What is the Compound Interest Formula? - 2021 - Robinhood ...

The compound interest formula, A=P(1+r/n)^nt, lets you quickly calculate the value of your total funds, aka the principal plus interest, ... UpdatedAugust25,2021WhatistheCompoundInterestFormula?Definition:Thecompoundinterestformula,A=P(1+r/n)^nt,letsyouquicklycalculatethevalueofyourtotalfunds,akatheprincipalplusinterest,whentheinterestiscompoundedoverthattimeperiod.🤔UnderstandingthecompoundinterestformulaThemathematicalformulaforcalculatingcompoundinterest,A=P(1+r/n)^nt,usesfoursimplenumberstoallowyoutoseehowmuchmoneyplusinterestyou’llhaveafterthenumberoftimeperiods,orcompoundperiods.‘A’representstheaccruedamountofyourprincipalplusinterest,whichisthetotal.‘P’standsfortheprincipal,whichisyouroriginalamountinvested.The‘r’showstheinterestrateindecimalform.The‘n’variableisusedintwoplacesandstandsforthenumberofcompoundingperiods.The‘t’representsthetimeinyears.Together,thesevariablesallowyoutocalculateyouraccruedamountforanyamountoftimeandinterestrate.ExampleConsiderforamomentthatyourgrandmotherisafirmbelieverinsavingmoneyandrefusestogivegiftcardsorcashatholidays.Instead,shegivesallofthegrandchildren$500investedinfive-yearCDs(CertificatesofDeposit)withcompoundinterestfiguredtwiceayearanda2%interestrate.Setasidethedelayedgratificationforamoment--Thequestionis,howmuchmoneywilltheCDbeworthin5years?Thatiswherecompoundinterestkicksin.FillinginthecompoundinterestformulaofA=P(1+r/n)^nt,yourholidaygiftlookslikethis:A=500(1+.022)^25.Followingtheorderofoperations,wecalculatetheamountintheparenthesisfirsttogetA=500(1.01)^25.Fromthere,weinputtheexponentstogetA=500(1.10).Nowinourfinalcalculation,thefinalvalueisA=$550.Attheendof5years,yourCDwillbeworth$550.TakeawayCompoundinterestiskindoflikeasnowballrollingquicklydownhill…Asmallsnowballisrolledfromthetopofatallmountaintopandspeedsdownhill,gatheringmorealongtheway.Then,thatnewsnowpicksupmoresnow,andthesnowballthatcrashesatthebottomofthemountainismanytimeslargerthanthesnowballrolledatthetop.Thecompoundinterestformula(A=P(1+r/n)^nt)isthemaththattellsyouhowbigthatsnowballwillbewhenitgetstothebottom.Readytostartinvesting?SignupforRobinhoodandgetyourfirststockonus.SignupforRobinhoodCertainlimitationsapplyThefreestockofferisavailabletonewusersonly,subjecttothetermsandconditionsatrbnhd.co/freestock.Freestockchosenrandomlyfromtheprogram’sinventory.SecuritiestradingisofferedthroughRobinhoodFinancialLLC.Tellmemore…Whatisthedifferencebetweensimpleandcompoundinterest?Whatarecompoundingperiods?Howdoyoucalculatesimpleandcompoundinterest?HowdoyoucalculatecompoundinterestusingExcel?What’stheformulaforcontinuouscompoundinterest?Whatisthe“Ruleof72”?Whatisthecompoundannualgrowthrate(CAGR)?Whatisannualpercentageyield(APY)?Dostocksearncompoundinterest?Whataresomecompoundinterestcalculatorapps?Whatisthedifferencebetweensimpleandcompoundinterest?Simpleinterestandcompoundinterestcanbegainedbyfundsovertime,basedonthefund’sinitialamount(whetheritisasacosttoaloanoranincreaseinfundsinaninvestmentorsavings)theinterestrate,andthenumberofcompoundingperiods.Thetwoformsofinterestdiffer,becausesimpleinterestisstatic,andcompoundinterestisdynamic.Withsimpleinterest,theinterestearnedisremovedorignoredwhencalculatingthenextinterestcycle.Inotherwords,interestisonlycalculatedonyouroriginalprincipalamount.Withcompoundinterest,thepreviousinterestearnedisaddedbacktotheprincipalforthenextinterestcycle.Thereisanoldmentalgamethatsupposesyousaveapennyaday.Saveonepennythefirstday,twopenniesthesecondday,threepenniesonthethirdday,andsoon.Thatisalittlelikecompoundinterestbeingaddedbacktotheprincipal(althoughtheinterestrateisnotreflectiveoftherealworldandisonlytoillustratetheconcept)ifyouhaddailycompoundingperiods.Forexample,theseconddaytwopenniesofinterestwouldbeaddedtoyourdepositedpenny,thethirddaythreepennieswouldbeaddedtothetotalyouhadthedaybefore,andsoon.Theinterestgrowsbecauseitisearnedontheinterestpreviouslyaddedplustheinitialdeposit.Attheendofoneyear,thatmentalgameresultsinatotalof$667.95savedfromtheinitialpennyinvestment.Ifweuseaversionofthisgamemoresimilartosimpleinterest,yousaveonepennythefirstday,onepennyofinterestisaddedthesecondday,onepennyofinterestisaddedonthethirdday,andsoon.Inthatcase,theinterestneverchangesevenasthetotalintheaccountgrows.Withthesimpleinterestversion,youwouldonlyhave$3.65attheendoftheyearfromtheinitialpennyofsavings.Whatarecompoundingperiods?Compoundingperiodsaresimplythelengthoftimebetweenthepointswheninterestiscalculatedonaninvestmentorloan.Compoundingperiodsshouldbespecifiedintheloan,savings,orotherinvestmentagreementdocuments.Somecommonlyusedcompoundingperiodsareannually(onceperyear),semi-annually(twiceayear),quarterly(fourtimesayear),andmonthly(twelvetimesayear).Morefrequentcompoundingperiodsincreasethespeedatwhichtheinitialinvestmentamountgrows.Infact,compoundingperiodsaresoimportanttothewaythatcompoundinterestworksthatitmustbeusedtwiceinthecompoundinterestformulatoaccountforitseffect.Loanswithmorefrequentcompoundingperiodsalsoincreasetheamountofinterestowed.Thatusuallymeanshigherminimumpaymentsarerequiredtoreducethetotalowed.Whentakingoutaloan,alowernumberofcompoundingperiodswouldgenerallybepreferableasitresultsinlessinterestowed.Onaninvestment,morecompoundingperiodsaretypicallysoughttomorequicklygrowthefunds.Howdoyoucalculatesimpleandcompoundinterest?Simpleinterestandcompoundinteresthaveverysimilarformulas.Thecompoundingeffectisthedifferencebetweenthetwointerestformulas.ThesimpleinterestformulaisA=P(1+rt)whilethecompoundinterestformulaisA=P(1+r/n)^nt.Thevariablesinbothformulasrepresentthesameconcepts.‘A’standsforaccruedamount(yourprincipalplustheinterestearned).‘P’representstheprincipal(youroriginalamount).The‘r’showstheinterestrateindecimalform.Thesmall‘t’representsthetimeinyears.Theadditionalvariableinthecompoundformulais‘n,’thenumberofcompoundingperiodsperyear.Considerthatababyinherits$10,000fromagreatauntandherparentswanttoputtheinheritanceinsavingsuntilthebabyis18.Twobanksintheirneighborhoodoffersavingsaccountchoices.BankAandBankBbothoffer2%interest.BankAhassimpleinterest,andBankBhascompoundinterestwithquarterlycompoundingperiods.ThesimpleinterestformulashowsthatiftheychooseBankAwithsimpleinterest,theaccountwillhave$13,600attheendof18years.$13,600=$10,000(1+(.02x18)).ThecompoundinterestformulashowsthatiftheychooseBankBwithcompoundinterest,theaccountwillhave$14,320.44attheendof18years.$14,320.44=$10,000(1+(.02/4))^(4x18).HowdoyoucalculatecompoundinterestusingExcel?Excelmakesiteasytocreateacompoundinterestcalculatorwithoutanyprogrammingskills.TofigurecompoundinterestinExcel,youwillneedacellforeachvariableandacellfortheanswer(formula).BecauseofthewayExcelfunctions,thereisaspecificprocessthatmustbeusedratherthanjustpastingtheformulaandassigningcells.Tobegin,openanewspreadsheet.IncellA1,type“CompoundInterestCalculator”asalabelforthesheet.Thisisusefulifyoulatercreatenewsheetswithsimpleinterestorotherinterestformulassuchascontinuouscompoundinterest.Next,enterlabelsforeachvariableandonefortotalincolumnA.Principal(A3),rate(A4),time(A5),numberofcompoundingperiodsperyear(A6),andtotal(A8)shouldeachhavespecificcellsasindicatedintheparentheses.Toentertheformula,clickoncellB8(besidesthetotallabel).Inthedataentrybar,clickthefxbuttonandtypefuturevalueintheformulasearchbox.Select‘FV’and‘go,’andapop-upboxshowingseveralvariableoptionswillopen.Inthe‘rate’sectionclickcellB4type"/"andthenclickcellB6.ThatsectiontellsExcelther/nportionoftheformula.Inthe‘nper’sectionclickcellB5,type"*"andthenclickcellB6.The‘nper’sectiontellsExceltheexponent,nt,partoftheformula.Leavethe‘pmt’fieldblank.Inthe‘pv’(presentvalue)field,clickcellB3.Leavethe‘type’fieldblankandclickOk.Untilyouentervalues,theformulacellwillshowanerror.Nowthattheformulaiscompleteyou’llneedtoenteryourvariables.Fortheprincipalamount,youmustenterthisnumberasanegative.ThisispartoftheExcelcodingandnothingthatcanbechanged.Thinkofitasthemoneyleftyourpocket,soit'snegativeforthesakeoftheformula.Entertheinterestrateindecimalforminsteadofasapercentageorwholenumber.Besuretoformatyourvariableandtotalcellstoyourpreference.Youcanformatacellbyright-clickingonitandthenchoosingtheformat.Fromthere,youcanadjustthecurrencyformatting,redfornegativeoption,thenumberofdecimalplaces/rounding,andmore.What’stheformulaforcontinuouscompoundinterest?Continuouscompoundinterestisatheoreticalpracticeusedasonewaytohelpcomparepossibleinvestmentgrowthatdifferenttimeandrateoptions.TheformulaforcontinuouscompoundinterestisP=e^rt.Theestandsforamathematicalconstantandisoftenwrittenouttoonlyfourdecimalplaces,2.7183,muchlikePiisonlywrittentotwodecimalplaces.The‘e’willnotchangeinthisformula,regardlessoftheothervaluesused.‘P’standsforprincipal,‘r’standsfortheinterestrateindecimalform,and‘t’standsfortheamountoftimeinyears.Thecontinuouscompoundinterestmodelcanapproximatetheactionofcontinualreinvestmentratherthantruecompoundinterestearnedonasetscheduleofcompoundingperiods.Sometimesit’susedasashortcuttoroughlyapproximateinvestmentgrowth.Forexample,whenthenumberofcompoundingcyclesisunknown.Whatisthe“Ruleof72”?TheRuleof72isafinancialruleofthumbtoroughlyestimatehowmanyyearsarerequiredtopassforthevalueofaninvestmenttodouble.Therulereliesonfixedinterestrates,andtheresultisnotentirelyaccurate.TheRuleof72worksbydividing72bytheannualrateofreturn(asawholenumber).Forexample,theRuleof72saysitwilltake14.4yearsforaninvestmentat5%returntodouble(72/5).Theexacttimecouldvarybasedoncompoundingfrequency.TheRuleof72becomeslessaccurateastherateofreturnriseswithreturnsover20%becomingunfavorableforthemethod.Likeallruleofthumbcalculations,therearevariationsofthemethod.Forcompoundinterestinvestments,theruleof69.3isconsideredmoreaccuratebysomeinvestors.TheRuleof69.3worksjustliketheRuleof72butuses69.3asthestartingnumberinsteadof72.Forexample,theRuleof69.3saysitwilltake13.38yearsforaninvestmentat5%returntodouble(69.3/5).Again,compoundingfrequencyaffectsaccuracy.Keepinmindthattheserulesareshownforillustrativepurposesonlyandtheydon’tguaranteethatanyinvestmentwilldouble.Whatisthecompoundannualgrowthrate(CAGR)?Sometimesinvestorswanttoknowwhatrateofreturnisneededtoreachaparticularvalueataspecifictime.Forexample,ifsavingforretirement,acouplemightwanttoknowwhatrateofreturnwouldbeneededtoreachtheirsavingsgoalbeforetheirplannedretirementyear.Thecompoundannualgrowthrate(CAGR)formulafigurestherequiredrateofreturntoreachagoal.Thecompoundannualgrowthrateformulatellstherateofreturnnecessarytomovefromtheprincipalamount(thebeginningbalance)tothedesiredaccruedamount(theendingbalance)inaspecificamountoftime.Theformulatocalculatecompoundannualgrowthrate(CAGR)is:CAGR=(EB/BB)^(1/n)-1‘EB’representstheendingbalance,and‘BB’standsforthebeginningbalance.The‘n’representsthedesiredtimeinyears.Forexample,ifacouplewantedtoinvest$250,000towardsretirementandhopetohave$1millionforretirementin20years,theywouldneeda7.18%CAGRtomeetthatgoal.7.18%=(1,000,000/250,000)^(1/20)-1CAGRislimitedbecauseitassumesacontinuouslystablegrowthrate,andmanyinvestmentsdonothaveaguaranteedreturnorsteadyreturnrate.Instead,manyinvestmentsfluctuateinrateofreturn.However,CAGRcanbeusefulincomparingtheoverallperformanceoftwodifferentinvestmentsovertime.CAGRcanalsorevealproblemswithinvestinggoalsiftherateofreturnneededisfaroutsideaveragereturnsinaspecifictypeofinvestment.Forexample,ifthecoupleabovehypotheticallywantedtomeettheirgoalthroughonlyinvestinginaninvestmentafriendtoldthemhadreturnsof5%,itisunlikelytheywouldmeettheirgoal.However,aswithanyinvestment,pastperformanceisnotindicativeoffutureresults.Whatisannualpercentageyield(APY)?Annualpercentageyield(APY)isawayofexpressingtheamountearnedonacompoundinterest-bearinginvestmentinayear.APYtakesthebaseinterestrate(APR-annualpercentagerate)andmakesadjustmentsfortheeffectofcompoundingandthecompoundingfrequencyonthetotal.TheresultisapercentageratethatishigherthantherawAPR.Formulassuchasthecompoundinterestformularelyonthebaseinterestrate,theAPR,nottheannualpercentageyield.UsingtheAPYinformulasaskingfortherawinterestrateorAPRcanleadtoincorrectresults.CareshouldalwaysbetakentoensureifAPRorAPYisbeingdiscussedwheninvesting.Infinancialadvertising,loansandcreditcardratesareoftenshowasAPR.However,theAPYcanbedrasticallyhigherbasedoncompoundingfrequency.Somecreditcardscompounddebtdaily,quicklyinflatingtheAPY.Forinvestmentsandsavings,advertisementsoftenfeatureAPYtoshowcasetheresultoftheinvestmentinamorepositivelight.BothmethodsareaccuratebutrequirethecustomertounderstandthedifferenceinAPRandAPY.Dostocksearncompoundinterest?Whilesomestocksdopaydividends,stocksdonotearnanyinterest,eithersimpleorcompound.Stocksareaninvestmentwithoutanyreturnguaranteeandmayevendecreaseinvalueinsomeconditions.Theonlywaytoearn“income’onstocksistoinvestinstocksthatpayoutdividends,whichcouldbereinvestedbypurchasingmorestock.Therearedifferentclassesofsharesofstocks.Preferredstockshareholderstypicallygetfirstdibsondividends,butevencommonstockcanbeeligibletoreceivedividendsinsomecases.Somebrokersoffercustomerstheabilitytosetupautomaticreinvestmentofdividends.Thisisoftendonewithsomethingcalledadividendreinvestmentplan(DRIP).Byreinvestingdividends,thosefundscanbegintoearnincomeinapatternthat’ssimilartothewaycompoundedinterest.However,unlikeaninterest-bearingaccount,therearenoguaranteesthatvaluewillincrease,andthereisachanceofvaluelossonboththeoriginalinvestmentandnewlyreinvesteddividends.Whataresomecompoundinterestcalculatorapps?Understandingthecompoundinterestformulaandallofitsusescanbeahelpfultoolinunderstandinginvestingoptions.Sometimestheactualcalculationsarejustmorestraightforwardwithacalculator.TherearenumerousfinancialcalculatorappsavailableforbothAppleandAndroiddevices.Nooneappisperfect,buttherearesomeusefulfreeappsavailable.Keepinmindthatsomeofthefreeappsdocontainads.Also,youcanfindacompoundinterestcalculatorontheSecuritiesandExchangeCommission’sInvestor.govsite:https://www.investor.gov/additional-resources/free-financial-planning-tools/compound-interest-calculatorTheaboveexamplesareforillustrativepurposesonlyanddonotreflecttheperformanceofanyinvestment.Investinginvolvesrisk-akayoucouldloseyourmoney.Pleasebeadvisedthatbyclickingathird-partyURLorhyperlink,you’llbeaccessingathird-partywebsite.RobinhoodFinancialLLCisnotimplyingthatanymonitoringisbeingdonebyRobinhoodFinancialLLCofanyinformationcontainedonthethird-partywebsite.RobinhoodFinancialLLCisnotresponsiblefortheinformationcontainedonthethird-partywebsiteoryouruseoforinabilitytousesuchsite.Nordoweguaranteetheiraccuracyandcompleteness.Readytostartinvesting?SignupforRobinhoodandgetyourfirststockonus.SignupforRobinhoodCertainlimitationsapplyThefreestockofferisavailabletonewusersonly,subjecttothetermsandconditionsatrbnhd.co/freestock.Freestockchosenrandomlyfromtheprogram’sinventory.SecuritiestradingisofferedthroughRobinhoodFinancialLLC.20210824-1713079-5513443RelatedArticlesWhatisaDividend?UpdatedFebruary23,2021WhatisaBond?UpdatedMarch11,2021WhatisanExchange-TradedFund(ETF)?UpdatedFebruary23,2021WhatisPreferredStock?UpdatedFebruary23,2021WhatisCAGR?UpdatedMarch12,2021YouMayAlsoLikeWhatisBankruptcy?UpdatedJune18,2020Bankruptcyisalegalprocessinwhichpeopleorcompaniesdeclaretheycan’tpaytheirandworktosettlewiththeircreditors.WhatisaHoldingCompany?UpdatedFebruary19,2021Ahold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