Compound Interest Calculator - Calculator.net

Free compound interest calculator to convert and compare interest rates ... and continuous (meaning an infinite number of periods) compounding frequencies. home/financial/compoundinterestcalculator CompoundInterestCalculator TheCompoundInterestCalculatorbelowcanbeusedtocompareorconverttheinterestratesofdifferentcompoundingperiods.PleaseuseourInterestCalculatortodoactualcalculationsoncompoundinterest. InputInterest Compound   OutputInterest Compound Annually(APY)SemiannuallyQuarterlyMonthly(APR)SemimonthlyBiweeklyWeeklyDailyContinuously = 6.16778% Annually(APY)SemiannuallyQuarterlyMonthly(APR)SemimonthlyBiweeklyWeeklyDailyContinuously Related InterestCalculator|InvestmentCalculator|AutoLoanCalculator Whatiscompoundinterest? Interestisthecostofusingborrowedmoney,ormorespecifically,theamountalenderreceivesforadvancingmoneytoaborrower.Whenpayinginterest,theborrowerwillmostlypayapercentageoftheprincipal(theborrowedamount).Theconceptofinterestcanbecategorizedintosimpleinterestorcompoundinterest. Simpleinterestreferstointerestearnedonlyontheprincipal,usuallydenotedasaspecifiedpercentageoftheprincipal.Todetermineaninterestpayment,simplymultiplyprincipalbytheinterestrateandthenumberofperiodsforwhichtheloanremainsactive.Forexample,ifonepersonborrowed$100fromabankatasimpleinterestrateof10%peryearfortwoyears,attheendofthetwoyears,theinterestwouldcomeoutto: $100×10%×2years=$20 Simpleinterestisrarelyusedintherealworld.Compoundinterestiswidelyusedinstead.Compoundinterestisinterestearnedonboththeprincipalandontheaccumulatedinterest.Forexample,ifonepersonborrowed$100fromabankatacompoundinterestrateof10%peryearfortwoyears,attheendofthefirstyear,theinterestwouldamountto: $100×10%×1year=$10 Attheendofthefirstyear,theloan'sbalanceisprincipalplusinterest,or$100+$10,whichequals$110.Thecompoundinterestofthesecondyeariscalculatedbasedonthebalanceof$110insteadoftheprincipalof$100.Thus,theinterestofthesecondyearwouldcomeoutto: $110×10%×1year=$11 Thetotalcompoundinterestafter2yearsis$10+$11=$21versus$20forthesimpleinterest. Becauselendersearninterestoninterest,earningscompoundovertimelikeanexponentiallygrowingsnowball.Therefore,compoundinterestcanfinanciallyrewardlendersgenerouslyovertime.Thelongertheinterestcompoundsforanyinvestment,thegreaterthegrowth. Asasimpleexample,ayoungmanatage20invested$1,000intothestockmarketata10%annualreturnrate,theS&P500'saveragerateofreturnsincethe1920s.Attheageof65,whenheretires,thefundwillgrowto$72,890,orapproximately73timestheinitialinvestment! Whilecompoundinterestgrowswealtheffectively,itcanalsoworkagainstdebtholders.Thisiswhyonecanalsodescribecompoundinterestasadouble-edgedsword.Puttingofforprolongingoutstandingdebtcandramaticallyincreasethetotalinterestowed. Differentcompoundingfrequencies Interestcancompoundonanygivenfrequencyschedulebutwilltypicallycompoundannuallyormonthly.Compoundingfrequenciesimpacttheinterestowedonaloan.Forexample,aloanwitha10%interestratecompoundingsemi-annuallyhasaninterestrateof10%/2,or5%everyhalfayear.Forevery$100borrowed,theinterestofthefirsthalfoftheyearcomesoutto: $100×5%=$5 Forthesecondhalfoftheyear,theinterestrisesto: ($100+$5)×5%=$5.25 Thetotalinterestis$5+$5.25=$10.25.Therefore,a10%interestratecompoundingsemi-annuallyisequivalenttoa10.25%interestratecompoundingannually. TheinterestratesofsavingsaccountsandCertificateofDeposits(CD)tendtocompoundannually.Mortgageloans,homeequityloans,andcreditcardaccountsusuallycompoundmonthly.Also,aninterestratecompoundedmorefrequentlytendstoappearlower.Forthisreason,lendersoftenliketopresentinterestratescompoundedmonthlyinsteadofannually.Forexample,a6%mortgageinterestrateamountstoamonthly0.5%interestrate.However,aftercompoundingmonthly,interesttotals6.17%compoundedannually. Ourcompoundinterestcalculatoraboveaccommodatestheconversionbetweendaily,bi-weekly,semi-monthly,monthly,quarterly,semi-annual,annual,andcontinuous(meaninganinfinitenumberofperiods)compoundingfrequencies. Compoundinterestformulas Thecalculationofcompoundinterestcaninvolvecomplicatedformulas.Ourcalculatorprovidesasimplesolutiontoaddressthatdifficulty.However,thosewhowantadeeperunderstandingofhowthecalculationsworkcanrefertotheformulasbelow: Basiccompoundinterest Thebasicformulaforcompoundinterestisasfollows: At=A0(1+r)n where: A0:principalamount,orinitialinvestment At:amountaftertimet r:interestrate n:numberofcompoundingperiods,usuallyexpressedinyears Inthefollowingexample,adepositoropensa$1,000savingsaccount.Itoffersa6%APYcompoundedonceayearforthenexttwoyears.Usetheequationabovetofindthetotaldueatmaturity: At=$1,000×(1+6%)2=$1,123.60 Forothercompoundingfrequencies(suchasmonthly,weekly,ordaily),prospectivedepositorsshouldrefertotheformulabelow. At=A0×(1+ rn )nt where: A0:principalamount,orinitialinvestment At:amountaftertimet n:numberofcompoundingperiodsinayear r:interestrate t:numberofyears Assumethatthe$1,000inthesavingsaccountinthepreviousexampleincludesarateof6%interestcompoundeddaily.Thisamountstoadailyinterestrateof: 6%÷365=0.0164384% Usingtheformulaabove,depositorscanapplythatdailyinterestratetocalculatethefollowingtotalaccountvalueaftertwoyears: At=$1,000×(1+0.0164384%)(365×2) At=$1,000×1.12749 At=$1,127.49 Hence,ifatwo-yearsavingsaccountcontaining$1,000paysa6%interestratecompoundeddaily,itwillgrowto$1,127.49attheendoftwoyears. Continuouscompoundinterest Continuouslycompoundinginterestrepresentsthemathematicallimitthatcompoundinterestcanreachwithinaspecifiedperiod.Thecontinuouscompoundequationisrepresentedbytheequationbelow: At=A0ert where: A0:principalamount,orinitialinvestment At:amountaftertimet r:interestrate t:numberofyears e:mathematicalconstante,~2.718 Forinstance,wewantedtofindthemaximumamountofinterestthatwecouldearnona$1,000savingsaccountintwoyears. Usingtheequationabove: At=$1,000e(6%×2) At=$1,000e0.12 At=$1,127.50 Asshownbytheexamples,theshorterthecompoundingfrequency,thehighertheinterestearned.However,aboveaspecificcompoundingfrequency,depositorsonlymakemarginalgains,particularlyonsmalleramountsofprincipal. Ruleof72 TheRuleof72isashortcuttodeterminehowlongitwilltakeforaspecificamountofmoneytodoublegivenafixedreturnratethatcompoundsannually.Onecanuseitforanyinvestmentaslongasitinvolvesafixedratewithcompoundinterestinareasonablerange.Simplydividethenumber72bytheannualrateofreturntodeterminehowmanyyearsitwilltaketodouble. Forexample,$100withafixedrateofreturnof8%willtakeapproximatelynine(72/8)yearstogrowto$200.Bearinmindthat"8"denotes8%,andusersshouldavoidconvertingittodecimalform.Hence,onewoulduse"8"andnot"0.08"inthecalculation.Also,rememberthattheRuleof72isnotanaccuratecalculation.Investorsshoulduseitasaquick,roughestimation. HistoryofCompoundInterest Ancienttextsprovideevidencethattwooftheearliestcivilizationsinhumanhistory,theBabyloniansandSumerians,firstusedcompoundinterestabout4400yearsago.However,theirapplicationofcompoundinterestdifferedsignificantlyfromthemethodsusedwidelytoday.Intheirapplication,20%oftheprincipalamountwasaccumulateduntiltheinterestequaledtheprincipal,andtheywouldthenaddittotheprincipal. Historically,rulersregardedsimpleinterestaslegalinmostcases.However,certainsocietiesdidnotgrantthesamelegalitytocompoundinterest,whichtheylabeledusury.Forexample,Romanlawcondemnedcompoundinterest,andbothChristianandIslamictextsdescribeditasasin.Nevertheless,lendershaveusedcompoundinterestsincemedievaltimes,anditgainedwiderusewiththecreationofcompoundinteresttablesinthe1600s. AnotherfactorthatpopularizedcompoundinterestwasEuler'sConstant,or"e."Mathematiciansdefineeasthemathematicallimitthatcompoundinterestcanreach. JacobBernoullidiscoveredewhilestudyingcompoundinterestin1683.Heunderstoodthathavingmorecompoundingperiodswithinaspecifiedfiniteperiodledtofastergrowthoftheprincipal.Itdidnotmatterwhetheronemeasuredtheintervalsinyears,months,oranyotherunitofmeasurement.Eachadditionalperiodgeneratedhigherreturnsforthelender.Bernoullialsodiscernedthatthissequenceeventuallyapproachedalimit,e,whichdescribestherelationshipbetweentheplateauandtheinterestratewhencompounding. LeonhardEulerlaterdiscoveredthattheconstantequaledapproximately2.71828andnamedite.Forthisreason,theconstantbearsEuler'sname. SearchFinancialCalculatorsMortgageLoanAutoLoanInterestPaymentRetirementAmortizationInvestmentCurrencyInflationFinanceMortgagePayoffIncomeTaxCompoundInterestSalary401KInterestRateSalesTaxMoreFinancialCalculatorsFinancial|FitnessandHealth|Math|Other aboutus|sitemap|termsofuse|privacypolicy ©2008-2021calculator.net