Compound InterestSimple Interest ExampleSimple Interest SolutionCompound Interest ExampleAnnual interest solutionMore Compound InterestSlide 9Slide 10Slide 11Compound Interest AnswerContinuously Compounded InterestSlide 14AnswerSlide 16The End!Compound InterestCompound InterestRoss ChapmanRoss ChapmanBrandon MillerBrandon MillerFinance 321Stephen D’Arcy8:30 AMSimple Interest – You only receive interest Simple Interest – You only receive interest on your initial investment, meaning every on your initial investment, meaning every period you take the interest out of your period you take the interest out of your account and the interest grows on the initial account and the interest grows on the initial investment. investment. Investment x (1 + t * i) = value after t- yearsInvestment x (1 + t * i) = value after t- yearsThis is not a very efficient way to invest This is not a very efficient way to invest your money.your money.Simple Interest ExampleSimple Interest ExampleSuppose you invest $10,000 in a bank, Suppose you invest $10,000 in a bank, which pays you simple interest of 12% which pays you simple interest of 12% annually. How much will you have in your annually. How much will you have in your bank account after five years?bank account after five years?Simple Interest SolutionSimple Interest Solution$10,000 * (1 + 5 * .12) = $16,000$10,000 * (1 + 5 * .12) = $16,000Compound Interest – each interest payment Compound Interest – each interest payment is reinvested to earn more interest in is reinvested to earn more interest in subsequent periods.subsequent periods.Investment * (1 + i)^ t = Value at time tInvestment * (1 + i)^ t = Value at time tCompound Interest Compound Interest ExampleExampleSuppose you put $10,000 into a CD at Suppose you put $10,000 into a CD at your local bank, at a rate of 12% your local bank, at a rate of 12% compounded annually for 5 years. How compounded annually for 5 years. How much will you have when you take out the much will you have when you take out the principle and interest at the end of the 5 principle and interest at the end of the 5 years.years.Annual interest solutionAnnual interest solution10,000*(1+.12)^5= $17,623.4210,000*(1+.12)^5= $17,623.42More Compound InterestMore Compound InterestSometimes the interest won’t be compounded annually, but rather m times a year.More Compound InterestMore Compound InterestIf the interest is convertible mIf the interest is convertible mthth-ly then-ly then The interest rate your money is The interest rate your money is compounded at is compounded at is i/mi/m Investment x (1+i/m)^t*m = Value at Investment x (1+i/m)^t*m = Value at time ttime tMore Compound InterestMore Compound InterestIf you want to know the equivalent If you want to know the equivalent annually compounded rate to the interest annually compounded rate to the interest rate compounded mrate compounded mthth-ly-lyThen use this formula:Then use this formula:iiaa = ((1+ i/m)^m) - 1 = ((1+ i/m)^m) - 1Compound Interest Compound Interest ExampleExampleSay you put $10,000 into the bank at Say you put $10,000 into the bank at 12% convertible monthly for 5 years. 12% convertible monthly for 5 years. How much do you have in your account How much do you have in your account after 5 year? What is the equivalent after 5 year? What is the equivalent annual compounded rate?annual compounded rate?Compound Interest Compound Interest AnswerAnswerFirst Question:First Question:10000 x (1 + .12/12) ^ 5 *12 =$18,166.9710000 x (1 + .12/12) ^ 5 *12 =$18,166.97Second Question:Second Question:iiaa = ((1 + .12/12) ^ 12) – 1= 12.68% = ((1 + .12/12) ^ 12) – 1= 12.68%Continuously Continuously Compounded InterestCompounded InterestIf you money is compounded If you money is compounded continuously that means at all times it’s continuously that means at all times it’s earning interest. earning interest. Principal ePrincipal ert rt (Pert) (Pert)Equivalent Annual Compounded Rate:Equivalent Annual Compounded Rate:(Accumulate Value/ Investment)(Accumulate Value/ Investment)^(1/t)^(1/t) - 1 - 1Continuously Continuously Compounded InterestCompounded InterestSay you $10000 in the bank at 12% Say you $10000 in the bank at 12% compounded continuously. How much compounded continuously. How much money do you have after 5 year? What is money do you have after 5 year? What is the equivalent annual compounded rate?the equivalent annual compounded rate?AnswerAnswerAccumulated Value:Accumulated Value:10000 e10000 e(.12)*5 (.12)*5 = $18,221.19 = $18,221.19Equivalent Annual Compounded Rate:Equivalent Annual Compounded Rate:(18221.19/10000)(18221.19/10000)(1/5)(1/5) -1 = 12.75% -1 = 12.75%So as you can see as m increases in size So as you can see as m increases in size the amount of interest you earn in the the amount of interest you earn in the year grows.year grows.The End!The End!Any Question?Any
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