.62 ppyy = 9.396.974 h) pv rf . Precibe xx= 9.337.849.966 +45.903.62 = 9.383753.58 i ) rentabilidad10.000.000 =9.396.974(1+i)87/360 .. I = (10.000.000/9.396.974)360/87- 1 i= 29.352