TIN205 - Ekonomi Teknik Materi #4 Genap 2014/2015 TIN205 EKONOMI TEKNIK

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6 6 2 3 -T a u fi q u r R a ch m a n

TIN205 – EKONOMI TEKNIK

Materi #4

h t t p : / / t a u f i q u r r a c h m a n . w e b l o g . e s a u n g g u l . a c . i d 6 6 2 3 -T a u fi q u r R a ch m a n

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

.

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Unit Waktu Suku Bunga

m

r

t

per

periods

g

compoundin

m

t

period

time

per

r%

CP

per

Rate

Effective



 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

).

Materi #4 Genap 2014/2015

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TIN2005 - Ekonomi Teknik

Simbol dan Rumus

m a

)

P(1

i)

i

P(1

F









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 periodecompound.  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).

4

1 )

i

(1

i

1/m a







(i)(m)

year)

per

CP

of

CP)(no.

per

(i%

year

per

r%



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Tabel Suku Bunga

Materi #4 Genap 2014/2015 TIN2005 - Ekonomi Teknik

5

Nominal Interest

Rate per Year when nominal rate is compoundedEffective interest rate/year (ieff),

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% h t t p : / / t a u f i q u r r a c h m a n . w e b l o g . e s a u n g g u l . a c . i d 6 6 2 3 -T a u fi q u r R a ch m a n

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.

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Perhitungan Suku Bunga Efektif

7 h t t p : / / t a u f i q u r r a c h m a n . w e b l o g . e s a u n g g u l . a c . i d 6 6 2 3 -T a u fi q u r R a ch m a n

Periode Waktu Suku Bunga Efektif



Frekjuensi dari pembayaran atau penerimaan

disebut

Payment Period

(PP).



Hubungan Ekuivalensi antara PP dan CP:



Single Amounts

dengan PP≥CP



Series

dengan PP≥CP



Single Amounts and Series

dengan PP<CP

8

1 r/m)

(1

i

Effective

_

_

m

_

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Hubungan Ekuivalensi PP dan CP

9

 Single Amounts dengan PP≥CP

 Metode 1: Tentukan suku bunga efektif terhadap CP dan setn sama

dengan jumlah CP antaraP dan F.

 Metode 2: Tentukan suku bunga efektif untuk periode waktut dari

suku bunga nominal, dan setn sama dengan total jumlah periode.

 Series dengan PP≥CP

 Tentukan effectivei per PP.  Tetapkann sebagai total dari PP.

 Single Amounts and Series dengan PP<CP

 Terdapat istilahinterperiod compounding.  Ada 2 kebijaksanaan penanganan:

 interperiod cash flows tidak kena bunga, atau  mendapatcompound 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

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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.

Payment PaymentTotal

int* 2 2+3 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 h t t p : / / t a u f i q u r r a c h m a n . w e b l o g . e s a u n g g u l . a c . i d 6 6 2 3 -T a u fi q u r R a ch m a n

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 _PaymentPrincip. _PaymentTotal

int*2 2+3 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

13



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

1 2 3 4 5 6

int*2 2+3 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 h t t p : / / t a u f i q u r r a c h m a n . w e b l o g . e s a u n g g u l . a c . i d 6 6 2 3 -T a u fi q u r R a ch m a n

Plan D Dari Contoh

14



Plan D: Pay principal and interest in one payment at end of

five.

1 2 3 4 5 6

int*2 2+3 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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66 23 -T au fiq ur R ac hm an Materi #4 Genap 2014/2015 TIN2005 - Ekonomi Teknik