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ENGR 3360U Winter 2014
Unit 4.7-8
Finding i%, n, Continuous Co!ounding
Dr. J. Michael Bennett, P. Eng., PMP,
UOIT,
Version 2014-I-01
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C(#nge Re'ord
2014-"-01 "niti#& Cre#tion
)e*t re+eren'es C(#!ters 3 #nd 4
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4.7 Finding #n Unnon "nterest R#te
Css o+ !ro&es (ere t(e interest r#te, i%, is t(e unnon #&ue
For si!&e, sing&e !#5ent !ro&es i.e.,
#nd F on&5, so&ing +or i% gien t(e ot(er !#r#eters is not di++i'u&t
For #nnuit5 #nd gr#dient t5!e !ro&es,
so&ing +or i% '#n e tedious)ri#& #nd error et(od
!!&5 s!re#ds(eet ode&s
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)(e "RR 9!re#ds(eet Fun'tion
e+ine t(e tot#& '#s( +&o #s # 'o&un o+#&ues it(in E*'e&
!!&5 t(e "RR +un'tion
: IRR(first_cell:last_cell, guess value)
"+ t(e '#s( +&o series is #n #&ue t(en
#!!&5 t(e R)E +un'tion
=RATE(number_years, A,P,F)
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E*#!&e 4.18
Fred u5s # ne '#r it( ;0 don. )ot#& 'ost is ;1
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2014-"-014-6
eterin#tion o+ #n Unnon Nuer o+ e#rs
Css o+ !ro&es (ere t(e nuer o+ tie !eriods 5e#rs is t(e unnon
"n sing&e !#5ent t5!e !ro&es, so&ing +orn is str#ig(t +or#rd
"n ot(er t5!es o+ '#s( +&o !ro+i&es, so&ing+or n re$uires tri#& #nd error or s!re#ds(eet
"n E*'e&, gien , , #nd?or F, #nd i% #&ues
#!!&5=NPER(i,A,P,F) to return t(e #&ue o+ n
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4.8 Nominal and Effective Interest Rates
D Noin#& "nterest R#te r in n#e on&5 "nterest r#te it(out 'onsider#tion o+
'o!ounding not used in #n#&5sisD E++e'tie "nterest R#te r
"nterest r#te t(#t t#es 'o!ounding into
'onsider#tion used in #n#&5sis
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Effective Interest
D E*#!&e 12% !er 5e#r 'o!ounded ont(&5
D Noin#& "nterest R#ter :12%?5e#r 'o!ounded ont(&5
D E++e'tie /ont(&5 R#te ii : r? (ere : 'o!ounding !eriodi : 0.12?12 : 1% !er ont( e++e'tieH
D E++e'tie e#r&5 R#te ii : 1Ar? 1i : 1A0.112 1 : 12.68%?5e#r e++e'tieH@Note t(#t is 0.68% (ig(er t(#n noin#& #t 12% !er 5e#r '..
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Continuous Compounding
D )(e nuer o+ 'o!ounding !eriods de!ends on t(e nuer o+sudiisions.
D noin#& interest r#te o+ 12%?5e#r 'o!oundedD m = 1: yearly (euals 1!" effective yearly#D m = !: semi$annually (euals 1!.%&'" effective yearly#
D m = 4: uarterly (euals 1!.1" effective yearly#D m = !: )ee*ly (euals 1!.+%4" effective
yearly#D m = %&: daily (euals 1!.+4+" effective
yearly#D m = !&'': ,ourly (euals 1!.+4-" effective yearly#
Note e #re #!!ro#'(ing # &iitH For in+inite 'o!ounding !eriods
'ontinuous&5 'o!ounded
i : er
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#si' Forue +or I 'o!ounding
?F,r,n: er 1?ern 1
?,r,n : ern er 1?ern 1
F?,r,n : ern-1?er 1
?,r,n : ern 1?erner 1
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9u#r5
"nterest +#'tors e*ist to #id in deterininge'onoi' e$ui#&en'e o+ #rious '#s( +&o
!#tterns
Not#tion is introdu'ed t(#t is #!!&iedt(roug(out t(e re#inder o+ t(e te*t
"ntrodu'tion o+ i!ort#nt E*'e& s!re#ds(eet
+in#n'i#& +un'tions to #id in e#&u#tion o+engineering e'ono5 !ro&es
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ummary/ cont0d.
D Gr#dients rit(eti' re$uires to '#&'utions
D #se 9eries #nd Gr#dient
D e.g., : ?, i%, n A G?G, i%, nD is one !eriod to t(e &e+t o+ t(e #se series #nd to
!eriods to t(e &e+t o+ t(e +irst gr#dient.
Geoetri' re$uires one '#&'utionD : 1?, g, i, n
D is one !eriod to t(e &e+t o+ 1
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ummary/ cont0d.
D Noin#& e#ns in n#e on&5 #nd '#nnot e used +or '#&'ution.
Conert to #n e++e'tie r#te !er !eriod.
D Co!ounding !eriods '#n e in're#sed toin+init5J '#&&ed 'ontinuous 'o!ounding.
D )(ere #re s!re#ds(eet +un'tions +or #
nuer o+ di++erent e'onoi' +#'tors. 9ee te*too +or ore det#i&.
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