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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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 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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