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Nilai Waktu dari Uang

Nilai Waktu dari Uang

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Nilai Waktu dari Uang

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  1. NilaiWaktudariUang Lecture Note: RiniAprilia, M.Sc

  2. GarisWaktu (Time Line) Waktu: 0 1 2 3 4 5 5% ArusKas: -100

  3. NilaiMasaDepan (Future Value) • Satu rupiah yang dipegangsekaranglebihberhargadaripadasatu rupiah yang diterimadimasa yang akandatang. • Nilaimasadepanadalahsebuahjumlah yang akandicapaioleharuskasatauserangkaianaruskasberkembangsetelahmelaluijangkawaktutertentubiladimajemukkandengantingkatsukubungatertentu.

  4. 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

  5. NilaiMasaDepan (Future Value) FV = Nilaimasadepan (future value) PV = Nilaisekarang (present value) i = sukubunga n = periodetahun

  6. 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

  7. NilaiSekarang (Present Value) • Kebalikandaripemajemukan (compounding) adalahpendiskontoan (discounting). • Pendiskontoan (discounting)adalahprosespencariannilaisekarangdariaruskasatauserangkaianaruskas.

  8. NilaiSekarang (Present Value) FV = Nilaimasadepan (future value) PV = Nilaisekarang (present value) i = sukubunga n = periodetahun

  9. NilaiMasaDepandariAnuitas Anuitas (annuity)adalahserangkaianpembayarandalamjumlah yang sama yang dilakukanselamajangkawaktu yang tetapdalamperiode yang telahditentukan. FVA = Nilaimasadepandarianuitas PMT = Pembayaran (payment) i = sukubunga n = periodetahun

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

  11. 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

  12. NilaiSekarangdariAnuitas AnuitasBiasa PVA = Nilaisekarangdarianuitas PMT = Pembayaran (payment) i = sukubunga n = periodetahun

  13. NilaiSekarangdariAnuitas AnuitasJatuh Tempo PVA = Nilaisekarangdarianuitas PMT = Pembayaran (payment) i = sukubunga n = periodetahun

  14. AnuitasAbadi Beberapaanuitasdapatberlangsungterustanpabataswaktu, atausecara perpetual, dananuitasinidisebutanuitasabadi (perpetuities).

  15. AliranArusKas yang TidakMerata

  16. Pinjaman yang Diamortisasi • Jikasuatupinjamanakandibayarkandalamperiode yang samapanjangnya (bulanan, kuartalan, atautahunan), makapinjamaninidisebutjugasebagaipinjaman yang diamortisasi (amortized loan).

  17. 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?

  18. 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?