CALCULO FINANCIERO

CAPITALIZACIÓN

Régimen Simple Régimen Compuesto

I(O;n) = eo·i·n I(O;n) =eo{(l+if -lJ

en =C¿'(l+if

ACTUALIZACIÓN

Descuento Comercial Descuento Compuesto

D(O;n) = Nrd-n

Va=N.(l-d·n) Va=N.(l-df

Descuento Racional

D(o;n) =N{l-{l+i.nt]

Va=N.(l+i.nt

RELACIÓN ENTRE TASAS VENCIDAS Y ADELANTADAS

Régimen Simple Régimen Compuesto

d i . d= yl=

l+i'n 1-d'ni . d

d=- Y 1=-l+i l-d

TASA APARENTE, TASA REAL Y TASA DE INFLACIÓN

Página 1 de 4

l.

-=

RENTA CIERTA, TEMPORARIA, INMEDIATA y DE CUOTA CONSTANTE

Cuotas Vencidas Cuotas Adelantadas

(l+i)n -1v:.(l;n;i) = e· .

1

(l+if -1v:.(O;n;i) = e· . .(l+i)1

1(O;n) = v:. (l;n;i)-n·e

1-(1+i)-nV (1' n: i) = e.----''---'--o , , .

1

1(O;n) = v:.(O;n;i) - n .e

l-(l+irnVa ( O;n; i) = e· . .(1 + i)

1

1(O;n) = n- e-Va (l;n;i) I(O;n) = n-C -Va (O;n;i)

RENTA CIERTA, PERPETUA, INMEDIATA Y DE CUOTA CONSTANTE

Cuotas Vencidas Cuotas Adelantadas

Va(1;00;i) = e.~1

Va ( O;00;i) = e.~.(1 + i)1

RENTA CIERTA, TEMPORt\..RIA, INl\1EDIATA y DE CUOTA VARIABLE. .

Proeresión Geométrica Progresión Aritmética

Sea C, =et_¡'q

l_(~)nV (l' n: i: q) = e . 1+ i con q:;t: 1+ io , , , ¡ 1 .+l-q

V'(l.n.¡.r)=(e +:.).l-(l+irn r _n_o , , , ¡. . ()n

1 1 i 1+i

Va(l;n;i;q)=e¡._l- .: n con q=l+i1+1

RENTA CIERTA, PERPETUA, INMEDIATA Y DE CUOTA VARIABLE

Progresión Geométrica Progresión Aritmética

Va(l;oo;i;q)=e¡. ~ con q<l+il+l-q V~(l;oo;i;r) =( el+;};

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r - .

SISTEMA DE A~lORTIZACIÓN FRANCÉS

T.T = C. 1- (1+ irn

Yo -'--o ~1

(l+i)' -1T; = tI' .1

Ct=--I (l+if

1- (1+ ir(n-t)~ = C .-"'--.-'---

1

I(a;b)=(b-a)·C-(v" -V¡,) t (l+iY-l~=Va·(l+i)-C ..

1

1 (a;b) = (b - a) .C - (~ - ~ )

SISTElVIA DE A~IORTIZACIÓN ALEMÁN

Vt =-2....

n

c -c =_V"a.it t-I n

n+lI(O·n)=-·Vi, 2 o·

SISTEMA DE A~10RTIZACIÓN AlVIERICANO PURO

1(O; n) = n .Va. i

Página 3 de 4

SISTEMA DE A1VfORTIZACIÓN DE TASA DIRECTA

C, =1+t VT=t·-2..t n

l(a;b)=(b-a)·Vo·r

SE:GUROS DE VIllA. &REN'l'AS CONTINGENTES

Valor Actual de un CapitalAsegurado de Vida

PPU = CAv-E(x;n)

D(x n)PPU = CAv- 'D(x)

ValOl' Actual Renta Contingente de cuota R

PPU =R-a(x· h n) =R- N(x+h)-N(x+h+n),, -----D-(~X~)--~

Valor Actual de un CapitalAsegurado de Muerte

PPU = CAM-A(x;h;n)

M(x+h)-M(x+h+n)PPU= CAM- D(x)

Cálculo de PPA's para cualquier Valor Actual (PPU)

PPU = PPA.a(x h: n) = PPA. N(x+h)-N(x+h+n), , -----D-(-x~)--~

Página 4 de 4

A 1p

RESE

VF, -[( Rt+i)"-I R 1R

N(1;,,;i;R) - C+-. -

VT

i i - j' n .(t +i) n

E

E F

I N1

-N VF (R)<l+ir-l R

e AL

(1;I1;i:R) = e +-.' . - - II

T I

1 l .1

p

DER

Mp

AE

VP. -( RfT

(l;o<>;i:R) - e +i .iuA

EpR

O ESE

V1[ - [( 11 rl+ i)"-1 11 ]

T AN

O;n;i;R) - C +- ...!..

T

i' ¡-in .(l+ir'HI

Di..-E

IE

FI

L N Vr¡"""RI ~[( C+ R rl+i)" -1 R J

AAl

i í =:: .(l+i)

e NT p

E

A R

Ap

D EVp _( R) 1

T

(O;oo;i;R) - e-/- i .¡"(l + i)I A u

A -

GEOMETRIeA

p

e,p

eT

U A

,,N

A

l

p,,Pf,U A

)ll . "' -~r+t. (1+i -=:2-.(I+i)¡?D ;;;: c. (1 .)_ a, r(O;,,;i~q) . + 1 :l

pura q t- (1+ i)

I'P¡O"!;i;q) = c.I1.(l +ir .(1.+ i}::: C.n para q=(l+i)

(l+i)" ~(/ .(l+i)~ Vl~O;n;i;q) = c. (1 + i) _ q

~, .para q:f. (l + i)

vr: . =c.n.(·I+i)" para q=(l+i)\O;n;,;q)

:> CVl( . :=; ~- (1 . i) (~-;';'l) (l+i)-q' T para q<l+i)

(1+ i)"_::i..(l + ir'v,{J; ••••;I!) =-C'-(i+i)_q para q;< (1+;)

Vil'''"'') '" c.n.(1 +ir' .(1 + ir", c:I7.(1 +ir' p"ra q =(1 + i)

(J+i)"-q"Vf~.l;h;¡;.¡) ~c. (l.! i)-q para q :f= (1-1' n. )

JT (l ')"'.'. "f'''''''I', ""C.l1. +Jl. " "

"[lora q =(.I+i)

v¡> _ e!I;~:¡;</)- (1 +i)-ll para q < (1 + i)

, ~--.:::

Tabla Mortalidad y Valores de Conmutación - CSO 1941 (i=O,025)

Edad (x) I(x) d(x) D(x) N(x) C(x) M(x)

O 1.023.102 23.102 1.023.10200 31.374.229 78 22.538,54 257.876881 1.000.000 5.770 975.60976 30.351.12778 5.49197 235.338352 994.230 4.116 946.322 43 29.375.518 02 3.822 12 229.846383 990.114 3.347 919.41928 28.429.19560 3.03222 226.024264 986.767 2.950 893.96220 27.509.776 32 2.60737 222.992055 983.817 2.715 869.55087 26.615.814 12 2.341 14 220.384686 981.102 2.561 846.001 18 25.746.26324 2.15448 218.043547 97!:L~4i 2.41/ 823.21252 24.900.262 06 ' 1.983 74 21').889068 976.124 2.255 801.150,43 24.077.049 54 1.80564 213.905319 973.869 2.065 779.80453 23.275.899 11 1.613 17 212.0996710 971.804 1.914 759.171 73 22.496.09459 1.458 75 210.4865011 969.890 1.852 739.19660 21.736.92285 1.377 07 209..02775-12 968.038 1.859 719.79035 20.997.72625 1.34856 207.6506913 966.179 1.913 700.88593 20.277.935 90 1.353,88 206.302 1314 964.266 1.996 682.43727 19.577.049 97 1.378 17 204.9482515 962.270 2.069 664.41429 18.894.612 69 1.39373 203.570,0816 960.201 2.103 646.815 33 18.230.19840 1.38208 202.1763517 958.098 2.156 629.65727 17.583.38307 1.38235 200.7942718 955.942 2.199 - 612.91742 -;16.953.725 80 1.37554 199.411 9119 953.743 2.260 596.592,68 16.340.808,38 1.37921 198.0363820 951.483 2.312 580.66243 15.744.21570 1.37653 196.6571721 949.171 2.382 565.12340 15.163.55327 1.38362 195.2806322 946.789 2.452 549.95628 14.598.429,87 1.38954 193.8970123 944.337 2.531 535.153 17 14.048.473 59 1.399 33 192.5074724 941.806 2.609 520.70133 13.513.32042 1.40727 191.1081425 939.197 2.705 506.59402 ••12.992.619 10 1.42346 189.700,8726 936.492 2.800 492.81461 12.486.025 07 1.43752 188.277 4127 933.692 2.904 479.35722 11.993.21047 1.45455 186.8398928 930.788 3.025 ' '. 466.211 03 '" 11.513.853 25 1.47820 185.3853429 927.763 3.154 453.36183 11.047.64222 1.50365 183.9071430 924.609 3.292 440.80058 10.594.280 39 1.531 16 182.4034931 921.317 3.437 428.518 19 10.153.47981 1.55961 180.872 3432 917.880 3.598 416.506 91 9.724.96163 1.59285 179.3127333 914.282 3.767 404.75536 9.308.454 71 1.62699 177.7198834 910.515 3.961 393.25629 8.903.699 35 1.66905 176.0928935 906.554 4.161 381.99563 8.510.443 06 1.710 56 174.4238436 902.393 4.386 370.968 10 8.128.447,43 1.75908 172.7132837 898.007 4.625 360.16102 7.757.479 33 1.80969 170.9542038 893.382 4.878 349.56691 7.397.318 32 1.862 13 169.1445139 888.504 5.162 339.178,75 7.047.751,41 1.92249 167.282 3840 883.342 5.459 328.983 61 6.708.572 66 1.983 51 165.359,8941 877.883 5.785 318.976 11 6.379.589 04 2.05069 163.376,3842 872.098 6.131 309.14551 6.060.612 93 2.120,34 161.3256843 865.967 6.503 299.48~iL04 5.751.46742 2.194 14 159.2053444 859.464 6.910 289.986,39 5.451. 982 39 2.27460 157.011 2145 852.554 7.340 280.63895 5.161.99600 2.35721 154.7366146 845.214 7.801 271.43689 4.881.35704 2.44415 152.3794047 837.413 8.299 262.372 33 4.609.920 15 2.53676 149.9352548 829.114 8.822 253.43624 4.347.547 82 2.63086 147.3984849 820.292 9.392 244.62400 4.094.111 59 2.732,53 144.7676250 810.900 9.990 235.92504 3.849.487 58 ·2.83562 142.035 10

,.

Tabla Mortalidad y Valores de Conmutación - CSO 1941 0=0,025)

Edad (x) I(x) d(x) D(x) N(x) C(x) M(x)51 800.910 10.628 227.335 15 3.613.562 55 2.943 14 139.19947-52 790.282 11.301 218.847 25 3.386.227 40 3.053 18 136.2563453 778.981 12.020 210.456,33 3.167.380 15 3.16822 133.203 1654 766.961 12.770 202.15503 ~ 2.956.92382 3.28381 130.0349455 754.191 13.560 193.94061 6 2.754.76879 3.401 91 126.7511256 740.631 14.390 185.80843 2.560.828 19 3.52209 123.3492157 726.241 15.251 177.75443 2.375.01975 3.641 78 119.827 1258 710.990 16.147 169.777.17 -..2.197.26532 3.761 70 116.1853459 694.843 17.072 161.874 57 2.027.488 15 3.880 19 112.4236460 677.771 18.022 154.04622 1.865.613 58 3.99620 108.5434561 659.749 18.988 146.292 80 1.711.56735 4.10771 104.5472562 640.761 19.979 138.61697 1.565.274 55 4.21668 100.4395563 620.782 20.958 131.01940 1.426.657 58 4.31541 96.2228764 599.824 21.942 123.50839 1.295.638 18 4.40783 91.9074665 577.882 22.907 116.088 16 @ 1.172.12979 4.48945 87.4996366 554.975 23.842 108.767 29 1.056.041,63 4.55873 83.010 1867 531.133 24.730 101.555,70 947.27435 4.613 19 78.4514568 506.403 25.553 94.46554 845.71865 4.65045 73.8382669 480.850 26.302 87.51105 751.253 10 4.67001 69.1878170 454.548 26.955 80.70662 663.74205 4.66923 64.517J971 427.593 27.481 74.06894 583.03543 4.64424 59.8485772 400.112 27.872 67.618 15 508.96649 4.59543 55.2043373 372.240 28.104 61.373 50 441.34834 4.52066 50.6089074 344.136 28.154 55.35592 379.97484 4.41825 46.0882475 315.982 28.009 49.587,53 324.61892 4.28829 41.6699976 287.973 27.651 44.08979 275.03140 4.13022 37.381 7077 260.322 27.071 38.88421 230.94161 3.94496 33.2514878 233.251 26.262 33.99085 192.05740 3.73373 29.3065279 206.989 25.224 29.42808 158.066.55 3.49868 25.572 8080 181.765 23.966 25.211 64 128.63848 3.243 12 22.0741181 157.799 22.502 21.353,60 103.42684 2.97074 18.831 0082 135.297 20.857 17.86205 82.073 24 2.68640 15.8602683 114.440 19.062 14.73998 ,64.2 !J.¡J.? 2.39532 13.1738684 95.378 17.157 11.98515 49.471 21 2.103,36 10.7785485 78.221 15.185 9.58947 37.48606 1.81619 8.675 1886 63.036 13.198 7.539,39 27.896,58 1.54004 6.8589987 49.838 11.245 5.81546 20.35719 1.280 15 5.31895

-- 88 38.593 9.378 4.39348 14.541 73 1.041 56 4.0388089 29.215 7.638 3.24475 10.14825 82762 2.9972490 21.577 6.063 2.33799 6.90350 64094 2.16961f-..

91 15.514 4.681 1.64003 4.56550 48277 1.5286892 10.833 3.506 1.11726 2.92547 35277 1.0459093 7.327 2.540 73724 1.808 21 24934 6931394 4.787 1.776 469,92 1.07098 17009 4437995 3.011 1.193 28837 60106 11147 2737196 1.818 813 16986 31270 7411 1622497 1.005 551 9161 14283 4900 881398 454 329 4038 5122 2855 391399 125 125 10 85 10 85 1058 1058