MaxMarkCh08QuestionsOnly.docx
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MaxMarkCh08QuestionsOnly.docx
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MaxMarkCh08QuestionsOnly
MenuItem8:
(Topic8)Mathematicsoffinance:
AnIntroductiontobasicconceptsandcalculations
Question1:
Someaspectsoffinancialcalculationsarebasedonmarketconventions.ForthepurposeofsimpleinterestcalculationsintheAustralianmarket,whatistheconventionconcerningthenumberofdaysinayear?
A:
360daysperyear
B:
365.25daysperyear
C:
365daysperyear
D:
365daysperyear,exceptforleapyears,whenitis366
Feedback:
TheconventionintheAustralianmarketistoassumethatthereare365daysinayear.Iftheperiodofaninvestmentinaleapyearincludes29February,the29thdayiscountedbuttheyearisstillassumedtohave365days.
MORE:
FinancialInstitutions,InstrumentsandMarkets5/e,p.327.
InExample3theamountwasborrowedforninetydays,whichmustbeconvertedintoafractionofayearinordertoapplyEquation8.1.Itisimportanttonotethatthemarketconventionrelatingtothenumberofdaysintheyearvariesbetweencountries.IntheUnitedKingdom,Australiaandanumberofothercountriestheconventionisthataperannumraterelatestoa365-dayyear.However,intheUnitedStatesandintheeuromarketstheconventionistousea360-dayyear.Inthischapterthe365-dayconventionisused.
Question2:
Someaspectsoffinancialcalculationsarebasedonmarketconventions.ForthepurposeofsimpleinterestcalculationsintheUSandeuromarkets,whatistheconventionconcerningthenumberofdaysinayear?
A:
360daysperyear
B:
365.25daysperyear
C:
365daysperyear
D:
365daysperyear,exceptforleapyearswhenitis366
Feedback:
Insomemarkets,includingtheUSandtheeuromarkets,itisconventionaltoassumethatthereare360daysinayear.Thissimplifiescalculationsforsecuritieswithtermstomaturityof90,180and270days.
MORE:
FinancialInstitutions,InstrumentsandMarkets5/e,p.327.
InExample3theamountwasborrowedforninetydays,whichmustbeconvertedintoafractionofayearinordertoapplyEquation8.1.Itisimportanttonotethatthemarketconventionrelatingtothenumberofdaysintheyearvariesbetweencountries.IntheUnitedKingdom,Australiaandanumberofothercountriestheconventionisthataperannumraterelatestoa365-dayyear.However,intheUnitedStatesandintheeuromarketstheconventionistousea360-dayyear.Inthischapterthe365-dayconventionisused.
Question3:
Asumof$60000isdepositedinabankaccountthatpaysinterestat5.50percentperannum.Iftheaccountisclosedafter270daysandallfundsarewithdrawn,howmuchwillbepaidtothedepositor?
A:
$62312.50
B:
$2441.10
C:
$62441.10
D:
$62475
Feedback:
UsingEquation8.1theinterestearnedis$600000.055(270/365)=$2441.10sothetotalpaidtothedepositorwillbe$62441.10.
MORE:
FinancialInstitutions,InstrumentsandMarkets5/e,p.326.
Theamountofinteresttobepaidonadebt,orearnedonadeposit,dependsonthreethings:
∙theamountinvolved,thatis,theprincipal(A)
∙
∙thetimeordurationoftheloan,wherenisthenumberofinterestpaymentperiods
∙
∙therateofinterest(i),whereiisexpressedasadecimal;thatis,i=5.25percentisexpressedas5.25/100or0.0525.
∙
Thetotaldollaramountofinterestpaidorearned(I)is:
I=A×(d/365)×i(Equation8.1)
Question4:
On1January2008,$20000isborrowedataninterestrateof8.75percentperannum.Iftheloanisrepaidinfullon30April2008,whatisthetotalamountthatmustbepaid?
A:
$20583.33
B:
$20575.34
C:
$20580.14
D:
$20590.64
Feedback:
Thetermoftheloanis31+29+31+30=121days.UsingEquation8.1theinterestontheloanis$200000.0875(121/365)=$580.14.Addingthistotheprincipalof$20000givesthetotalof$20580.14.
MORE:
FinancialInstitutions,InstrumentsandMarkets5/e,p.327.
Oncetheamountofinterestiscalculated,itiseasytodeterminethefinalamountpayable.Theamountwouldsimplybethesumoftheprincipalandtheinterestamount.Alternatively,thefinalamountpayablecanbecalculatedinasingleequation.LetSstandfortheaccumulatedamountpayable,then:
RefertoEquation8.2.
Question5:
Thesumof$250000ispayablein270daystime.Iftheinterestrateis9.5percentperannum,whatisthepresentvalue?
A:
$233372.23
B:
$233385.05
C:
$233855.05
D:
$233585.05
Feedback:
UsingEquation8.3thepresentvalueisequalto$250000/(1+(270/365)0.095)=$233585.05.
MORE:
FinancialInstitutions,InstrumentsandMarkets5/e,p.328.
Thepresentvaluemaybedefinedasthecurrentvalueofafuturecashflow,orseriesofcashflows,discountedbytherequiredrateofreturn.Thenotionofpresentvalueisclearfromthefollowingtwostatements:
∙thefuturevalueof$100inoneyear,withsimpleinterestof10percentperannum,is$110,so
∙
∙thepresentvalueof$110receivedinoneyear,withsimpleinterestof10percentperannum,is$100.
∙
Thepresentvalueofanamountofmoneycanbethoughtofastheamountneededtobeinvestedtodaytoyieldaparticularvalueinthefuture.Tocalculatethepresentvalueofafutureamount,simplyrearrangeEquation8.2(thefuturevalueequation).Thatis:
S=A[1+(ni)]
whichcanbesolvedforA(theprincipalorpresentvalue)which,ifitwereinvestedtodayfornperiodsatasimplerateofinteresti,wouldaccumulatetoafuturevalueS:
A=S/[1+(ni)]
Thisstatesthatthepresentvalueofafutureamountisthefutureamountdiscounted(ormathematicallydivided)bythesimpleinterestfactor.Examples4to6illustratetheuseofEquation8.3.
Question6:
AnAustraliancompanyissuesa90-daybillofexchangewithafacevalueof$1millionandayieldof7.5percentperannum.Howmuchwillthecompanyreceivewhenthebillisissued?
A:
$1000000.00
B:
$981842.64
C:
$981595.09
D:
$981482.64
Feedback:
ThecompanywillreceivethepresentvalueofthefuturecashflowandusingEquation8.3itisequalto$1000000/(1+(90/365)0.075)=$981842.64.
MORE:
FinancialInstitutions,InstrumentsandMarkets5/e,p.329.
Example5
Acompanydiscounts(sells)acommercialbillwithafacevalueof$500000,atermtomaturityof180daysandayieldof8.75percentperannum.Howmuchwillthecompanyreceivewhenitsellsthebill?
(CommercialbillsarediscussedinChapter9.Briefly,abillisasecurityissuedbyacompanytoraisefunds.Abillisadiscountsecurity;thatis,itisissuedwithafacevaluepayableatadateinthefuture,butinordertoraisethefundstodaythecompanysellsthebillforlessthanthefacevalue.Theinvestorwhobuysthebillwillreceivethefacevalueatthematuritydate.)Thepriceofthebillwillbe:
RefertotheequationinExample5.
Question7:
AUScompanyissuesa60-daycommercialpaperwithafacevalueof$1millionandayieldof6.25percentperannum.Whatamountwillthecompanyreceiveattheissuedate?
A:
$994076.39
B:
$1000000.00
C:
$989690.72
D:
$993949.62
Feedback:
SincetheissueisintheUSmarketthecalculationisbasedon360daysperyear.Thepresentvalueis$1000000/(1+(60/360)0.0625)=$989690.72.
MORE:
FinancialInstitutions,InstrumentsandMarkets5/e,p.329.
Example5
Acompanydiscounts(sells)acommercialbillwithafacevalueof$500000,atermtomaturityof180daysandayieldof8.75percentperannum.Howmuchwillthecompanyreceivewhenitsellsthebill?
(CommercialbillsarediscussedinChapter9.Briefly,abillisasecurityissuedbyacompanytoraisefunds.Abillisadiscountsecurity;thatis,itisissuedwithafacevaluepayableatadateinthefuture,butinordertoraisethefundstodaythecompanysellsthebillforlessthanthefacevalue.Theinvestorwhobuysthebillwillreceivethefacevalueatthematuritydate.)Thepriceofthebillwillbe:
RefertotheequationinExample5.
Question8:
Aninstitutionalinvestorbuys26-weekT-notesatayieldof8.65percentperannum.Whatistheissuepriceper$100offacevalue?
A:
$95.87
B:
$100.00
C:
$104.31
D:
$95.81
Feedback:
Thenoteshaveatermtomaturityof726=182days,sothepresentvalueis$100/(1+(182/365)0.0865)=$95.87.
MORE:
FinancialInstitutions,InstrumentsandMarkets5/e,p.330.
Example6
Whatpriceper$100offacevaluewouldafundsmanagerbepreparedtopaytopurchase180-dayT-notesifthecurrentyieldontheseinstrumentsis7.35percentperannum?
RefertotheequationinExample6.
Question9:
Asumof$100000isdepositedfor120daysandaccumulatesto$102025.Whatistheyieldonthisinvestment?
A:
$2025
B:
6.075percentperannum
C:
2.025percent
D:
6.16percentperannum
Feedback:
Theinterestearnedis$2025.UsingEquation8.5,theyieldisequalto(365/120)(2025/100000)=0.06159or6.16percentperannum.
MORE:
FinancialInstitutions,InstrumentsandMarkets5/e,
p.330.
8.1.3Calculationofyields
Intheexamplesgivenabove,theinterestrateoryieldontheinstrumentwasgiven.However,attimestheyieldmaynotbegivenandthenitwillbenecessarytocalculatetheyieldonaninvestment,orthecostofborrowing.Equation8.1canberearrangedtoobtainthesolutionfortheyield.Giventhat:
I=Ani
andsincetheyieldistherelationshipbetweentheprincipalandtheinterestearnedoveracertainperiod,then:
i=365/dI/A(Equation8.5)
Question10:
TwoT-notesareavailable.Thefirstnotematuresin63daysandissellingfor$98.16per$100offacevalue.Thesecondnotematuresin98daysandisselling
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