12-1 Compound Interest. 12-2 Compound Interest and Present Value.
Percentages, Simple and compound interest · Section 4.2: Compound Interest !=! 1+ ! 100! Where: A...
Transcript of Percentages, Simple and compound interest · Section 4.2: Compound Interest !=! 1+ ! 100! Where: A...
%,Simple&CompoundInterests Form4
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Percentages,SimpleandCompoundinterestsSection1:IntroductiontoPercentages
‘PerCent’meansoutof100Frompercenttofraction
1) 20%toafraction
Write20%asafraction(20%means20outof100)20%= !"
!""= !
!
2) 7%toafraction
7%= !!""
3) 35%toafraction
35%= !"!""
= !!"
4) 75%toafraction
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PercentageofaQuantity
1) 20%of60
20100×60 = 12
2) 60%of350
60100×350 = 210
3) If5%ofAustraliansplaytennis,howmanypeoplewouldyouexpecttoplaytennisoutofagroupof320people?
%,Simple&CompoundInterests Form4
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Consolidation
Percentage Decimal Fraction34% 0.85 3/4045% 0.3 2/384% 0.45 3/8
1. Calculatethefollowing:
a. 15%of$300 b. 12%of9hours
c. 12.5%of$26 d. 16.2%of265m
2. Anestateagentcharges2%commissiononeveryhousehesells.Howmuchcommissionwillheearnonahousethathesellsfor$120500?
3. Itisthoughtthatabout20%offansatasoccermatcharewomen.Foronematchtherewere42600fans.Howmanyofthesedoyouthinkwerewomen?
SupportExercisePg176Ex12A
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Section2:AquantityasaPercentageofanother,ProfitandLoss
Example1Whatpercentis€100of€320?Express€100in€320asafraction!""
!"#
Thereforetogetapercentage
100320×100 =
1254 = 31
14%
Example2Johnobtained60marksoutof75inaMathematicstest.Findthepercentageofmarkshegot.Fraction:!"
!"
Percent:!"
!"×100 = 80%
Example3Whatpercentof€5is28cents?€5=500centsFraction: !"
!""
Percent: !"
!""×100 = !"
!= 5.6%
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ProfitandLossExample4Alanboughtabowlingballfor€12andsolditfor€15.Whatwashispercentageprofit?Profit:$15-$12=$3Percent: !
!"×100 = 25%
Example5
Zackboughtacarfor$20000andsolditfor$18000.Whatishispercentageloss?
Loss:$20000-$18000=$2000
Percent: !"""!""""
×100 = 10%
Consolidation
1. Whatpercentageis€5of€20?
2. Whatpercentageis105gof1kg?
3. InGreece,thereare3654000acresofagriculturalland.Olivesaregrownon
237000acresofthisland.Whatpercentageofagriculturallandisusedfor
olives?
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4. Findthepercentageprofitonthefollowing.Giveyouranswersto1decimal
place.
Item Retailprice(sellingprice) Wholesale(price
shoppaid)
a. CDplayer $89.50 $60
b. TVset $345.50 $210
c. Computer $829.50 $750
SupportExercisePg182Exercise12C
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Section3:Increase,decrease,andreversepercentages–Original,Change&Finalmethod.
1. In2005thepopulationofacitywas1565000.By2011ithadanincreaseby8%.Whatwasthepopulationofthecityin2010?
Original 100% 1565000Change +8% Final 108% ?
100%=1565000108%=?!"#!""
× 1 565 000 = 1 690 200 𝑝𝑒𝑜𝑝𝑙𝑒
2. Alargefactoryemployed640people.Ithadtostreamlinetheworkforceandlose30%oftheworkers.Howbigistheworkforcenow?
3. Abankpays7%interestonthemoneythateachsaverkeepsinthebankforayear.Allisonkeeps$385inthebankforayear.Howmuchwillshehaveinthebankaftertheyear?
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4. Atelevisioncosts$400beforesalestaxat17.5%isadded.Howmuchwillthetelevisioncostafterthetaxisadded?
5. Anewdietguaranteesthatyouwilllose12%ofyourmassinthefirstmonth.Whatmassshouldthefollowingpeoplehaveafteronemonthofdiet?
a. Greta,whostartedat52kg b. Pierre, who started at75kg
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6. Ina sale the jacketsare reducedby40%.Thesalepriceofa jacket is€24.Workouttheoriginalpriceofthejacket.
Original 100% ?Change −40% Final 60% €24
60%=€24100%=?
10060 × 24 = € 40
7. Franco receives a 15%discount on a TV, and he pays $510.Whatwas thepricebeforethediscount?
8. Melissabuysblousesforherclothesstore.Shemarksthepriceupby60%.Ifshesellsablousefor$74.25,howmuchdidtheblousecosther?
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Consolidation
1. Tina’sweeklypayisincreasedby5%to$315.WhatwasTina’spaybeforethe
increase?
2. The number ofworkers in a factory fell by 5% to 228. Howmanyworkers
werethereoriginally?
3. [email protected]%.Whatwas
thecostpriceofthecar?
4. Afteran8%increase,themonthlysalaryofachefwas$1431.Whatwasthe
originalmonthlysalary?
5. Oliverbuysachair.Hesellsitfor$63inanauctionandmakesalossof55%.
Whatdidhepayforthechair?
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SupportExercisePg179Ex12B,ESection4:SimpleInterest&CompoundInterestSection4.1:SimpleInterest
Whensomeonelendsmoneytosomeoneelse,theborrowerusuallypaysafeeto
thelender.Thisfeeiscalled‘interest’.Thesimpleinterestformulaisasfollows:
where:
I=Interest–thetotalamountofinterestpaid
P=Principal–theamountofmoney
T=Time–thetimeoftheloan
R=Rate–isthepercentagechargedasinteresteachyear.
ThreeotherformulasareusedtofindP,RandT.
𝑃 = !""!!" 𝑇 = !""!
!" 𝑅 = !""!
!"
Whenever,themoneyisborrowed,thetotalamounttobepaidbackisthe
principalborrowedplustheinterestcharged.
I=!"#!""
TotalRepayments=Principal+Interest
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Example1:Astudentpurchasesacomputerbyobtainingasimpleinterestloan.
Thecomputercosts$1500andinterestrateontheloan12%.Theloanistobe
paidbackin2years.Howmuchinterestisincurredovertheyears?
I=PTR/100
=1500x2x12/100
=360
TotalPaid=$1500+$360=$1860
Example2:Youborrow$10000for3yearsatasimpleinterestrateof5%.Find
thetotalamountpaid.
I=PTR/100
=10000x3x5/100
=1500
Total=$10000+$1500=$11500
Example3:Susanborrows$8650tobuyausedcarandischarged4.5%
interest.Ifthetermofherborrowingis5years,howmuchinterestdoesshepay
intotal?
I=PTR/100
=8650x5x4.5/100
=1946.25
Interest=$1946.25
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Example4:Withaninterestrateof10%for18months,theinterestincurred
overthemonthsisof$1199.47.Findtheamountwhichheborrowed.
18months=1year6months=1.5years
R=10%
𝐼 = 𝑃𝑇𝑅100
𝑃 =100𝐼𝑇𝑅
1199.47 × 100
1.5 × 10 = 𝑃
$7996.47=P
Section4.2:CompoundInterest
𝐴 = 𝑃 1 + 𝑅100
!
Where:A=AmountP=PrincipalR=RateT=TimeNB:Rememberthatthisformulagivestheamountnottheinterest.Tofindtheinterestyouhavetosubtracttheprincipalattheend.Example1:FindtheCompoundIntereston€6000depositedfor3yearsattherateof6%p.a.SupportExerciseHandoutSimpleInterest&CompoundInterest