Ekonomi Teknik - Tugas 1

 

 Tugas  Tugas Ek Ekonomi onomi Teknik / BRY BRYAN / 15011108

1. What will will be the accumula accumulated ted amount amount of Rp 1.750.000,1.750.000,- compound compounded ed annually annually for three three years at the rate of 15% p.a? awab ! "eadaan satu, compound interest, portion of principal repaid annually i # 15% $ n #  End of   Year  Year 0 1 & )  Total  Total

Interest for  Year  Year " R#&'&$500 R#1%5$000 R#8%$500

 T  Total otal Owed at End End of   Y  Year ear " R#&$01&$500 R#1$)(1$''% R#'%0$8))

End of Year a!ment " R#8(5$8)) R#%58$))) R#'%0$8)) R#&$&%5$000

 T  Total otal Owed After After a!ment R#1$%50$000 R#1$1''$''% R#58)$))) "

&ontoh perhitun'an !

 P0 Totalowed after payment payment di tahun tahun pertama pertama= Pn − n

Totalowed after payment payment di tahun tahun pertama pertama=1.75 1.750 0 .00 .000 0−

1.750 1.7 50 .00 .000 0 3

1.166 66 .667 .667 Total otal owed owed after after paymen paymentt di tahun tahun perta perta ma=1.1

 Interest  Inter est for year di tahun pertama= P n∗i

1.750 0 .000∗15  Interest  Inter est for year di tahun pertama=1.75

 Interest for year di tahun pertama =262.500

Totalowed at end of year year ditahun pertama pertama= Pn + interest for year Totalowed at end of year ditah di tahun un pertama pertama=1.75 1.750 0 .00 .000 0 + 262.500 Total otal owed owed at at end of year year ditahun pertam pertama a =2.012 .500

 End of payment ditahun di tahun pertama=Totalowed at end of year year −Total owedafte owed afterr payment  payment 

 

 Tugas  Tugas Ek Ekonomi onomi Teknik / BRY BRYAN / 15011108

 End of payment ditahun di tahun pertama=2.012.500 −1.16 1.166 6 .667  End of payment di tahun pertama =845.833

 

 Tugas  Tugas Ek Ekonomi onomi Teknik / BRY BRYAN / 15011108

"eadaan dua, compound interest, pay all at end End of   Year  Year 0 1 &

Interest for  Year  Year " R#&'&$500 R#)01$8%5

 T  Total otal Owed at End End of Year " R#&$01&$500 R#&$)1($)%5

End of Year a!ment " " "

 T  Total otal Owed After After a!ment R#1$%50$000 R#&$01&$500 R#&$)1($)%5

)  Total  Total

R#)(%$15'

R#&$''1$5)1

R#&$''1$5)1 R#&$''1$5)1

"

&ontoh perhitun'an !

 Interest  Inter est for year di tahun pertama= P n∗i =1750000∗15  Interest  Inter est for year di tahun pertama=262.500 Totalowed at end of year year ditahun pertama pertama= Pn + inte intere rest st of year year Totalowed otalowed at en end d of ye year ar ditahun ditahun pert pertama ama=1750000 + 262500

Totalowed at end of year ditah di tahun un pertama pertama=2012500

(eadaan ti'a, compound interest, e)ual payments annually End of   Year  Year 0

Interest for  Year  Year "

 T  Total otal Owed at End End of Year "

End of Year a!ment

 T  Total otal Owed After After a!ment R#1$%50$000

1 R#&'&$500 R#&$01&$500 R#%''$('0 R#1$&('$0(0 & R#18'$*0' R#1$()&$*(' R#%''$('0 R#'''$(8% ) R#**$*%) R#%''$('0 R#%''$('0 "  Total  Total R#&$&**$)%* *nd of year payment pada p ada tabel ini di'una(an rumus +interest$ /umlah year$ modal$ hasil yan' din'in(an

. 2ow much much do you ha3e ha3e to sa3e sa3e now if you4d li(e li(e to ha3e ha3e Rp. 1.500.00 1.500.000,0,- to start start a new company  years from now at the interest rate of 1% per year? awab! sumsi compound interest den'an i#1% dan n#.

 

 Tugas  Tugas Ek Ekonomi onomi Teknik / BRY BRYAN / 15011108 n

 F = P ( 1 + i )

3

12.500.000 = P ( 1 + 0,12 )

 P=

12.500.000

  =8.89 8.897 7 .253

( 1,12 )3

sumsi simple interest den'an i#1% dan n#.  F = P ( 1 + n∗i ) 12500000= P (1 + 3∗0,12 )

 P=

12500000

( 1,36 )

  =9.19 9.191 1 .176

adi, untu( mendapat(an Rp 1.500.000,-, (ita harus menabun' sebesar Rp 6.67.5, bila compound interest. "ita harus menabun' sebesar Rp. .11.178,. What is the the rate of return return of an an initial initial in3estment in3estment worth worth Rp. 0 millio millions ns that yield yield Rp. 95.000.000,- after  years? awab ! sumsi satu compound interest den'an n#. n  F = P ( 1 + i ) 45.000 45.0 00 .000= 30.000.000 ( 1 + i )

3

30000000 ( 1 + i ) √ 45000000= √ 30000000 3

3

355,689 =310,723 ( 1 + i ) 1,145= 1 + i

i =1,145−1 =0,145=14,5 adi, bila men''una(an compound intererest, interest pertahunnya 19,5% sumsi dua simple interest den'an n#.  F = P ( 1 + n∗i ) 45.000 .000= 30.000.000 ( 1 + 3∗i )

1,5=1 + 3∗i 0,5= 3∗i

i =0,1667 =16,67 adi, bila men''una(an compound intererest, interest pertahunnya 18,87%

 

 Tugas  Tugas Ek Ekonomi onomi Teknik / BRY BRYAN / 15011108

9. initial initial in3estment in3estment of Rp. 50.000.000,00 50.000.000,00 is is bein' conside considered. red. he he re3enues from this this in3estment are Rp. 0.000.000,00 at the end of first year, Rp. 5.000.000,00 and Rp. 15.000.000,00 at the end of second and third years. :f the alternati3e will 'i3e a re3enue of Rp. 57.500.000,00 at the end of the third year, which in3estment would be recommended? he interest rate is set at 10% annually. annua lly. awab ! +rincipal

# P # Rp. 50.000.000,00

;uture

# F # Rp. 80.000.000,00