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Nilai Waktu dari Uang. Lecture Note: Trisnadi Wijaya , SE., S.Kom. Garis Waktu ( Time Line ). Waktu :. 0. 1. 2. 3. 4. 5. 5%. Arus Kas :. -100. Nilai Masa Depan ( Future Value ).

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nilai waktu dari uang

NilaiWaktudariUang

Lecture Note:

Trisnadi Wijaya, SE., S.Kom

garis waktu time line
GarisWaktu (Time Line)

Waktu:

0

1

2

3

4

5

5%

ArusKas:

-100

nilai masa depan future value
NilaiMasaDepan (Future Value)
  • Satu rupiah yang dipegangsekaranglebihberhargadaripadasatu rupiah yang diterimadimasa yang akandatang.
  • Nilaimasadepanadalahsebuahjumlah yang akandicapaioleharuskasatauserangkaianaruskasberkembangsetelahmelaluijangkawaktutertentubiladimajemukkandengantingkatsukubungatertentu.
nilai masa depan future value1
NilaiMasaDepan (Future Value)
  • Proses yang mengarahdarinilaisekarang (present value-PV) menujunilaimasadepan (future value-FV) disebutdenganpemajemukan (compounding).

0

1

2

3

4

5

5%

Setoranawal:

-100

Pendapatanbunga:

5,00

5,25

5,51

5,79

6,08

Saldoakhir (FV):

105,00

110,25

115,76

121,55

127,63

nilai masa depan future value2
NilaiMasaDepan (Future Value)

FV = Nilaimasadepan (future value)

PV = Nilaisekarang (present value)

i = sukubunga

n = periodetahun

membaca tabel bunga
MembacaTabelBunga

Caripadatabel PVIF, PVIFA, FVIF, atau FVIFA

Lihatsukubungapadasumbu horizontal

Lihatperiodepadasumbuvertikal

Temukannilaipadakeduatitikpoinpertermuanantarasukubungadanperiode

Periode

3%

1%

2%

6%

4%

5%

9%

7%

8%

1

Carinilai FVIF dengantingkatsukubunga 4% padaperiode 3 tahun.

2

1.1249

3

4

Tabel FVIF

5

6

7

8

9

nilai sekarang present value
NilaiSekarang (Present Value)
  • Kebalikandaripemajemukan (compounding) adalahpendiskontoan (discounting).
  • Pendiskontoan (discounting)adalahprosespencariannilaisekarangdariaruskasatauserangkaianaruskas.
nilai sekarang present value1
NilaiSekarang (Present Value)

FV = Nilaimasadepan (future value)

PV = Nilaisekarang (present value)

i = sukubunga

n = periodetahun

nilai masa depan dari anuitas
NilaiMasaDepandariAnuitas

Anuitas (annuity)adalahserangkaianpembayarandalamjumlah yang sama yang dilakukanselamajangkawaktu yang tetapdalamperiode yang telahditentukan.

FVA = Nilaimasadepandarianuitas

PMT = Pembayaran (payment)

i = sukubunga

n = periodetahun

jenis anuitas
JenisAnuitas
  • Anuitasbiasaterdiriatasserangkaianpembayaran yang samajumlahnyapadaakhirtiapperiode.
  • Anuitasjatuh tempo (annuity due)terdiriatasserangkaianpembayaran yang samajumlahnyapadaawaltiapperiode.
  • Anuitasabadi (perpetuities)adalahserangkaianpembayaran yang samajumlahnyadandiharapkanakanberlangsungterus-menerus.
slide11

AnuitasBiasa

0

1

2

3

5%

100

100

100

100

105

0

1

2

3

110,25

5%

AnuitasJatuh Tempo

FVA3 = 315,25

100

100

100

105

110,25

115,76

FVA3 (Anuitasjatuh tempo)= 331,01

nilai sekarang dari anuitas
NilaiSekarangdariAnuitas

AnuitasBiasa

PVA = Nilaisekarangdarianuitas

PMT = Pembayaran (payment)

i = sukubunga

n = periodetahun

nilai sekarang dari anuitas1
NilaiSekarangdariAnuitas

AnuitasJatuh Tempo

PVA = Nilaisekarangdarianuitas

PMT = Pembayaran (payment)

i = sukubunga

n = periodetahun

anuitas abadi
AnuitasAbadi

Beberapaanuitasdapatberlangsungterustanpabataswaktu, atausecara perpetual, dananuitasinidisebutanuitasabadi (perpetuities).

pinjaman yang diamortisasi
Pinjaman yang Diamortisasi
  • Jikasuatupinjamanakandibayarkandalamperiode yang samapanjangnya (bulanan, kuartalan, atautahunan), makapinjamaninidisebutjugasebagaipinjaman yang diamortisasi (amortized loan).
exercise page 324
Exercise (Page 324)
  • If you deposit $10,000 in a bank account that pays 10 percent interest annually, how much money will be in your account after 5 years?
  • What is the present value of a security that promises to pay you $5,000 in 20 years? Assume that you can earn 7 percent if you were to invest in other securities of equal risk.
  • If you deposit money today into an account that pays 6.5 percent interest, how long will it take for you to double your money?
  • John Roberts has $42,180.53 in a brokerage account, and he plans to contribute an additional $5,000 to the account at the end of every year. The brokerage account has an expected annual return of 12 percent. If John’s goal is to accumulate $250,000 in the account, how many years will it take for John to reach his goal?
  • Your parents are planning to retire in 18 years. They currently have $250,000, and they would like to have $1,000,000 when they retire. What annual rate of interest would they have to earn on their $250,000 in order to reach their goal, assuming they save no more money?
exercise page 3241
Exercise (Page 324)
  • What is the future value of a 5-year ordinary annuity that promises to pay you $300 each year? The rate of interest is 7 percent.
  • What is the future value of a 5-year annuity due that promises to pay you $300 each year? Assume that all payments are reinvested at 7 percent a year, until Year 5.
  • An investment pays you $100 at the end of each of the next 3 years. The investment will then pay you $200 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If the interest rate earned on the investment is 8 percent, what is its present value? What is its future value?
  • You are thinking about buying a car, and a local bank is willing to lend you $20,000 to buy the car. Under the terms of the loan, it will be fully amortized over 5 years (60 months), and the nominal rate of interest will be 12 percent, with interest paid monthly. What would be the monthly payment on the loan? What would be the effective rate of interest on the loan?