TIN205 - Ekonomi Teknik Materi #4 TIN205 EKONOMI TEKNIK Pendahuluan 2 Suku bunga nominal dan Suku bunga efektif mempunyai hubungan dasar yang sama dengan simple interest dan compound interest. Perbedaannya adalah konsep ini harus digunakan ketika bunga berbunga lebih dari satu kali setiap tahun. Bunga yang dipakai untuk pinjaman, mortgage, bonds dan stocks adalah berdasarkan compounded yang lebih sering dibandingkan tahunan. Suku bunga nominal = r. Suku bunga efektif = i a. r% per periode waktu t, compounded m-ly 6623 - Taufiqur Rachman 1
TIN205 - Ekonomi Teknik Unit Waktu Suku Bunga 3 APR (Annual Percentage Rate) sama dengan suku bunga nominal. APY (Annual Percentage Yield) sama dengan suku bunga efektif. Ada 3 unit waktu yang digunakan untuk suku bunga, yaitu: Periode waktu (Time Period). Periode compound (compounding period/cp). Frekuensi compound (compounding frequency). Effective Rate per CP r% per time period t m compounding periods per t r m Simbol dan Rumus 4 Simbol yang digunakan untuk suku bunga nominal dan suku bunga efektif adalah: r = suku bunga nominal per tahun. m = jumlah periode compound per tahun. i = suku bunga efektif per periode compound. CP = compounding period (periode compound) = r/m i a = suku bunga efektif per tahun. Sewaktu suku bunga nominal dihitung tahunan (compounded annually), maka nilainya akan sama dengan suku bunga efektif (lihat tabel). F P(1 ia) P(1 i) m i (1 ia) 1/m 1 r% per year (i%per CP)(no.of CP per year) (i)(m) 6623 - Taufiqur Rachman 2
TIN205 - Ekonomi Teknik Tabel Suku Bunga 5 Nominal Interest Rate per Year Effective interest rate/year (i eff ), when nominal rate is compounded r Yearly Semi Annually Monthly Daily Continuously 1% 1% 1.0025% 1.0046% 1.0050% 1.0050% 2% 2% 2.0100% 2.0184% 2.0201% 2.0201% 3% 3% 3.0225% 3.0416% 3.0453% 3.0455% 4% 4% 4.0400% 4.0742% 4.0809% 4.0811% 5% 5% 5.0625% 5.1162% 5.1268% 5.1271% 6% 6% 6.0900% 6.1678% 6.1831% 6.1837% 8% 8% 8.1600% 8.3000% 8.3278% 8.3287% 10% 10% 10.2500% 10.4713% 10.5156% 10.5171% 15% 15% 15.5625% 16.0755% 16.1798% 16.1834% 25% 25% 26.5625% 28.0732% 28.3916% 28.4025% Contoh Suku Bunga Efektif 6 Jacki obtained a new credit card from a national bank, MBNA, with stated rate of 18% per year, compounded monthly. For a $1000 balance at beginning of the year, find the effective annual rate and the total amound owed to MBNA after 1 year, provided no payments are made during the year. 6623 - Taufiqur Rachman 3
TIN205 - Ekonomi Teknik Perhitungan Suku Bunga Efektif 7 Periode Waktu Suku Bunga Efektif 8 Frekjuensi dari pembayaran atau penerimaan disebut Payment Period (PP). Effective i Hubungan Ekuivalensi antara PP dan CP: Single Amounts dengan PP CP Series dengan PP CP (1 r/m) m Single Amounts and Series dengan PP<CP 1 6623 - Taufiqur Rachman 4
TIN205 - Ekonomi Teknik Hubungan Ekuivalensi PP dan CP 9 Single Amounts dengan PP CP Metode 1: Tentukan suku bunga efektif terhadap CP dan set n sama dengan jumlah CPantara P dan F. Metode 2: Tentukan suku bunga efektif untuk periode waktu t dari suku bunga nominal, dan set n sama dengan total jumlah periode. Series dengan PP CP Tentukan effective i per PP. Tetapkan n sebagai total dari PP. Single Amounts and Series dengan PP<CP Terdapat istilah interperiod compounding. Ada 2 kebijaksanaan penanganan: interperiod cash flows tidak kena bunga, atau mendapat compound interest. Rencana Pembayaran 10 Example: You borrowed $5,000 from a bank at 8% interest rate and you have to pay it back in 5 years. There are many ways the debt can be repaid. Plan A: At end of each year pay $1,000 principal plus interest due. Plan B: Pay interest due at end of each year and principal at end of five years. Plan C: Pay in five end-of-year payments. Plan D: Pay principal and interest in one payment at end of five years. 6623 - Taufiqur Rachman 5
TIN205 - Ekonomi Teknik Plan A Dari Contoh 11 Plan A: At end of each year pay $1,000 principal plus interest due. 1 2 3 4 5 6 Year Amnt. Owed Int. Owed Total Owed Princip. int* 2 2+3 Payment Total Payment 1 5,000 400 5,400 1,000 1,400 2 4,000 320 4,320 1,000 1,320 3 3,000 240 3,240 1,000 1,240 4 2,000 160 2,160 1,000 1,160 5 1,000 80 1,080 1,000 1,080 Sum 15,000 1,200 16,200 5,000 6,200 Plan B Dari Contoh 12 Plan B: Pay interest due at end of each year and principal at end of five years. 1 2 3 4 5 6 Year Amnt. Owed Int. Owed Total Owed Princip. int*2 2+3 Payment Total Payment 1 5,000 400 5,400 0 400 2 5,000 400 5,400 0 400 3 5,000 400 5,400 0 400 4 5,000 400 5,400 0 400 5 5,000 400 5,400 5,000 5,400 Sum 25,000 2,000 27,000 5,000 7,000 6623 - Taufiqur Rachman 6
TIN205 - Ekonomi Teknik Plan C Dari Contoh 13 Plan C: Pay in five end-of-year payments. 1 2 3 4 5 6 Year Amnt. Owed Int. Owed Total Owed Princip. int*2 2+3 Payment Total Payment 1 5,000 400 5,400 852 1,252 2 4,148 332 4,480 920 1,252 3 3,227 258 3,485 994 1,252 4 2,233 179 2,412 1,074 1,252 5 1,160 93 1,252 1,160 1,252 Sum 15,768 1,261 17,029 5,000 6,261 Plan D Dari Contoh 14 Plan D: Pay principal and interest in one payment at end of five. 1 2 3 4 5 6 Year Amnt. Owed Int. Owed Total Owed Princip. int*2 2+3 Payment Total Payment 1 5,000 400 5,400 0 0 2 5,400 432 5,832 0 0 3 5,832 467 6,299 0 0 4 6,299 504 6,802 0 0 5 6,802 544 7,347 5,000 7,347 Sum 29,333 2,347 31,680 5,000 7,347 6623 - Taufiqur Rachman 7
TIN205 - Ekonomi Teknik 6623 - Taufiqur Rachman 15 6623 - Taufiqur Rachman 8