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UT Knoxville FINC 300 - Interest Rates

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FINC 300 1st Edition Lecture 8Outline of Last Lecture I. AnnuityA. Stream of equal cash flowsII. PerpetuityA. Equal intervals that last foreverB. Present Value of PerpetuityIII. Growing Perpetuitya. Growth at a constant rateb. Present ValueOutline of Current Lecture I. Nominal Rates Vs. Effective RatesII. Periodic RateIII. Effective Annual RateIV. Interest RatesV. InflationVI. Yield CurvesCurrent LectureCh. 5: Interest RatesNominal Rates (APR) versus Effective Rates (EAR)So far:We have often used Annual Percentage Rates (APR or nominal rates) when solving problems:�=�����������= ���=������������∗��������������������������Periodic Rate = ���/�where m is the number of compounding periodsAPRs (nominal rates) do NOT include the effect of compounding.These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.So far, we have let our calculators compute the compound interest for us. We will continue to do this but what if we want to know the interest rate that includes the effects of compounding?The Effective Annual Rate (EAR) includes the effects of compounding and the total interest earned.EAR = APY (Annual Percentage Yield) = EFFTherefore, the EAR is often greater than the APR.���≥ R�����=〖(1+���/�)〗^�−1where m is the number of compounding periodsNote: This is an annual rate! This is not to be confused with the periodic rate we use when solving problems with monthly payments.Real Interest RatesThus far, we have ignored the effect of inflation. When we ignore inflation, interest rates don’t represent the true increase in purchasing power.The real interest rate is the rate of growth of purchasing power after adjusting for inflation.The real rate is approximately equivalent to:nominal rate – rate of inflationMore precisely:��������= (����������� −���������������)/((1 + ���������������))Note: If the nominal rate is not greater than the rate of inflation, purchasing power doesn’t increase.InflationRisks associated with:- Default- Liquidity- Taxes- Maturity (length of time)Yield CurvesThe yield curve is a plot of Treasury bond yields (considered to be risk-free) as a function of maturity terms:- Yield curves are normally upward sloping. - Long term rates are normally higher in order to attract investors when rates are expected to rise and to compensate them for being “locked-in” for a longer period of time. - Because interest rates tend to drop in response to a slowdown in the economy, an inverted curve is often interpreted as a negative forecast for economic

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