Chapter 4 Interest Rates  Annual and Periodic Rates  Impact on TVM  Consumer Loans and Monthly Amortization Schedules  Nominal and Real Interest Rates  Risk-free Rate and Premiums  Default, Maturity, Liquidity  Brief History of Interest Rates

Annual and Periodic Rates  Annual Percentage Rate (APR)  The standard way to quote interest rate  Actual rate may be different  Period 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 for the year

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 = %  Effective Annual Rates  Semi-Annual Rate of 2.5%, EAR = %  Monthly Rate of %, EAR = %

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 = %

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

Impact on TVM  Increasing the number of compounding periods changes results (changes effective interest rate)  Example 4.1 – Annual compounding versus Monthly compounding  $2,000,000 retirement goal at 6% APR  40 years to retirement  Deposit today with annual compounding, $194,  Deposit today with monthly compounding, $182,  EAR difference, Annual is 6%, Monthly is %

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 if for principal reduction  Use TVM equations with monthly interest rate and number of periods to find payment (equation 4.5)  PV is the amount of the loan

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

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 4.3 – 21 books next year versus 20 books now  Real Rate = 21/20 – 1 = 5%  Expected Inflation is the rising price of a good

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

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  Liquidity

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  Liquidity Premium – Different investments can be converted back to cash at different speeds and ease

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), maturity (mp), and liquidity (lp)  r ≈ r f * + inflation + dp + mp + lp

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%

Problems  Problem 3 – Effective Annual Rate  Problem 5 – PV with Periodic Rates  Problem 7 – FV with Periodic Rates  Problem 9 – Payments with Periodic Rates  Problem 11– Amortization Schedule