What Is Compound Interest? | The Motley Fool

Compound interest is the phenomenon that allows seemingly small amounts of money to grow into large amounts over time. In order to take full ... MatthewFrankel,CFP® (TMFMathGuy) Updated:Jul6,2021at11:07AM AuthorBio MattisaCertifiedFinancialPlannerbasedinSouthCarolinawhohasbeenwritingforTheMotleyFoolsince2012.Mattspecializesinwritingaboutbankstocks,REITs,andpersonalfinance,buthelovesanyinvestmentattherightprice.FollowhimonTwittertokeepupwithhislatestwork! Follow@TMFMathGuy Whenitcomestocalculatinginterest,therearetwobasicchoices:simpleandcompound.Simpleinterestsimplymeansasetpercentageoftheprincipalamounteveryyear.Forexample,ifyouinvest$1,000at5%simpleinterestfor10years,youcanexpecttoreceive$50ininteresteveryyearforthenextdecade.Nomore,noless.Intheinvestmentworld,bondsareanexampleofaninvestmenttypethattypicallypayssimpleinterest. Ontheotherhand,compoundinterestiswhathappenswhenyoureinvestyourearnings,whichthenearninterestaswell.Compoundinterestessentiallymeans"interestontheinterest"andisthereasonmanyinvestorsaresosuccessful. Imagesource:GettyImages. Thinkofitthisway.Let'ssayyouinvest$1,000at5%interest.Afterthefirstyear,youreceivea$50interestpayment.But,insteadofputtingitinyourpocket,youreinvestitatthesame5%rate.Forthesecondyear,yourinterestiscalculatedona$1,050investment,whichcomesto$52.50.Ifyoureinvestthat,yourthird-yearinterestwillbecalculatedona$1,102.50balance.Yougettheidea.Compoundinterestmeansthatyourprincipal(andtheinterestitgenerates)getslargerovertime. Thedifferencebetweensimpleandcompoundinterestcanbemassive.Takealookatthedifferenceona$10,000investmentportfolioat10%interestovertime: TimePeriod SimpleInterest@10% CompoundInterest(Annually@10%) Start $10,000 $10,000 1Year $11,000 $11,000 2Years $12,000 $12,100 5Years $15,000 $16,105 10Years $20,000 $25,937 20Years $30,000 $67,275 30Years $40,000 $174,494 Calculationsbyauthor. It'salsoworthmentioningthatthere'saverysimilarconceptknownas cumulativeinterest.Cumulativeinterestreferstothesumoftheinterestpaymentsmade,butittypicallyreferstopaymentsmadeonaloan.Forexample,thecumulativeinterestona30-yearmortgagewouldbehowmuchmoneyyoupaidtowardinterestoverthe30-yearloanterm. Howcompoundinterestiscalculated Compoundinterestiscalculatedbyapplyinganexponentialgrowthfactortotheinterestrateorrateofreturnyou'reusing.Tocalculatecompoundinterestoveracertainperiodoftime,hereisamathematicalformulayoucanuse: Where"A"isthefinalamount,"P"istheprincipal,"r"istheinterestrateexpressedasadecimal,"n"isthecompoundingfrequency,and"t"isthetimeperiodinyears.Here'swhatallofthesevariablesmean: Principalreferstothestartingbalanceonwhichinterestisbeingcalculated.Thetermismorecommonlyusedinthecontextofaloan'soriginalbalancebutcanbeappliedtoyouroriginalinvestmentamountaswell.Forexample,ifyoudecidetoinvest$10,000forfiveyears,thatamountwouldbeyourprincipalforthepurposesofcalculatingcompoundinterest. Ratereferstotheinterestrate(orexpectedrateofreturnininvesting),expressedasadecimal.Forcalculationpurposes,ifyouexpectyourinvestmentstogrowatanaveragerateof7%peryear,youwoulduse0.07here. Compoundingfrequencyreferstohowfrequentlyyou'readdinginteresttotheprincipal.Usingtheexampleof7%interest,ifweweretouseannualcompounding,youwouldsimplyadd7%totheprincipalonceperyear.Ontheotherhand,semi-annualcompoundingwouldinvolveapplyinghalfofthatamount(3.5%)twiceayear.Othercommoncompoundingfrequenciesincludequarterly(fourtimesperyear),monthly,weekly,ordaily.There'salsoamathematicalconceptcalledcontinuouscompounding,whereinterestisconstantlyaccumulating.  Timeisaprettyself-explanatoryconcept,butforthepurposesofcalculatingcompoundinterest,besuretoexpressthetotaltimeperiodinyears.Inotherwords,ifyou'reinvestingfor30months,besuretouse2.5yearsintheformula. Compoundingfrequencymakesadifference Inthepreviousexample,weusedannualcompounding--meaningthatinterestiscalculatedonceperyear.Inpractice,compoundinterestisoftencalculatedmorefrequently.Commoncompoundingintervalsarequarterly,monthly,anddaily,buttherearemanyotherpossibleintervalsthatcanbeused. Thecompoundingfrequencymakesadifference--specifically,morefrequentcompoundingleadstofastergrowth.Forexample,hereisthegrowthof$10,000at8%interestcompoundedatseveraldifferentfrequencies: Time AnnualCompounding Quarterly Monthly 1year $10,800 $10,824 $10,830 5years $14,693 $14,859 $14,898 10years $21,589 $22,080 $22,196   Exampleofcalculatingcompoundinterest Asabasicexample,let'ssayyou'reinvesting$20,000at5%interest,compoundedquarterly,for20years.Inthiscase,"n"wouldbefoursincequarterlycompoundingoccursfourtimesperyear.Fromthisinformation,wecancalculatetheinvestment'sfinalvalueafter20yearslikethis: Compoundearningsvs.compoundinterest Thedifferencebetweencompoundinterestandcompoundearningsisthatcompoundearningsreferstothecompoundingeffectsof bothinterestpaymentsanddividends,aswellasappreciationinthevalueoftheinvestmentitself.  Forexample,ifastockinvestmentpaidyoua4%dividendyield,andthestockitselfincreasedinvalueby5%,you'dhavetotalearningsfortheyearof9%.Whenthesedividendsandpricegainscompoundovertime,itisaformofcompoundearningsandnotinterest(sincenotallofthegainscamefrompaymentstoyou). Inanutshell,whenyou'retalkingaboutlong-termreturnsfromstocks,ETFs,ormutualfunds,it'stechnicallycalledcompoundearnings,althoughitcanstillbecalculatedinthesamemannerifyouknowyourexpectedrateofreturn. Whycompoundinterestissuchanimportantconceptforinvestors Compoundinterestisthephenomenonthatallowsseeminglysmallamountsofmoneytogrowintolargeamountsovertime.Inordertotakefulladvantageofthepowerofcompoundinterest,investmentsmustbeallowedtogrowandcompoundforlongperiods.  MotleyFoolReturns StockAdvisor S&P500 672% 144% JoinStockAdvisor Discountedoffersareonlyavailabletonewmembers.StockAdvisorwillrenewatthethencurrentlistprice.StockAdvisorlistpriceis$199peryear. StockAdvisorlaunchedinFebruaryof2002.Returnsasof11/11/2021. 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