Chapter 4 [Kuliah] - Interest Rate and Equivalence
Short Description
engineering economic...
Description
1 Rejab 1438
Ya Ya Allah, tambahkanlah kepadaku ilmu dan berikanlah aku pengertian yang baik
C O N TE N T S
4. 1
Simple Interest
4. 2
Compound Interest
4. 3 4. 4 4.
INTERE INT EREST ST RA R A T E AND A ND Nominal and Efective Interest ates EQUIVALENCE !he Concept E"uivalence E"uivalence Dr Nordiana Azlin binti Othman Cash #lo$%&ia'ram #lo$%&ia'ra m !a(le !a(le
!im" # T$O"
A(le to per*orm calculations *or interest rates and cash +o$s that occur on a time (asis other than yearly
4. 1
Simple Interest
%ntr&du'ti&n %ntere"t !he cost o* usin' someone elses money It that sense, it may (e thou'ht o* as rent. !he money you (orro$ *rom the (an8 (elon's to savers $hom the (an8 pays interest. In turn, the (an8 char'es you interest. What you pay to the (an8 as interest is more than $hat the (an8 pays to the saver. !he (an8 is thus the 9middle man: poc8etin' the diference in interest.
%ntere"t A measure o* Rate interest *or a 'iven loan durin' the loan period &enoted as i and expressed in percenta'e /01 per year Annual interest rate o* 20 sated as i 3 20 4et say that you (orro$ a sum o* 5-67 *or one year. !his sum called as principal. *S. K Vajpayee in Fundamentals of Economics for Engineering Technologists and Engineers, page 7
Simple %ntere"t n n = o Interest earned on only the principal e i t i & durin' each interest period time" a year.
Some nominal statementsH
Some statements indicatin' an efective rateH
60 per %months
).60 per month *or ) months
)60 per year, compounded monthly
0 per month compounded monthly
N&minal and E5e'ti/e %ntere"t Rate"
:&'u" &n the ;i5eren'e"< Nominal ates
Efective ates
r ? rate@peri&d A peri&d" ExampleH ate is ).60 per month. &etermine nominal rate per "uarter, year, and over years
Btr6
r 3 ).6 K - mth 3 ;.60
ear6 r 3 ).6 K) mth 3 )20 3 ;.6 K ; "tr 3 )20
ExampleH Credit card rate is ).60 per month compounded monthly. &etermine efective rate per "uarter and per year
rtrH r 3 ).6 K - mth 3 ;.60 , m 3 per "tr
yearH 2 yr"6
r 3).6 K ; mth 3 -0
i 3 /) L 7.7;6M-13 ) 3 ;.6D0
r 3 )20 , m 3 ) i
12
E5e'ti/e %ntere"t Rate"
E+ample
#or an interest rate o* )70 per year '&mp&unded '&ntinu&u"ly, =nd i.
the nominal rate per "uarter
ii. the efective rate per month
Time Da"ed nit • !he
period o* time over $hich the interest is expressed. • !his is the t in the statement o* r 0 per time period t , *or example, )0 per month. %ntere"t • !he time unit o* ) year is (y *ar the most common. peri&d )t* • It is assumed $hen not stated other$ise.
• !he
shortest time unit over $hich interest is char'ed or earned. • !his is de=ned (y the compoundin' term in the interest rate statement, C&mp&undi *or example, 20 per year, compounded monthly. ng peri&d • I* C is not stated, it is assumed to (e the same as the interest period. )C* • !he
t.
num(er o* times that compoundin' occurs $ithin the interest period
C&mp&undi • I* the compoundin' period C and the time period t are the same, the ng compoundin' *re"uency is ), *or example, )0 per month, compounded ,reuen'y monthly. )m*
:inal E+am Bue"ti&n
E+ample You are 'iven three diferent plans $ith diferent interest char'in'. !hree interest plans are presentedH a1 F0 per year, compounded "uarterly. (1 -0 per "uarter, compounded "uarterly. c1 2.20 per year, compounded monthly.
%, payment" are made &n a l&an e/ery m&nth". Fhi'h Dank ha" the l&-e"t annual intere"t rateG
4. 4
!he Concept E"uivalence
The C&n'ept Eui/alen'e
Termin&l&gy
ayment eri&d )* T p % 4en'th o* time durin' $hich cash +o$s are not reco'nied except as end o* period cash +o$s.
C&mp&unding eri&d /C or interest period1, !c % 4en'th o* time (et$een compoundin' operations.
%ntere"t Rate eri&d T % Interest rates are stated as 0 per time period. ! is the time period.
C&mp&unding ,reuen'y m % the num(er o* times that compoundin' occurs $ithin the time period o* !.
The C&n'ept Eui/alen'e
C&mparing /". C 3 C O*ten the *re"uency o* cash +o$s d&e"n>t eual the *re"uency o* interest compoundin'. T& '&rre'tly per*orm any e"uivalence computation, it is essential that the and C (e placed on the same time (asis, and that the interest rate and the num(er o* periods (e adPusted accordin'ly.
Q C R C
The C&n'ept Eui/alen'e
Ca"e 16 ? C An en'ineer plans to (orro$ 5-,777 *rom his company credit union, to (e paid in ; e"ual monthly instalments. !he credit union char'es interest at the rate o* )0 per month on the unpaid (alance. ?o$ much money must the en'ineer repay each monthB 3 5-,777 C C C C C C C C C C C C r 3 )0
Mmonth 3 )m C 3 )m
S&luti&n6 ?ere (oth the payment and compound periods are e"ual to one month. !here*ore, A 3 /AM, )0, ;1 3 5-,777 /7.7;D7D1 3 5);).).
The C&n'ept Eui/alen'e
Ca"e 26 H C An en'ineer deposits 5),777 in a savin's account at the end o* each year. I* the (an8 pays interest at the rate o* 0 per year, compounded "uarterly, ho$ much money $ill (e accumulated in the account a*ter 6 yearsB C
C
C
S&luti&n6 ?ere (oth the Q C, there*ore, # 3 ),777/#M,).60,)1 L ),777/#M,).60,)1 L),777/#M,).60,21 L
C
3 5),777 r 3 0 My c" 3 )y /)m1 C 3 )" /-m1
The C&n'ept Eui/alen'e
Ca"e 36 I C
Interest is earned only (y those payments that have (een deposited or invested *or the entire interest period /C1. usual mode o* operation o* (an8s and lendin' institutions.
!he
Any amount o* money that is deposited (et$een compoundin' times earns compound interest.
Num(er o* Cs per is no$ less than ).
Gse the efective rate *ormula to =nd efective rate. Gse that rate assumin' compoundin' occurs at that rate every .
*ollo$in' rules are appliedH
All deposits made durin' an interest period are 9moved: to the end o* the interest period.
i t All $ithdra$als made durin' an a ) u interest period are 9moved: to the t (e'innin' o* the interest period. i n S o roceed as in the case $here
ExampleH i t 3) $ee8 C3) "uarter r3-0 per a u "uarter. Efective $ee8ly i t i n 03/).7-1)M)-%). S o
The C&n'ept Eui/alen'e
Ca"e 36 I C
C
C
C
C
4.
Cash #lo$%&ia'ram
Ca"h :l&-#;iagram
Repre"entati&n
Cash +o$s are in+o$s and out+o$s o* money.
Every person or company has cash receipts revenue and income /in+o$s1 E + and cash dis(ursements expenses or costs /out+o$s1.
lus si'ns indicate cash in+o$s and minus si'ns indicate cash out+o$s. C!SJ OT:$OF
C!SJ %N:$OF Salaries, revenues Income tax savin's
En'ineerin' desi'n costs eriodic maintenance costs Income taxes
a m p l e
Ca"h :l&-#;iagram
Repre"entati&n
Cash +o$ estimates are Pust estimates.
Al$ays some uncertainty involved in
Once cash in+o$ and out+o$ estimates are developed, the net cash +o$ can (e determinedH Net cash +o$ 3 cash in+o$s cash out+o$s
ImportantH End o* period convention means that all cash +o$s are assumed to occur at the end o* an interest period.
When several receipts and dis(ursements occur $ithin a 'iven interest period the net cash +o$ is assumed to occur at the end o* the interest period
Ca"h :l&-#;iagram
;iagram" •
Cash +o$ dia'ram is an important tool in economic analysis.
It is a 'raphical representation o* cash +o$s dra$n on a time scale.
In a cash +o$ dia'ram, period ). Year )
7
)
is the present, and is end o* time Year 6
-
;
6
Ca"h :l&-#;iagram
;iagram" #
E , $ o + h s a C
)
A si'n convention is applied
ositive cash +o$s /in+o$s1 are normally dra$n up$ard *rom the time line
-
;
!ime
Ne'ative cash +o$s /out+o$s1 are normally dra$n do$n$ard *rom the
Ca"h :l&-#;iagram
E+ample 1 Assume 6,777 is (orro$ed today and payments are ),)77 per year startin' next year *or ; years. &ra$ the cash +o$ dia'ram *rom the lender>" and b&rr&-er>" perspective. A 3 ),)77Myear
7
)
-
$ender>" per"pekti, % 6,777
6,777
D&rr&-er>" per"pekti,
; Years 7
)
-
A 3 ),)77Myear
;
Years
Ca"h :l&-#;iagram
E+ample 2 A mechanical device $ill cost 7,777 $hen purchased. aintenance $ill cost 5)777 per year. !he device $ill 'enerate revenues o* 6, 777 per year *or 6 years. !he salva'e value is D, 777 a*ter 6 years. I* the rate o* return is estimated to (e )6.60 per year, construct the cash +o$ dia'ram *rom the lenders perspective.
D777 L ;777 3 ))777 A 3 ;777Myear i ) #.#7
% 7,777
)
-
;
6
Years
( ) positi'e cash o+ minus negati'e cash o+
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