Act2120
UniversityOfManitobaActuarialClub–2016/2017
InterestTheoryMidterm1–Time:70min
1)Moneyaccumulatesinafundataneffectiveannualinterestrateofiduringthefirst5years,andatan
effectiveinterestrateof2ithereafter.Adepositof1ismadeintothefundattime0.Itaccumulatesto
3.09attheendof10yearsandto13.62attheendof20years.Whatisthevalueofthedepositatthe
endof7years?
2)Twofunds,AandB,startwiththesameamount.FundAgrowsatanannualinterestrateofi>0forn
years,andatanannualinterestrateofj>0forthenextnyears.FundBgrowsasanannualinterestrate
ofk>0for2nyears.FundAequals1.5timesfundBafternyears.Theamountinthetwofundsare
equalafter2nyears.Whichofthefollowingaretrue?
i)j<k<i
ii)k<(i+j)/2
iii)j=k(2/3)1/n
3)Whichofthefollowingarecorrectexpressionsford(360)?
i)1–v1/360
ii)360–360(1+i(12)/12)-30
iii)1/(1/360+1/i(360))
4)Atthebeginningofeachyearfor10years,$100isdepositedintoasavingsaccount.
Atasimpleannualinterestrateofi,thetotalamountintheaccountis$1,275attheendoftenyears.
Tothenearest$5,whatwouldbethetotalamountintheaccountattheendoftenyearsifinteresthad
beencompoundedataneffectiveannualinterestrateofi%?
5)Devinborrowed$10,000frombankXatanannualeffectiverateof8%.Heagreedtorepaythebank
withfivelevelannualinstallmentsattheendofeachyear.
Atthesametime,healsoborrowed$15,000frombankYatanannualeffectiverateof7.5%.Heagreed
torepaythisloanwithfivelevelannualinstallmentsattheendofeachyear.
Helent$25,000toCedricimmediatelyinexchangeforfourannuallevelrepaymentsattheendofeach
year,atanannualeffectiverateof8.5%.
Devincanonlyreinvesttheproceedsatanannualrateof6%.
Immediatelyafterrepayingtheloanstothebanksinfull,determinehowmuchDevinhasleft.
6)Sergedeposits$100attheendofeachyearfor20yearsintoafundearninganannualeffective
interestrateof7%.
Gabbymakes20depositsintoafundattheendofeachyearfor20years.Thefirst10depositsare$100
each,whilethelast10depositsare$100+$Xeach.Thefundearnsanannualeffectiveinterestrateof
8%duringthefirst10yearsand6%annualeffectiveinterestthereafter.
Attheendof20years,theamountinSerge’sfundequalstheamountinGabby’sfund.
CalculateX.
Act2120
UniversityOfManitobaActuarialClub–2016/2017
7)Thepresentvaluesofthefollowingthreeannuitiesareequal:
i)Perpetuity-immediatepaying$1eachyear,calculatedatanannualeffectiverateof7.25%
ii)50-yearannuity-immediatepaying$1eachyear,calculatedatanannualeffectiveinterestrateofj%
iii)n-yearannuity-immediatepaying$1eachyear,calculatedatanannualeffectiveinterestrateofj-1%
Calculaten.
Note:Certainquestionsaskingforthecalculationofaneffectiveinterestrateoftenrequiretheuseofa
financialcalculator.ThesequestionswillnotbetestedintheInterestTheorycourse,butaremorethan
likelytomakeanappearanceonExamFM.Itisstillrecommendedthatstudentsreviewthisquestionfor
thepurposeofunderstandingitssolutionprocess.
8)Youaregivenδt=2/(10+t),t>0.
Calculatethepriceofanannuity-immediatepaying$1attheendofeveryyearfor4years.
9)Anannuity-duepaying$1forn+2yearsishasapresentvalueof$13.987.Anannuity-duepaying$1
fornyearshasanaccumulatedvalueof$51.632.Calculatetheeffectiveannualrateofinterest.
Disclaimer:thisexamisnotonethathasactuallybeenpreviouslytestedinInterestTheory.Thiswas
anexamcreatedbyUMACinordertoprovidestudentswithamorerecentrealisticrepresentationof
whatonemayexpectonbothInterestTheoryExams,andExamFM.Thereisastrongpossibilitythat
thisexamisofeasierdifficultythanwhatwillbetestedinInterestTheory.
- SergiuBuda