Compound Interest Finance 321 Professor D’ArcyIntroduction to Compound InterestSimple InterestCompound Interest vs. Simple InterestCompound InterestAdjusting Interest RatesAdjusting Interest RatesAdjusting Interest Rate ExampleTimelineSlide 10Compound Interest Example 1Solution to Example 1Compound Interest Example 2Solution to Example 2Continuous CompoundingContinuous Compounding ExampleSolutionQuestion for the ClassSlide 19Compound InterestFinance 321Professor D’ArcyAdam JohariLauren DufourIntroduction to Compound InterestDefinition: interest that is calculated both on the principal as well as accumulated interestWhere is it used?Loans, mortgages, annuities, etc…Why is it used?-It refers to the interest on interest principle.Simple InterestDefinition: Interest calculated on solely the principal, and not off of past earned interestFormula:I = Prt(where I = interest, P = principle, r = annual interest rate, t = time in years)Compound Interest vs. Simple InterestSimple CompoundSolely earning int. on PrincipleBetter when borrowingEarns int. on P and Int.Better when lending and investingCompound Interest Formula:FV = PV(1+r)nExplanation of Variables:FV = future valuePV = present valuer = annual interest raten = number of compounding periodsAdjusting Interest RatesWhy do we have to adjust?Interest rates are not always given to us as an annual percentageThey are sometimes stated as semi-annually, monthly, etc...How?Adjusting Interest RatesFV = PV (1 + r(n)/n)ntr(n) = nominal interest raten = number of compounding periods in a yeart = time in yearsr(n)/n = is the effective interest rate for n periodsAdjusting Interest Rate ExampleFind the future value of $500 invested for five years with a nominal interest rate of 8% compounded quarterly.FV = PV (1 + r (n) /n) ntFV = 500(1 + 0.08/4) 4*5FV = $742.97TimelinePVFVn=1n=0n=2i = 6%Timeline$1000n=1n=0n=2i = 6%$1123.6FV = PV(1+i)nFV = 1000(1.06)2Compound Interest Example 1Dyer needs $5000 five years from now to fund his Simpson collection. The current annual interest rate is 6%, and is expected to remain the same. How much would he have to invest today in order to reach his goal?Solution to Example 1FV = $5000R = 6%N = 5PV = ?FV = PV(1+r)n 5000 = PV(1.06)5PV = $3736.29Compound Interest Example 2Dyer invests $5000 today. The current nominal interest rate is 6%, which is compounded monthly. How much will he have 5 years from now?Solution to Example 2PV = $5000R = 0.06/12 = 0.005N = 5*12 = 60 monthsFV = ?FV = PV(1+r)n FV = 5000(1.005)60FV = $6744.25Continuous CompoundingDefinition: Interest that is compounded on a continuous basis, rather than at fixed intervalsFormula:FV = PVectwhere e is approximately 2.718where c is the continuously compounded interest rate*Note: c = ln(1+r), where r is the annual interest rateContinuous Compounding ExampleYou have $400 and it grows at a continuous rate to $500 over 3 years. Find the continuously compounded interest rate.SolutionFV = PVect 500 = 400e c*3C = 7.44%Question for the ClassUncle Joe wants to purchase a Porsche at the end of the year 2008. Today is January 1, 2007. The Porsche is expected to cost $100000 on December 31, 2008. The current interest rate for 2007 is 7%, and the interest rate is expected to go up to 8% for the year 2008. On January 1, 2008, Aunt Edna promises to give Uncle Joe a $50000 New Years present. How much money would Uncle Joe need today in order to finance his dream car?Thank
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