Taller Interés simple - Interés compuesto. Karen Elizabeth Bedoya Laguna

Karen Elizabeth Bedoya Laguna INTERES SIMPLE

P i n

8500000 2.50%

TIEMPO

P

0 1 2 3 ! 5 " 7 8 

8,500,000 8,500,000 8,712,500 8,25,000 ,137,500 ,350,000 ,5"2,500 ,775,000 ,87,500 10,200,000

FECHA INICIAL

11#15#2015 1!1 13 EJERCICIO 1

El dia de hoy $e deo$ita a un ban&o en el 'e$ en el 'e$ en el 'e$

7 12 2!

&uanto (ene a&u'ulado en el 'e$ a un intere$ de TIEMPO

P

0 1 2 3 ! 5 " 7 8

8,00 8,000, 0,000 000 8,00 8,000, 0,000 000 8,2! 8,2!0, 0,000 000 8,!8 8,!80, 0,000 000 8,72 8,720, 0,000 000 8," 8,"0, 0,000 000 ,20 ,200, 0,000 000 ,!!0, ,!!0,000 000 12," 12,"80 80,0 ,000 00

DEPOSITA

3,000, 3,000,000 000

RETIRA

 10 11 12 13 1! 15 1" 17 18 1 20 21 22 23 2! 25 2" 27 28 2 30 31 32 33 3! 35 3"

12, 12,20 20,0 ,000 00 13,1"0 13,1"0,000 ,000 13,!00 13,!00,000 ,000 13,"!0,000 13,"!0,000 10,380 10,380,000 ,000 10,"20 10,"20,000 ,000 10,8"0 10,8"0,000 ,000 11,100 11,100,000 ,000 11,3!0 11,3!0,000 ,000 11,580 11,580,000 ,000 11,820 11,820,000 ,000 12,0"0 12,0"0,000 ,000 12,300 12,300,000 ,000 12,5!0 12,5!0,000 ,000 12,780 12,780,000 ,000 13,020,000 13,020,000 1!,2"0 1!,2"0,000 ,000 1!,500 1!,500,000 ,000 1!,7!0 1!,7!0,000 ,000 1!,80 1!,80,000 ,000 15,220 15,220,000 ,000 15,!"0 15,!"0,000 ,000 15,700 15,700,000 ,000 15,!0 15,!0,000 ,000 1",180 1",180,000 ,000 1",!20 1",!20,000 ,000 1",""0 1",""0,000 ,000 1",00 1",00,000 ,000

3,500,000 3,500,000

1,000,000 1,000,000

)*+- E/ EL /+L +L +L EL E/ 3", / L+ -+/+ E -E4E/ E/*+L E/ P61i P9+ 9 i-+/+ nPE4 +P+: INTERES COMPUESTO TIEMPO

P

0 1 2 3

DEPOSITA

8,00 8,000, 0,000 000 8,00 8,000, 0,000 000 8,2! 8,2!0, 0,000 000 8,!8 8,!87, 7,200 200

RETIRA

! 5 " 7 8  10 11 12 13 1! 15 1" 17 18 1 20 21 22 23 2! 25 2" 27 28 2 30 31 32 33 3! 35 3"

8,7! 8,7!1, 1,81" 81" ,00 ,00!, !,070 070 ,27 ,27!, !,13 13 ,552, ,552,!18 !18 12,8 12,838 38, ,1 1 13,2 13,22! 2!,1 ,1"1 "1 13,"20 13,"20,885 ,885 1!,02 1!,02,512 ,512 1!,!50,37 1!,!50,37 11,383 11,383,0 ,0 11,725 11,725,!27 ,!27 12,077 12,077,18 ,18 12,!3 12,!3,505 ,505 12,812 12,812,"0 ,"0 13,17 13,17,071 ,071 13,52 13,52,83 ,83 1!,000 1!,000,773 ,773 1!,!20 1!,!20,7" ,7" 1!,853 1!,853,!20 ,!20 15,2 15,2,022 ,022 15,757,3 15,757,3 17,230 17,230,733 ,733 17,7!7 17,7!7,"55 ,"55 18,280 18,280,08! ,08! 18,828 18,828,!87 ,!87 1,33 1,33,3!1 ,3!1 1,75 1,75,1!2 ,1!2 20,57! 20,57!,3" ,3" 21,11 21,11,"28 ,"28 21,827 21,827,377 ,377 22,!82 22,!82,18 ,18 23,15" 23,15",""! ,""! 23,851 23,851,3"! ,3"!

3,000, 3,000,000 000

3,500,000 3,500,000

1,000,000 1,000,000

EJERCICIO 3

) L+/ /+/ ))E/ EL E;E4)) 2 + <*E -+/+ E -E4E/ /PLE = )P*E/- EBE >+BE4 )+P-+L?+ / +L 3" = 4E-4 4E-4 30,000,000 30,000,000 El dia de hoy $e deo$ita a un ban&o en el 'e$ en el 'e$ en el 'e$ &uanto (ene a&u'ulado en el 'e$

7 12 2!

en el 'e$ 3" tengo a&u'ulado + <*E -+/+ E -E4E/ /PLE )+P-+L?+  /PLE TIEMPO

P

0 1 2 3 ! 5 " 7 8  10 11 12 13 1! 15 1" 17 18 1 20 21 22 23 2! 25 2" 27 28 2 30 31 32 33 3! 35 3"

8,00 8,000, 0,000 000 8,00 8,000, 0,000 000 8,5 8,57, 7,222 222 ,1 ,1!, !,!!! !!! ,7 ,71, 1,""7 ""7 10,3 10,388 88,8 ,88 8 10, 10,8" 8",1 ,111 11 11,583,333 11,583,333 15,1 15,180 80,5 ,55" 5" 15,7 15,777 77,7 ,778 78 1",375 1",375,000 ,000 1",72 1",72,222 ,222 17,5",!!! 17,5",!!! 1!,""" 1!,""",""7 ,""7 15,2"3 15,2"3,88 ,88 15,8"1 15,8"1,111 ,111 1",!58 1",!58,333 ,333 17,055 17,055,55" ,55" 17,"52 17,"52,778 ,778 18,250 18,250,000 ,000 18,8!7 18,8!7,222 ,222 1,!!! 1,!!!,!!! ,!!! 20,0!1 20,0!1,""7 ,""7 20,"38 20,"38,88 ,88 21,23",111 21,23",111 22,833 22,833,333 ,333 23,!30 23,!30,55" ,55" 2!,027 2!,027,778 ,778 2!,"25 2!,"25,000 ,000 25,222 25,222,222 ,222 25,81 25,81,!!! ,!!! 2",!1" 2",!1",""7 ,""7 27,013 27,013,88 ,88 27,"11 27,"11,111 ,111 28,208 28,208,333 ,333 28,805 28,805,55" ,55" 2,!02 2,!02,778 ,778

DEPOSITA

3,000,000 3,000,000

3,500,000 3,500,000

1,000,000 1,000,000

-E4E/ )P*E/- TIEMPO

P

RETIRA

0.0357192186 DEPOSITA

RETIRA

0 1 2 3 ! 5 " 7 8  10 11 12 13 1! 15 1" 17 18 1 20 21 22 23 2! 25 2" 27 28 2 30 31 32 33 3! 35 3"

8,00 8,000, 0,000 000 8,00 8,000, 0,000 000 8,28 8,285, 5,75! 75! 8,58 8,581, 1,71! 71! 8,88 8,888, 8,2!7 2!7 ,20 ,205, 5,728 728 ,53 ,53!, !,5! 5! ,875, ,875,11" 11" 13,2 13,227 27,8 ,8!7 !7 13,7 13,700 00,3 ,33" 3" 1!,18 1!,18,701 ,701 1!,"" 1!,"",5!" ,5!" 15,221,!5 15,221,!5 12,2"5 12,2"5,15 ,15 12,703 12,703,28 ,28 13,157 13,157,050 ,050 13,"27 13,"27,010 ,010 1!,113 1!,113,75" ,75" 1!,"17 1!,"17,888 ,888 15,1!0 15,1!0,028 ,028 15,"80 15,"80,817 ,817 1",2!0 1",2!0,2! ,2! 1",821 1",821,037 ,037 17,!21 17,!21,871 ,871 18,0!!,1"7 18,0!!,1"7 1,"88 1,"88,"1 ,"1 20,31 20,31,55 ,55 21,120 21,120,3!0 ,3!0 21,87! 21,87!,7!2 ,7!2 22,"5" 22,"5",01 ,01 23,!"5 23,!"5,3! ,3! 2!,303 2!,303,512 ,512 25,171 25,171,"15 ,"15 2",070 2",070,725 ,725 27,001 27,001,51 ,51 27,"" 27,"",!!0 ,!!0 28,"5 28,"5,37 ,37

3,000, 3,000,000 000

3,500,000 3,500,000

1,000,000 1,000,000

P61i n

EJERCICIO 4

+ <*E -+/+ E -E4E/ /PLE = )P*E/-+ /E -4PL)+ *+ )+-+ E

E/E/@ /PLE P i n 

1000 0.3"3"3"3"3" 5.5 3000

)P*E/- 9+P 9 n i-+/+ +P+:

1000 3000 5.5 22.11% 0

EJERCICIO 5

eter'in eter'inar ar el 'onto 'onto &o'ue &o'ue$to $to de$u de$ue$ e$ de !,8 aAo$ aAo$ $i $e inie inierten rten C130.00 C130.000 0au ta$a del 8% 9+P 130000 9 C5",7!3."0 n !.8 i-+/+ 8% +P+: 0 EJERCICIO 6

;*+ 4E+L?+ *+ 9E4/ P4 L+ 4E-+BL+ 4E+L EL E:) E/ E +L )+B E * -EP LE E-4E:+ + ;*+

"0000000 21% 157500000

+ )*+- -EP E/-*9 9E4- EL E4 9+P 9 n PE4 i-+/+ +P+:

"0000000 157500000 5.0"28!2"" +D/ 21% 0

B / E E/E/ -EP L+ L+) i )*+L E/ L+ -+/+ E -E4E/ )44E-E EL E:) ic!!"#$1%i&'($1%i!')*1

i &orr

!7."2%

22%

EJERCICIO 7

*na iner$iFn iner$iFn de C 250.000 */ $e ee&tGa ee&tGa a 15 aAo$. urante urante lo$ ri'ero$ ri'ero$ 8 aAo la ta$a de interH$ e$ del 12% /. Po$terior'ente, la ta$a au'enta al 15% /, durante I)uJl e$ el 'onto nal de la iner$iFn@.

9+P 9 n PE4 i-+/+ +P+:

250000 C1,532,58.!1 1" 12% 0

9+P 9 n PE4 i-+/+ +P+:

C1,532,58.!1 C5,31,!1."2  15% 0

9+P 9 n PE4 i-+/+ +P+:

C5,31,!1."2 C7,82",3"1.27 30 1.25% 0

*4+-E L/ P4 /EP4E EBE E EL -EP E *

L+ -+/+ +*E

EJERCICIO 8

/e inir( inir(er eron on C 20.000.000 20.000.000 en un ban&o ban&o or or 5 aAo$. )uand )uando o $e realiz realizF F el deF$it deF$it -re$ aAo$ aAo$ de$uH$, de$uH$, la ta$a ta$a &a'bio &a'bio al 1,5% 'en$ual 'en$ual.. )al&ule )al&ule el 'onto 'onto al nalizar nalizar l 9+P 9 n PE4 i-+/+ +P+:

C20,000,000.00 C!0,2!3,2.!! 12 ".00% 0

9+P 9 n PE4 i-+/+ +P+:

C!0,2!3,2.!! C57,528,810.2 2! 1.50% 0

EJERCICIO 9

o$ er$ona$ $e a$o&iaron a$o&iaron ara 'ontar un nego&ioM &ada &ada uno aortF aortF C !0.000.00 1 La $o&iedad re&ono&erJ a &ada uno el 2.5% $obre el &aital aortado, 2 El El ri' ri'er ero o ar( ar(&i &iar arJJ de la$ u(lida u(lidade$ de$,, de$u de$uH$ H$ del re&o re&ono& no&i'i i'ien ento to de lo$ lo$ int inte e 3 ing ingGn Gn $o&i $o&io o odr odrJJ re( re(ra rarr u(lid u(lidade ade$$ o int inter ere$e e$e$$ ante ante$$ de 5 aAo$. aAo$. Por Por in&o in&on neni eni

y el total total realizad realizado o C 1"0.000.000, 1"0.000.000, deter'i deter'inar nar &uJnto &uJnto re&ib re&ibiF iF &ada uno uno de lo$ $o&i $o&i

/) + 9+P 9 n PE4 i-+/+ +P+:

P+4-)P+ 55% C!0,000,000.00 C!2,5!7,0".71 2.5 2.50% 0

--+L 4E+L 4E+L?+ ?+ 9+P 9 n PE4 i-+/+ +P+:

C

9+P 9 n PE4 i-+/+ +P+:

1"0, 1"0,00 000, 0,00 000 0 C70,000,000.00 C1"0,000,000.00 2.5 3.1% 0

SOLUCION

!0,000,000 !0,000,000 30,000,000 30,000,000

SOCIO A SOCIO +

55% C !5% C

88,000,000 88,000,000 72,000,000 72,000,000

EJERCICIO 10

 La $eAor $eAoraa &aro &arolilina, na, deo$i deo$ita ta C 1500000 1500000 en en una una &uen &uenta ta de de ahorr ahorro$ o$ Oue Oue ag agaa un in do$ do$ aAo aAo$$ 'J$ 'J$ tar tarde ha&e ha&e un deF deF$i $ito to igua iguall a la la 'it 'itad ad del del $al $aldo do ei$ ei$te tent nte e en en e$e e$e ' -+/+ TIEMPO

P

0 1 2 3 ! 5 " 7 8  10 11 12 13 1! 15 1" 17

DEPOSITA

1,50 1,500, 0,000 000 1,50 1,500, 0,000 000 1,"0 1,"05, 5,000 000 1,71 1,717, 7,350 350 1,83 1,837, 7,5"5 5"5 1," 1,"", ",1! 1! 2,10 2,103, 3,828 828 2,25 2,251, 1,0" 0" 2,!0 2,!08, 8,"72 "72 2,57 2,577, 7,27 27 2,75 2,757, 7,"8 "8 2,5 2,50, 0,727 727 3,157,278 3,157,278 2,32 2,325, 5,8"1 8"1 2,!8 2,!88, 8,"72 "72 2,"" 2,""2, 2,87 87 2,8! 2,8!, ,280 280 3,0! 3,0!8, 8,730 730

RETIRA

1,052,!25.8 1,052,!25.8

18 1 20 21 22 23 2! 25 2" 27 28

3,2" 3,2"2, 2,1!1 1!1 3,! 3,!0, 0,!1 !1 3,73!,825 3,73!,825 5,8" 5,8"3, 3,"7" "7" ",27 ",27!, !,133 133 ",71 ",713, 3,322 322 7,18 7,183, 3,255 255 7,"8 7,"8", ",082 082 8,22 8,22!, !,108 108 8,7 8,7, ,7" 7" ,!1 ,!15, 5,782 782

1,8"7,!12.58 1,8"7,!12.58

PA,O DE i

F

  212,500 212,500 212,500 212,500 212,500 212,500 212,500 212,500 212,500

8,500,000 8,712,500 8,25,000 ,137,500 ,350,000 ,5"2,500 ,775,000 ,87,500 10,200,000 10,!12,500

FECHA FINAL

!#!#201"

  deo$ita re(ra deo$(a

8,000,000 3,000,000 3,500,000 1,000,000 3"

3% 'en$ua 'en$uall PA,O DE i

F

  2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000

8,000,000 8,2!0,000 8,!80,000 8,720,000 8,"0,000 ,200,000 ,!!0,000 12,"80,000 12,20,000

2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000 2!0,000

13,1"0,000 13,!00,000 13,"!0,000 10,380,000 10,"20,000 10,8"0,000 11,100,000 11,3!0,000 11,580,000 11,820,000 12,0"0,000 12,300,000 12,5!0,000 12,780,000 13,020,000 1!,2"0,000 1!,500,000 1!,7!0,000 1!,80,000 15,220,000 15,!"0,000 15,700,000 15,!0,000 1",180,000 1",!20,000 1",""0,000 1",00,000 17,1!0,000

)P*E/-+

PA,O DE i

F

  2!0,000 2!7,200 25!,"1"

8,000,000 8,2!0,000 8,!87,200 8,7!1,81"

2"2,25! 270,122 278,22" 28",573 385,170 3",725 !08,"27 !20,885 !33,512 3!1,517 351,7"3 3"2,31" 373,185 38!,381 35,12 !07,78 !20,023 !32,"2! !!5,"03 !58,71 !72,7!0 51",22 532,!30 5!8,!03 5"!,855 581,800 5,25! "17,232 "35,7! "5!,821 "7!,!"" "!,700 715,5!1

,00!,070 ,27!,13 ,552,!18 12,838,1 13,22!,1"1 13,"20,885 1!,02,512 1!,!50,37 11,383,0 11,725,!27 12,077,18 12,!3,505 12,812,"0 13,17,071 13,52,83 1!,000,773 1!,!20,7" 1!,853,!20 15,2,022 15,757,3 17,230,733 17,7!7,"55 18,280,08! 18,828,!87 1,33,3!1 1,75,1!2 20,57!,3" 21,11,"28 21,827,377 22,!82,18 23,15",""! 23,851,3"! 2!,5"",05

+L EL E/

  deo$ita re(ra deo$(a

8,000,000 3,000,000 3,500,000 1,000,000 3"

 

30,000,000 0.0747 PA,O DE i

F

  57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222 57,222

PA,O DE i

8,000,000 8,57,222 ,1!,!!! ,71,""7 10,388,88 10,8",111 11,583,333 15,180,55" 15,777,778 1",375,000 1",72,222 17,5",!!! 1!,""",""7 15,2"3,88 15,8"1,111 1",!58,333 17,055,55" 17,"52,778 18,250,000 18,8!7,222 1,!!!,!!! 20,0!1,""7 20,"38,88 21,23",111 22,833,333 23,!30,55" 2!,027,778 2!,"25,000 25,222,222 25,81,!!! 2",!1",""7 27,013,88 27,"11,111 28,208,333 28,805,55" 2,!02,778 30-000-000

F

  285,75! 25,"1 30",532 317,!81 328,821 3!0,5"7 352,731 !72,!88 !8,3"5 50",8!5 52!,! 5!3,700 !38,103 !53,752 !","0 !8",7!" 50!,132 522,1!0 5!0,70 5"0,107 580,113 "00,83! "22,2" "!!,52! 703,2"5 728,385 75!,!02 781,3! 80,258 838,1"! 8"8,102 8,110 31,22" "!,!8 8,3 1,03!,"21

8,000,000 8,285,75! 8,581,71! 8,888,2!7 ,205,728 ,53!,5! ,875,11" 13,227,8!7 13,700,33" 1!,18,701 1!,"",5!" 15,221,!5 12,2"5,15 12,703,28 13,157,050 13,"27,010 1!,113,75" 1!,"17,888 15,1!0,028 15,"80,817 1",2!0,2! 1",821,037 17,!21,871 18,0!!,1"7 1,"88,"1 20,31,55 21,120,3!0 21,87!,7!2 22,"5",01 23,!"5,3! 2!,303,512 25,171,"15 2",070,725 27,001,51 27,"",!!0 28,"5,37 30,000,000

5.5

na 9+P 9 n i-+/+ +P+:

+*+L

reortada or el E

130000 C5",7!3."0 1.2 8% 0

$ !,5 aAo$. El re$to del (e'o la ta$a au'enta 1,25% .

E4/ 8 +D/ L+ -+/+ E -E4E/ E/ EL 12% /EE/-4+L /-E4 *+ )44E/PE)+ )44E/PE)+ E-4E PE4/ = +D/ ) E L+ -+/+

+ +L 15%/ *4+-E !,5 +D/

, el ban&o e$taba agando el "% -. $ &in&o aAo$.

y C 30.000.000 re$e&(a'ente re$e&(a'ente y a&ordaron a&ordaron la$ $iguiente$ $iguiente$ &lJu$ula$N re$e$, &on el 55% y el !5% re$e&(a'ente y, ente$ entre entre lo$ $o&io$, el nego&io $e liOuida a lo$ 2,5 aAo$

$ y &uJl ue la ta$a de rendi'iento rendi'iento anual rodu&ida en el nego&io.

/) B P+4-)P+ !5% C30,000,000.00 C31,10,302.28 2.5 2.50% 0

2.5% 1,000,000 750,000

2.50 2,500,000 1,875,000

0,500,000 73,875,000

erH$ del 7% tri'e$tralM dentro de 3 aAo$ re(ra la ter&era arte del total a&u'ulado en $u &uenta, o'ento o'ento y do$ aAo$ aAo$ de$uH de$uH$$ re(r re(raa la total totalidad idad del diner dinero o ei$t ei$tent ente e en e$a e&ha. e&ha. >allar >allar el alor alor de e$te e$te Gl('o Gl('o r 7% PA,O DE i

F

  105,000 112,350 120,215 128,"30 137,"3! 1!7,2"8 157,577 1"8,"07 180,!10 13,038 20",551 221,00 1"2,810 17!,207 18",!02 1,!50 213,!11

1,500,000 1,"05,000 1,717,350 1,837,5"5 1,"",1! 2,103,828 2,251,0" 2,!08,"72 2,577,27 2,757,"8 2,50,727 3,157,278 2,325,8"1 2,!88,"72 2,""2,87 2,8!,280 3,0!8,730 3,2"2,1!1

228,350 2!!,33! 2"1,!38 !10,!57 !3,18 !",33 502,828 538,02" 575,"88 "15,8" "5,105

3,!0,!1 3,73!,825 5,8"3,"7" ",27!,133 ",713,322 7,183,255 7,"8",082 8,22!,108 8,7,7" ,!15,782 10,07!,88"

 

e(ro.