2015 TIN205 EKONOMI TEKNIK

TIN205 - Ekonomi Teknik

Materi #4 Genap 2014/2015

6623 - Taufiqur Rachman

h t t p://ta ufiqurrach man.webl og.e sa unggu l.ac.id

Materi #4

TIN205 – EKONOMI TEKNIK

Pendahuluan http://taufiqurrachman.weblog.esaunggul.ac.id

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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 = ia. “r% per periode waktu t, compounded m-ly”




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Unit Waktu Suku Bunga http://taufiqurrachman.weblog.esaunggul.ac.id

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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 r  m compounding periods per t m



Simbol dan Rumus http://taufiqurrachman.weblog.esaunggul.ac.id


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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 ia = 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) TIN2005 - Ekonomi Teknik



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Tabel Suku Bunga http://taufiqurrachman.weblog.esaunggul.ac.id

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Nominal Interest Rate per Year 6623 - Taufiqur Rachman

r

Yearly

Effective interest rate/year ( i eff), when nominal rate is compounded 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 http://taufiqurrachman.weblog.esaunggul.ac.id

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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.




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Perhitungan Suku Bunga Efektif http://taufiqurrachman.weblog.esaunggul.ac.id


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Periode Waktu Suku Bunga Efektif http://taufiqurrachman.weblog.esaunggul.ac.id

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Frekjuensi dari pembayaran atau penerimaan disebut Payment Period (PP).

Effectivei  (1  r/m)m  1 

Hubungan Ekuivalensi antara PP dan CP:  Single Amounts dengan PP≥CP  Series dengan PP≥CP  Single Amounts and Series dengan PP



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Hubungan Ekuivalensi PP dan CP http://taufiqurrachman.weblog.esaunggul.ac.id

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Single Amounts dengan PP≥CP Metode 1: Tentukan suku bunga efektif terhadap CP dan set n sama dengan jumlah CP antara 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

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Rencana Pembayaran http://taufiqurrachman.weblog.esaunggul.ac.id

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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. 

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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.




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Plan A Dari Contoh http://taufiqurrachman.weblog.esaunggul.ac.id

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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

int* 2

2+3

Princip. 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 http://taufiqurrachman.weblog.esaunggul.ac.id

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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

int*2

2+3

Princip. 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




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Plan C Dari Contoh http://taufiqurrachman.weblog.esaunggul.ac.id

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Plan C: Pay in five end-of-year payments. 1

2

3

4

5

6

Year

Amnt. Owed

Int. Owed

Total Owed

int*2

2+3

Princip. 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 http://taufiqurrachman.weblog.esaunggul.ac.id

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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

int*2

2+3

Princip. 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




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h t t p://ta ufiqurrach man.webl og.e sa unggu l.ac.id

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2015 TIN205 EKONOMI TEKNIK

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