3360 Unit 04.1 2014-I-01

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ENGR 3360U Winter 2014Unit 4.1-3

Interest, Equivalence and Repeated as! "l#$s

Dr. J. Michael Bennett, P. Eng., PMP,UOIT,

Version 2014-I-01

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Unit 4 Interest and Equivalence

!an%e Rec#rd

2014-I-01 Initial reati#n&e't re(erences) !apters 3 and 4

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#urse /utline

1. En%ineerin% Ec#n# ics2. General Ec#n# ics

1. icr#ec#n# ics2. acr#ec#n# ics

3. #ne and t!e an #(anada3. En%ineerin% Esti ati#n4. Interest and Equivalence

. resent W#rt! nal sis6. nnual as! "l#$5. Rate #( Return nal sis

. ic in% t!e est !#ice7. /t!er !##sin% &ec!niques

10. Uncertaint and Ris 11. Inc# e and *epreciati#n12. (ter-ta' as! "l#$s13. Replace ent nal sis

14. In(lati#n1 . RR 8electi#n16. u9lic 8ect#r Issues15. W!at En%ineerin% s!#uld n#$

a9#ut cc#untin%1 . ers#nal Ec#n# ics (#r t!e

En%ineer

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Unit 4 #ntents

4-1 &i e :alue #( #ne4-2 Equivalence4-3 8in%le a ent # p#und Interest4-4 nnual a ents4- rit! etic Gradient

4-6 Ge# etric Gradient4.5 "indin% Interest Rates #r n eri#ds4- #ntinu#us # p#undin%


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Learning Objectives

; &i e :alue #( #ne; 8i ple and # p#und Interest

; Equivalence; 8in%le a ent # p#und Interest"#r ulas

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4-1 Time Value of Money

; W!at $#uld #u rat!er !avein(lati#n?.

; &!ere(#re, in t!e a9#ve e'a ple t!e actual @valueA #(#ne c!an%es at s# e rate #ver ti e.

; &!is rate is t picall e'pressed as s# e percenta%e per peri#d #( ti e.


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Interest: Simple Interest

; 8i ple interest is interest applied /NBC t# t!e#ri%inal su .

; Interest is never calculated #n previ#us interestcalculati#ns.

Interest earned D ' i ' n!ere: " # present sum$ i # interest rate%perio&$ n # ' of time perio&s

tal #ne a(ter n peri#ds >"?)" D ' i ' n /R "D >1 i ' n?

!ere: ( # future sum


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N#tati#n

D present su t#da >ti e 0?" D (uture su #( #ne a(ter t!e last #( nti e peri#dsn D nu 9er #( ti e peri#ds >n#r all

ears?i D interest rate >n#r all percenta%eF ear?

D annual pa ent per ear

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2014-I-014-7

N8I 8tandard N#tati#n (#r Interest "act#rs

8tandard n#tati#n !as 9een ad#pted t#represent t!e vari#us interest (act#rs #nsists #( t$# cas! (l#$ s 9#ls, t!einterest rate, and t!e nu 9er #( ti e peri#ds General (#r )> FC,iH,n?

represents $!at is un n#$n

C represents $!at is n#$n i and n represent input para eters can 9e n#$n#r un n#$n dependin% up#n t!e pr#9le

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2014-I-014-10

N#tati#n - c#ntinued

E'a ple) >"F ,6H,20? is read as) (ind ", %iven $!en t!e interest rate is 6Hand t!e nu 9er #( ti e peri#ds equals 20.

In pr#9le (#r ulati#n, t!e standardn#tati#n is #(ten used in place #( t!e cl#sed-(#r equivalent relati#ns >(act#r?

&a9les at t!e 9ac #( t!e te't pr#videta9ulati#ns #( c# #n values (#r iH and n>see &a9le "//"// ?


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)ompoun& Interest

; N#r all , t!e c# p#und interest et!#d isused.

; 8i ple interest is n#t used unlessspeci(icall stated #t!er$ise.

; Interest is calculated #n t!e accu ulateda #unt and n#t si pl #n t!e #ri%inal

a #unt.; @Interest #n t#p #( interestA


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)ompoun& Interest

#nsider a =2 ,000 invest ent at 10HF ear,c# p#unded)

!ear

"n#

Total atstart o$!ear "n#

Interestacc%&%late'

at en' o$(ear "n#

)&o%ntacc%&%late'

at en' o$(ear "n#

1 *2+000 *2+00 *2 +002 *2 +00 *2 +0 * 02+0

* 02+0 * 02+ * 2 +

4 * 2 + * 2 .+0 * 02.+0


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4*+ , uivalence

; Equivalence $it! respect t# t!e @ti e value#( #ne A i plies t!at) J su #( #ne in #ne ti e peri#d a !ave

t!e sa e @valueA t# a di((erent su in an#t!erti e peri#d $it! respect t# an interest rate.

; E'a ple) J =1000 n#$ is equivalent t#)

;

=1100 #ne ear (r# n#$ at 10H per ear ; =10 0 #ne ear (r# n#$ at H per ear ; =1210 t$# ears (r# n#$ at 10H per ear ; =1102 t$# ears (r# n#$ at H per ear


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, uivalence

; Equivalence is dependent #n Interest RateK; Equivalence is use(ul $!en)

J &!ere are cas! (l#$s > ve andF#r Jve? #ver @nAti e peri#ds t!at need t# 9e c# pared

J &!ere are alternative c# paris#ns #( ultiplecas! (l#$s

;alternative pr#Lects $it! cas! (l#$s #ver @nA ti e peri#ds


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4*. Single "ayment )ompoun& Interest (ormulas

; 8 $e !ave seen)" D >1 i?n

; &!e a9#ve (#r ula is t!e) J @8in%le pa ent c# p#und a #unt (#r ulaA $!ic! is

$ritten in (uncti#nal n#tati#n as)( # "/(%"$ i$ n0

J &!e n#tati#n in 9rac ets eanin%)(uture sum (2$ given present sum "2 at interest rate I2per interest perio& for n3 perio&s


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, ample

; =3000.00 dep#sited in a 9an acc#unt at 5H per ear interest $#uld 9e !#$ uc! a(ter(#ur ears<

" D >"F , 5H, 4? " D 3000>1 0.05? 4

" D =3732.37


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Single "ayment )ompoun& Interest (ormulas

; 8upp#se #u $ant t# (ind an equivalentvalue n#$ (#r a desired (uture value<

" D >1 i?n

J Rearran%in%) D "F>1 i?n D ">1 i?-n

J &!e n#tati#n 9ec# es)

D "> F", i, n?


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, ample

; I( #u $ant t# !ave =3000.00 in t!e 9ana(ter (#ur ears at 5H per ear interest,$!at $#uld #u !ave t# dep#sit n#$<

D "> F", 5H, 4? D 3000>1 0.05?-4

D =22 .67


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Summary

; &!e @ti e value #( #ne A is an i p#rtant c#ncept inen%ineerin% ec#n# ics.

; calculate equivalenc acr#ss ultiple peri#ds #neust include t!e calculati#n #( a percenta%e rate per

peri#d >e.%., interest rate?." D >1 i?n D >"F , i, n?

D "F>1 i?n D ">1 i?-n D "> F", i, n?

; &!e n#tati#n (act#rs can 9e calculated (r# t!e (#r ula#r l## ed up in standard ta9les. 8ee t!e 9ac #( t!ete't9## .


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2014-I-01 *r. +. . ennett, .En%., ENGR 3360U En% Ec#4-20

"//"//

d l

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2014-I-014-21

E'a ple

&!e recent en!ance ents ade 9 Ipsc#, Inc. t# its lar%e-dia eter pipe ill in Re%ina are esti ated t# save = 0,000 in reduced

aintenance t!is ear.a? I( t!e steel a er c#nsiders t!ese t pes #( savin%s $#rt! 20H

per ear, (ind t!e equivalent value #( t!is result in ears. 9? I( t!e = 0,000 aintenance savin%s #ccurs n#$, (ind its

equivalent value 3 ears earlier $it! an interest #( 20H


U i 4 I d E i l

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2014-I-014-22

>a?

D = 0,000 " D < i D 20HF ear n D ears

F D P > F / P , i , n? D = 0,000> F F P , 20H, ?

D 0,000>2.4 3? D =124,41 .00

We c#uld als# use E'cel ":>20, ,, 0000?


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>9?

In t!is case, t D 0 and (#r , t D -3

P D F > P / F , i,n ? D 0,000> P / F , 20H, 3? D 0,000>0. 5 5? D =2 ,73 .00

/r :>20,3,, 0000? in E'cel.

* + tt E % ENGR 3360U E % E #

3360 Unit 04.1 2014-I-01

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