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Chapter 4 – Interest Rates  Learning Objectives  Quoting Interest Rates (APR)  Effective Annual Rate (EAR)  TVM formulas with periodic interest rates.

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Presentation on theme: "Chapter 4 – Interest Rates  Learning Objectives  Quoting Interest Rates (APR)  Effective Annual Rate (EAR)  TVM formulas with periodic interest rates."— Presentation transcript:

1 Chapter 4 – Interest Rates  Learning Objectives  Quoting Interest Rates (APR)  Effective Annual Rate (EAR)  TVM formulas with periodic interest rates  Monthly Amortization vs. Annual  Nominal and Real Interest Rates  Risk-free Rate and Premiums  Default and Maturity Premiums  Brief History of Interest Rates

2 Annual and Periodic Rates  Annual Percentage Rate (APR)  The standard way to quote interest rate  Actual rate may be different  Period or Periodic Interest Rate  The rate for the period  Quarterly, Monthly, Daily, etc.  Annual Percentage Rate divided by Compounding periods per year  Effective Annual Rate (EAR) is the periodic rate compounded over a year

3 Annual and Periodic Rates  Periodic Rates with 5.0% APR  Semi-Annual Rate (compounds twice a year)  5.0% / 2 = 2.5%  Monthly Rate (compounds twelve times a year)  5.0% / 12 = 0.04167%  Effective Annual Rates  EAR = (1 + [APR / (C/Y)]) C/Y – 1, equation 4.2  Semi-Annual Rate of 2.5%, EAR = 5.0625%  Monthly Rate of 0.04167%, EAR = 5.1162%

4 Annual and Periodic Rates  Effective Annual Rate is the rate that you earn with your investment and it increases with the number of compounding periods per year (C/Y)  Maximum compounding is continuous compounding and  EAR = e APR -1  EAR = e 0.05 -1= 5.12711%  e is the exponential function

5 Impact on TVM  The r in the TVM equations is the periodic rate  It is the APR when compounding is annually  The n in the TVM equation matches r and is the number of periods (compounding periods per year times number of years)  Changing calculator mode for P/Y and C/Y

6 Impact on TVM  Increasing the number of compounding periods changes results (changes effective interest rate)  Basic Mortgage Payment (Interest and Principal as you go on ordinary annuity)  Example 4.1 page 80  Loan Amount $190,000 (PV)  Interest quoted at 8% APR  Payments are monthly (ordinary annuity) for 30 years or 360 monthly payments  Monthly Payment for P & I is $1,394.15

7 Impact on TVM  Example 4.2 – Annual compounding versus Monthly compounding  $1,000,000 retirement goal at 9% APR  30 years to retirement  Annual Payment with annual compounding, $7,336.35  Monthly Payment with monthly compounding, $546.23 ($546.23 x 12 = $6,554.76)  EAR difference, Annual is 9%, Monthly is 9.381%

8 Consumer Loans and Monthly Amortization Schedule  Most Consumer Loans are annuity stream fixed payments with interest accruing at end of month  Payment is for monthly interest expense and remainder is for principal reduction  Use TVM equation with monthly interest rate as r, number of payments or periods as n, and the amount of the loan as PV to find the monthly payment required.

9 Consumer Loans and Monthly Amortization Schedule  Monthly amortization schedule for car loan of $25,000 for 72 months at 8% APR (Table 4.3)

10 Nominal and Real Interest Rates  APR and Periodic Rates are nominal rates  Nominal Rates have two components  Real Rate  Expected Inflation Rate  Nominal ≈ Real Rate + Expected Inflation  Real Rate is reward for saving  Example 4.5 – 21 books next year versus 20 books now  Real Rate = 21/20 – 1 = 5%  Expected Inflation is the rising price of a good

11 Nominal and Real Interest Rates  Fisher Effect  Relationship between real rate, expected inflation, and nominal rate  (1+r) = (1+r * ) x (1+h)  r is the nominal rate  r * is the real rate  h is expected inflation  r = r * + h + (r * x h)  r * is the same the world round

12 Risk-free Rate and Premiums  Risk-free rate (a nominal or real rate) with a guaranteed return  Nominal risk-free rate such as Treasury Bill  Real risk-free rate (excludes inflation)  Premiums impact the interest rates on different types of investments  Default Risk  Maturity

13 Risk-free Rate and Premiums  Default Risk  Different Investments have different default risk based on the issuers ability to meet future promised payments  Low risk – U.S. Government  High risk – New Start-up Company  Maturity Premium – Investors demand more compensation for waiting longer

14 Risk-free Rate and Premiums  Summary of Interest Rates  TVM equation uses a period nominal interest rate  The nominal interest rate is made up of two components, the real rate and inflation  Different investments have different nominal rates due to potential default (dp), and maturity (mp)  r ≈ r f * + inflation + dp + mp

15 Brief History of Interest Rates  Four Different Investments over 50 Years  3-Month Treasury Bill (risk-free rate)  Range 1% to 15%  Inflation in United States  Range -0.5% to 13%  Long-Term Treasury Bonds  Range -9% to 32%  Large U.S. Company Stocks  Range -27% to 52%

16 Homework  Problem 3 – Effective Annual Rate  Problem 6 – PV with Periodic Rates  Problem 12– Amortization Schedule  Problem 18 – Nominal Rate


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