Compound Interest: Definition, Formula, How It's Calculated

Compound interest occurs when previously earned interest is added to the principal amount invested or borrowed. It is commonly described as ... 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Profile Newsletters FAQs Subscription Logout Closeicon Twocrossedlinesthatforman'X'.Itindicatesawaytocloseaninteraction,ordismissanotification. Economics&Markets InvestmentAssets InvestmentAccounts InvestingStrategies Professionals&Advisors MoreButtonIcon Circlewiththreeverticaldots.Itindicatesawaytoseemorenavmenuitemsinsidethesitemenubytriggeringthesidemenutoopenandclose. Economics&Markets InvestmentAssets InvestmentAccounts InvestingStrategies Professionals&Advisors Chevronicon Itindicatesanexpandablesectionormenu,orsometimesprevious/nextnavigationoptions. HOMEPAGE Subscribe Subscribe Home Chevronicon Itindicatesanexpandablesectionormenu,orsometimesprevious/nextnavigationoptions. Finance Understandingcompoundinterestiskeytobuildingwealthoravoidingcrushingdebt ElizabethAldrich Updated 2021-10-22T21:22:51Z FacebookIcon TheletterF. Emailicon Anenvelope.Itindicatestheabilitytosendanemail. Twittericon Astylizedbirdwithanopenmouth,tweeting. Twitter LinkedInicon Theword"in". LinkedIn Fliboardicon AstylizedletterF. Flipboard Linkicon Animageofachainlink.Itsymobilizesawebsitelinkurl. CopyLink Themorefrequentlyinterestcompounds,thefasteranoverallamountofmoneyaccumulates. Pier/GettyImages Compoundinterestoccurswhenpreviouslyearnedinterestisaddedtotheprincipalamountinvestedorborrowed.Itiscommonlydescribedas"interestearnedoninterest." Compoundinterestcanworktoyouradvantageasyourinvestmentsgrowovertime,butagainstyouifyou'repayingoffdebt,likecreditcards.   Ifyou'reborrowingmoney,youwantinterestcompoundedasinfrequentlyaspossible;ifyou'reinvesting,youwantinterestcompoundedasoftenaspossible. VisitInsider'sInvestingReferencelibraryformorestories. WarrenBuffetoncefamouslysaidthathiswealthcamefrom"acombinationoflivinginAmerica,someluckygenes,andcompoundinterest." Thebillionaireinvestormeantthattheinteresthisinvestmentsearnedhelpedcreatehisfortune.ButBuffettalsolikedtowarnpeopleaboutthedangersofendinguponthewrongsideofthecompoundinterestequation.Whilecompoundinterestisarguablythemostimportantcomponenttowealth-building,itcanalsobeoneofthebestwaystowreckyourfinances:Havingtopaycompoundinterestcancausedebttospiraloutofcontrol. Mostpeopleonlythinkofinterestintermsofhowhighorlowarateis.Butunderstandinghowinterestiscalculated,orcompounds,isimportanttoo.Knowinghowcompoundinterestworkscanhelpyouavoidexpensivemistakesandmakethemostofyourmoney,whetheryou'redepositingit,investingit,borrowingit,orspendingit.  Whatiscompoundinterest?Allinterestisapercentagechargedon,orearnedby,alumpsumofmoney.Compoundinterestisakindofinterestbasedonaddingtheoriginalprincipal—thatis,theinitialamountinvestedorborrowed—withtheaccumulatedinterestfrompreviousperiods.Forexample,sayyouhave$100inasavingsaccount,anditearnsinterestata10%rate,compoundedannually.Attheendofthefirstyear,you'dhave$110(100inprincipal+10ininterest).Attheendofthesecondyear,you'dhave$121(110inprincipal+11ininterest).Attheendofthethirdyear,you'dhave$133.10(121inprincipal+12.10ininterest).Andsoon.Inotherwords,withcompoundinterest,youearninterestoninterest. Therevelationcomeswhenyourealizethatcompoundinginterestmakestheprincipalgrowexponentially,meaningasinterestaccruesandthequantityofmoneyincreases,therateofgrowthbecomesfaster.Howquicklyyourmoneygrowsdependsontheinterestrate,andthefrequencyofcompounding.Interestcanbecompoundeddaily,monthly,quarterly,orannually,andthemorefrequentlyit'scompounded,thefasteritaccumulates. Overthelongterm,"themagicofcompounding"canreallyaddup.Here'showaninitialinvestmentof$5,000wouldgrowifcompoundedsemi-annuallyoveraperiodof35years,atanannualized5%interestrate:Ifyou'retheoneearningmoneyofftheinterest,dailyormonthlycompoundingarepreferabletoyearly.Ontheotherhand,ifyou'rebeingchargedinterest,monthlyoryearlycompoundingwillsaveyoumoneycomparedtodaily. Compoundinterestvs.simpleinterestWhilecompoundinterestis"interestoninterest"—calculatedonboththeprincipalamountandtheaccumulatedinterest— simpleinterest iswhollydifferent.Simpleinterestiscalculatedonlyontheoriginalprincipalbalanceordeposit.Let'stakeour$100savingsaccountagain,onlythistimeit'spaying10%insimpleinterest.Thatmeansthe10%interestrateappliesonlytoyouroriginalprincipalamountof$100,soyouearn$10eachyear.Period.Attheendofthefirstyear,you'dhave$110.Butattheendofthesecondyear,you'dhave$120.Attheendofthethirdyear,$130—comparedto$133.10inthecompoundedinterestaccount.Eventhoughwe'veusedsmallnumbershere,youcanseehowthefartheroutyougo,themorecompoundinterestnetsyou—andthemoreitoutstripssimpleinterest.Simpleinteresttendstobeusedinmoststudentloans,mortgages,andinstallmentloans—whenyou'repayingastoreforthepurchaseofabigapplianceoveraperiodoftime,forexample. HowtocalculatecompoundinterestCalculatingcompoundinterestlookscomplicated,butit'sactuallyassimpleaspluggingsomenumbersintotherightformula.  Thecompoundinterestequationbasicallyadds1totheinterestrate,raisesthissumtothetotalnumberofcompoundperiods,andmultipliestheresultbytheprincipalamount. ShayanneGal/BusinessInsider Let'ssayyoudecidetodeposityour$10,000annualbonusintoa5-yearcertificateofdeposit(CD).YouleavethatmoneyintheCDforthefullfiveyears,anditearnsa4%annualrateofinterestthat'scompoundeddaily.Thenumbersyou'dplugintoeachvariableareasfollows:P=$10,000r=0.04n=365t=5Theformulagivesyou$12,213.89forA.That'sthetotalamountofmoneyyou'dhaveinyourmoneymarketaccountattheendoffiveyears.Thismeansyouearned$2,213.89ininterest. HowcompoundinterestcanworkagainstyouAsbeneficialcompoundinginterestcanbeforsavings,investments,andwealthcreation,it'simportanttonotethatitcanworkagainstyouifyou'repayingoffdebt.Infact,compoundingispartofwhatmakescarryinganoutstandingcreditcardbalancesodeadly.Infact,theaboveexamplecouldbeturnedupsidedownbyimaginingthatyoucarrya$10,000balanceonacreditcard(we'llassumeit'sthesame4%compoundeddaily,eventhoughcreditcardAPRsareusuallymuchhigher).Youplannottoputanythingelseonthecard,andtopayitalloffinfiveyears.Eventhoughyou'dbechippingawayatyourbalanceandpayinganextremelylowinterestrate,youcouldstillenduppayingalotininterestcharges—morethan$1,000infact.Andifyouwerebeingcharged18%compoundeddaily—whichisclosertotheaveragecreditcardinterestrate—youwouldpay$5,236ininterestafterfiveyears. HowtogetthemostoutofcompoundinterestThebestwaytotakeadvantageofcompoundinterestisthroughsavingandinvesting. Optingforasavingsaccountthatearnsinterest—suchas high-yieldsavingsaccounts , moneymarketaccounts ,andCDs—isonewaytomakecompoundinterestworkinyourfavor.Whenchoosinganaccount,you'llwanttolookforonewithminimalfeesandthehighestannualpercentageyield(APY),whichistheinterestyoucanearnonyourdepositina12-monthperiod.It'sworthnotingthattheinterestratesoneventhebestsavingsaccountsbarelyoutpaceinflation,sothey'rebestforshort-termsavings.Ifyouwanttobuildlong-termwealth,whetherthat'ssavingsforretirementoragoalthat'syearsaway,investingyourmoneywillreallygetitworkingforyou. Savingsproductsofferinterestratesthattypicallyrangefrom0.01%to3%,dependingonthestateoftheeconomy,whiletheaveragehistoricalrateofreturnonthestockmarketis10%,beforeadjustingforinflation.Whenopeninganinvestmentaccountlikea401(k),IRA,brokerageaccount,ormutualfund,youhavetheoptiontoautomaticallyreinvestthedividendsorinterestyourinvestmentsearn.Doingsomeansyourreturnswillcompound. ThefinancialtakeawayCompoundinterestcanbeyourfriendoryourenemy,withthepowertoenrichyouorbankruptyou—dependingwhichsideofityou'reon.Luckily,youdon'tneedtobeamathgeniustounderstandwhethertheinterestonanaccountwillhelporhurtyou.Ifyou'reborrowingmoney,youwantthelowestinterestratepossible,compoundedasinfrequentlyaspossible.Ifyou'reinvestingmoney,theoppositeapplies:Youwantnotonlyagoodinterestrate,butonethatcompoundsearlyandoften.Andwhencomparingloans,creditcardAPRs,savingsaccountAPYs,orothersecurities'returns—checkthefrequencyatwhichtheinterestcompounds,andmakesureyou'recomparingliketolike.Twointerestratescanbenominallythesame,butiftheycompoundatdifferentspeeds,itcanmakeabigdifference. Whetherearningitorpayingit,thenatureofcompoundinterestmeansthatgettingontopofitearlyonisexponentially—punintended—betterforyourwallet. ElizabethAldrich ElizabethAldrich isafinancewriterspecializingincreditcardsandloans,retirementplanning,investing,economics,andsmallbusiness.HerworkhasappearedonTheMotleyFool,USAToday,MSNMoney,Yahoo!Finance,Bankrate,andBusinessInsider.She'sanavidcreditcardpointscollectorandperpetualtraveler. Readmore Readless Relatedarticles PERSONALFINANCE Investingforincome:7money-generatingassetsforyourportfolioandhowtogetstarted MARKETS Whattoknowaboutsavingsbonds—securitiesyoucanbuyfromtheUSTreasury FINANCE Understandingwhatqualifieddividendsarewhythey'retaxedatlowerrates PERSONALFINANCE Bondsvs.CDs:Thekeydifferencesandhowtodecidewhichincome-producingoptionisbetterforyou Wasthisarticlehelpfulforyou? Yes No Additionalcomments Email(optional) Receiveaselectionofourbeststoriesdailybasedonyourreadingpreferences. 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