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


J.Camenzuli 2

PercentageofaQuantity

1) 20%of60

20100×60 = 12

2) 60%of350

60100×350 = 210

3) If5%ofAustraliansplaytennis,howmanypeoplewouldyouexpecttoplaytennisoutofagroupof320people?


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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

Percentages, Simple and compound interest · Section 4.2: Compound Interest !=! 1+ ! 100! Where: A...

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