Chapter 4 Interest Rates

1
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

2
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

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
• 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 eAPR -1
• EAR e0.05 -1 5.12711

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)
• 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,
  194,444.38
• Deposit today with monthly compounding,
  182,524.16
• EAR difference, Annual is 6, Monthly is 6.1678

7
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

8
Consumer Loans and Monthly Amortization Schedule

• Monthly amortization schedule for car loan of
  25,000 for 72 months at 8 APR (Table 4.3)

9
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

10
Nominal and Real Interest Rates

• Fisher Effect
• Relationship between real rate, expected
  inflation, and nominal rate
• (1r) (1r) x (1h)
• 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

11
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

12
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

13
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 rf inflation dp mp lp

14
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

15
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