Chapter 4 Interest RatesAnnual and Periodic RatesSlide 3Slide 4Impact on TVMSlide 6Consumer Loans and Monthly Amortization ScheduleSlide 8Nominal and Real Interest RatesSlide 10Risk-free Rate and PremiumsSlide 12Slide 13Brief History of Interest RatesProblemsChapter 4 Chapter 4 Interest RatesInterest RatesAnnual and Periodic RatesAnnual and Periodic RatesImpact on TVM Impact on TVM Consumer Loans and Monthly Consumer Loans and Monthly Amortization SchedulesAmortization SchedulesNominal and Real Interest RatesNominal and Real Interest RatesRisk-free Rate and PremiumsRisk-free Rate and PremiumsDefault, Maturity, LiquidityDefault, Maturity, LiquidityBrief History of Interest RatesBrief History of Interest RatesAnnual and Periodic RatesAnnual and Periodic RatesAnnual Percentage Rate (APR) Annual Percentage Rate (APR) The standard way to quote interest rateThe standard way to quote interest rateActual rate may be differentActual rate may be differentPeriod RatePeriod RateThe rate for the periodThe rate for the periodQuarterly, Monthly, Daily, etc.Quarterly, Monthly, Daily, etc.Annual Percentage Rate divided by Compounding periods Annual Percentage Rate divided by Compounding periods per yearper yearEffective Annual Rate (EAR) is the periodic rate Effective Annual Rate (EAR) is the periodic rate compounded for the yearcompounded for the yearAnnual and Periodic RatesAnnual and Periodic RatesPeriodic Rates with 5.0% APRPeriodic Rates with 5.0% APRSemi-Annual Rate (compounds twice a year)Semi-Annual Rate (compounds twice a year)5.0% / 2 = 2.5%5.0% / 2 = 2.5%Monthly Rate (compounds twelve times a Monthly Rate (compounds twelve times a year)year)5.0% / 12 = 0.04167%5.0% / 12 = 0.04167%Effective Annual RatesEffective Annual RatesSemi-Annual Rate of 2.5%, EAR = 5.0625%Semi-Annual Rate of 2.5%, EAR = 5.0625%Monthly Rate of 0.04167%, EAR = 5.1162%Monthly Rate of 0.04167%, EAR = 5.1162%Annual and Periodic RatesAnnual and Periodic RatesEffective Annual Rate is the rate that you Effective Annual Rate is the rate that you earn with your investment and it increases earn with your investment and it increases with the number of compounding periods with the number of compounding periods per year (C/Y)per year (C/Y)Maximum compounding is continuous Maximum compounding is continuous compounding andcompounding andEAR = eEAR = eAPRAPR -1 -1EAR = eEAR = e0.050.05 -1= 5.12711% -1= 5.12711%Impact on TVMImpact on TVMThe r in the TVM equations is the periodic The r in the TVM equations is the periodic rate rate It is the APR when compounding is It is the APR when compounding is annuallyannuallyThe n in the TVM equation matches r and The n in the TVM equation matches r and is the number of periods (compounding is the number of periods (compounding periods per year times number of years)periods per year times number of years)Changing calculator mode for P/Y and C/YChanging calculator mode for P/Y and C/YImpact on TVMImpact on TVMIncreasing the number of compounding periods Increasing the number of compounding periods changes results (changes effective interest rate)changes results (changes effective interest rate)Example 4.1 – Annual compounding versus Example 4.1 – Annual compounding versus Monthly compoundingMonthly compounding$2,000,000 retirement goal at 6% APR$2,000,000 retirement goal at 6% APR40 years to retirement40 years to retirementDeposit today with annual compounding, $194,444.38Deposit today with annual compounding, $194,444.38Deposit today with monthly compounding, Deposit today with monthly compounding, $182,524.16$182,524.16EAR difference, Annual is 6%, Monthly is 6.1678%EAR difference, Annual is 6%, Monthly is 6.1678%Consumer Loans and Consumer Loans and Monthly Amortization ScheduleMonthly Amortization ScheduleMost Consumer Loans are annuity stream Most Consumer Loans are annuity stream fixed payments with interest accruing at fixed payments with interest accruing at end of monthend of monthPayment is for monthly interest expense Payment is for monthly interest expense and remainder if for principal reductionand remainder if for principal reductionUse TVM equations with monthly interest Use TVM equations with monthly interest rate and number of periods to find rate and number of periods to find payment (equation 4.5)payment (equation 4.5)PV is the amount of the loan PV is the amount of the loanConsumer Loans and Consumer Loans and Monthly Amortization ScheduleMonthly Amortization ScheduleMonthly amortization schedule for car loan of Monthly amortization schedule for car loan of $25,000 for 72 months at 8% APR (Table 4.3)$25,000 for 72 months at 8% APR (Table 4.3) rrPVPMTn111Nominal and Real Interest RatesNominal and Real Interest RatesAPR and Periodic Rates are nominal ratesAPR and Periodic Rates are nominal ratesNominal Rates have two componentsNominal Rates have two componentsReal RateReal RateExpected Inflation RateExpected Inflation RateNominal Nominal ≈ Real Rate + Expected Inflation≈ Real Rate + Expected InflationReal Rate is reward for savingReal Rate is reward for savingExample 4.3 – 21 books next year versus 20 books Example 4.3 – 21 books next year versus 20 books nownowReal Rate = 21/20 – 1 = 5%Real Rate = 21/20 – 1 = 5%Expected Inflation is the rising price of a goodExpected Inflation is the rising price of a goodNominal and Real Interest RatesNominal and Real Interest RatesFisher EffectFisher EffectRelationship between real rate, expected Relationship between real rate, expected inflation, and nominal rateinflation, and nominal rate(1+r) = (1+r(1+r) = (1+r**) x (1+h)) x (1+h)r is the nominal rater is the nominal raterr** is the real rate is the real rateh is expected inflationh is expected inflationr = rr = r** + h + (r + h + (r** x h) x h)rr* * is the same the world roundis the same the world roundRisk-free Rate and PremiumsRisk-free Rate and PremiumsRisk-free rate (a nominal or real rate) with Risk-free rate (a nominal or real rate) with a guaranteed returna guaranteed returnNominal risk-free rate such as Treasury Bill Nominal risk-free rate such as Treasury Bill Real risk-free rate (excludes inflation)Real risk-free rate (excludes inflation)Premiums impact the interest rates on Premiums impact the