Continuous Compounding Formula (with Calculator)

The continuous compounding formula is used to determine the interest earned on an account that is constantly compounded, essentially leading to an infinite ... ContinuousCompounding ContinuousCompoundingCalculator(ClickHereorScrollDown) Thecontinuouscompoundingformulaisusedtodeterminetheinterestearnedonanaccountthatisconstantlycompounded, essentiallyleadingtoaninfiniteamountofcompoundingperiods. Theeffectofcompoundingisearninginterestonaninvestment,orattimespayinginterestonadebt,thatisreinvested toearnadditionalmoniesthatwouldnothavebeengainedbasedontheprincipalbalancealone.Byearninginterestonprior interest,onecanearnatanexponentialrate. Thecontinuouscompoundingformulatakesthiseffectofcompoundingtothefurthestlimit.Insteadofcompoundinginterest onanmonthly,quarterly,orannualbasis,continuouscompoundingwilleffectivelyreinvestgainsperpetually. ExampleofContinuousCompoundingFormula Asimpleexampleofthecontinuouscompoundingformulawouldbeanaccountwithaninitialbalanceof$1000andanannual rateof10%.Tocalculatetheendingbalanceafter2yearswithcontinuouscompounding,theequationwouldbe Thiscanbeshownas$1000timese(.2)whichwillreturna balanceof$1221.40afterthetwoyears.Forcomparison,anaccountthatiscompoundedmonthlywillreturnabalanceof $1220.39afterthetwoyears.Althoughtheconceptofinfiniteseemsthatitwouldreturnaverylargeamount,theeffectof eachcompoundbecomessmallereachtime. HowtheContinuousCompoundingFormulaisderived Thecontinuouscompoundingformulacanbefoundbyfirstlookingatthecompoundinterestformula wherenisthenumberoftimescompounded,tistime,and ristherate. Whenn,orthenumberoftimescompounded,isinfinitetheformulacanberewrittenas Thelimitsectioninthemiddleoftheformulacanbeshownaser,whichleadstothe formulaatthetopofthepage. ReturntoTop FormulasrelatedtoContinuousCompounding CompoundInterest DoublingTime-ContinuousCompounding PV-ContinuousCompounding FV-ContinuousCompounding FVofAnnuity-ContinuousCompounding NewtoFinance? StartwiththeBasics PresentValue FutureValue CompoundInterest SimpleInterest ContinuousCompoundingCalculator Yourbrowserdoesnotsupportiframes. AlphabeticalIndex: A-C D-F G-I J-L M-P Q-S T-V W-Z Home PrivacyPolicy *Thecontentofthissiteisnotintendedtobefinancialadvice. Thissitewasdesignedforeducationalpurposes. Theusershoulduseinformationprovidedbyanytoolsormaterialathis orherowndiscretion,asnowarrantyisprovided. Whenconsideringthissiteasasourceforacademicreasons,please rememberthatthissiteisnot subjecttothesamerigorasacademicjournals,coursematerials, andsimilarpublications. FeelFreetoEnjoy! Contactusat: [email protected]