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Faktor Bunga (Time Value Of Money)


  1. Future Value

Vn = P (1+i) n

Ket :
Vn = Jumlah akhir yang diterima
P = Nilai uang awal periode
i = Bunga
n = Tahun keberapa

  1. Present Value
P = V
       (1+i)n

  1. Future Value Of Annuity

Sn = P1(1+i)n-1 + P2(1+i)n-2 + P3(1+i)n-3…. Pn(1+i)n-n

  1. Present Value Of Annuity

An = V1    +   V2   +   V3…….. Vn
          (1+i)1   (1+i)2   (1+i)3….(1+i)n


Contoh Soal:

  1. Future Value
  • Diket: P = 1.000.000
i = 5 % / tahun
n = 5 tahun
Ditanya : V5……?
Jawab : V5 = P (1 +i) n
= 1.000.000 (1+0.05)5
= 1.000.000 (1,276)
= 1.276.000

  • Diket: P = 5.000.000
i = 6 % / tahun
n = 7 tahun
Ditanya : V7……?
Jawab : V7 = P (1 +i) n
= 5.000.000 (1+0.06)7
= 5.000.000 (1,503)
= 751.500

Kalo dibayar per 1 tahun sekali
  • Diket: P = 500.000
i = 6 % / tahun
n = 1 tahun
m = 12
Ditanya : Vn……?
Jawab : Vn = P (1 +i) m.n
       m
= 500.000 (1+0.06)12.1
 12
= 500.000 (1,061)
= 530.500

Penawaran tuan B
P = 1.000.000
i = 15%
n = 5th
Ditanya: V5=P(1+i)n
=1.000.000 (1+0.15)5
=1.000.000 (2,011)
= 2.011.00

Jadi, saya nemilih tuan B karena selisih angkanya lebih besar karena keuntungan nya lebih besar senilai 6.000.000-2.011.000= 3.989.000

  1. Present Value
  • Diket : P=1.150.000
i = 15%
n = 1 th
Jawab : P = V
     (1+i)n
= 1.150.000
    (1+0,15)1
= 1.000.000

  • Diket : P=5.555.444
i = 5%
n = 5 th
Jawab : P = V
     (1+i)n
= 5.555.444
    (1+0,05)5
= 5.555.444
     1,276
= 4.353.796,238

  • Diket : P=6.000.000
i = 10%
n = 2 th
Jawab : P = V
     (1+i)n
= 6.000.000
    (1+0,1)2
= 6.000.000
     1,21
= 4.958.677,685

  • Diket : P=10.000.000
i = 12%
n = 2 th
Jawab : P = V
     (1+i)n
= 10.000.000
    (1+0,12)2
= 10.000.000
     1,254
= 7.974.471,658

  1. Future Value Of Annuity
  • Diket : P =1.000.000
i = 5%/tahun (bunga majemuk)
n = 5th
Ditanya : S5…?
Jawab : Sn = P1(1+i)n-1+ P2(1+i)n-2 +P3(1+i)n-3 +P4(1+i)n-4+P5(1+i)n-5
=1.000.000(1+0.05)5-1+1.000.000(1+0.05)5-2+1.000.000(1+0.05)5-3+1.000.000(1+0.05)5-4+1.000.000(1+0.05)5-5
=1.215.000+1.157.000+1.102.000+1.050.000+1.000.000
=5.524.000

  • Diket : P =500.000
i = 6%/tahun (bunga majemuk)
n = 7th
Ditanya : S7…?
Jawab : S7 =500.000(1,06)7-1+500.000(1,06)7-2+500.000(1,06)7-3+500.000(1,06)7-4+500.000(1,06)7-5+500.000(1,06)7-6+500.000(1,06)7-7
=709.000+669.000+631.000+595.000+561.500+530.000+500.000
=4.196.000

  1. Present Value Of Annuity
  • Diket : P =1.150.000
i = 15%/tahun (bunga majemuk)
n = 1th
Ditanya : A1…?
Jawab : A1=1.150.000
        (1+0,15)1
=1.000.000

  • Diket : P=5.555.444
i= 5%/th (bunga majemuk)
n= 5th
Ditanya : A5…?
Jawab : A5 =5.555.444 +
(1+0,05)1
5.555.444 +
(1+0,05)2
5.555.444 +
(1+0.05)3
5.555.444 +
(1+0.05)4
5.555.444
(1+0.05)5
=5.290.899+5.041.237+4.801.593+4.572.381+4.353.796
                                    =24.059.906

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