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1、SimpleInterestIntroducingtheMathematicsofFinanceNotesaboutSimpleInterestForashort-termloan(perhapsaloantoafriend),simpleinterestmaybeused.Forsimpleinterest,theinterestisdeterminedjustonce,attheendoftheloan.Later,we’llstudycompoundinterestwheretheinterestisappliedatregularperiods
2、.3monthsofinterestSupposeyoumakealoanof$2000forwhichyoucharge8%annuallyinsimpleinterest.Iftheloanisrepaidattheendof3months,howmuchinterestshouldyoubepaid?3monthsofinterestIftherateis8%,theinterestis8%of$2000peryear.Atotalof($2000)(0.08)=$160interestforoneyear.Butsincetheloanwasf
3、orjust3monthsor3/12 ofayear,youarepaidthisfractionoftheyearlyinterest.Theinterestpaidis($2000)(0.08)(3/12)=$40.00SimpleInterestFormulaForaloanofPdollarsatasimpleinterestrater,theinterestIisgivenbywheretistheduration(inyears)oftheloan.ThetotalamountAdueattheendoftheloanisdollarsb
4、orrowed+interestcharged18monthinvestmentSupposeashort-terminvestmentoffers10%simpleinterest.Ifyouinvest$4000insuchanaccount,whatisthevalueoftheinvestment18monthslater?TheinterestearnedisPrt=($4000)(0.10)(18/12)=$600.Andso,thetotalvalueoftheinvestmentisA=P+Prt=$4000+600=$4600.Inv
5、estingtodayAgain,supposeashort-terminvestmentoffers10%simpleinterest.Howmuchshouldbeinvestedintheaccounttodayinorderfortheaccounttohaveafuturevalueof$7500attheendof18months?Here,we’reaskedtofindtheinitialamountP.Andso,wenotethe“presentvalue”oftheaccount.PresentValueTohaveafuture
6、valueof$7500attheendof18months,istheamountweneed toinvesttoday.Notetheparentheses!NowandLaterInitialamountorprincipal,P“presentvalue”Accumulatedtotalvalue,A“futurevalue”0yearsafter1.5years$6521.74$7500.ExamplesSupposeashort-terminvestmentoffers6.5%simpleinterest.Ifyouinvest$1200
7、insuchanaccount,what isthevalueoftheinvestment14monthslater?Howmuchneedstobeinvestedtodayinorder fortheaccounttohaveavalueof$1500atthe endof14months?FindthesimpleinterestrateYouborrow$1400andagreetopaysimpleinterest.Attheendof18months,youwriteacheckfor$1589topayofftheloan.Whatwa
8、stherateofsimpleinterest?SetuptheequationA=P+Pr
