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Interest Rates (Ch. 4)

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Title: Time Value of Money (contd.) Author: Prem Mathew Last modified by: mathewp Created Date: 10/9/2004 5:10:50 PM Document presentation format – PowerPoint PPT presentation

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Title: Interest Rates (Ch. 4)


1
Interest Rates (Ch. 4)
  • 04/17/06

2
Compounding interest
  • Thus far, we have assumed that interest is
    compounded (or paid/earned) once during the
    period.
  • However, often interest is compounded more
    frequently than once a period.
  • This means that interest is earned (but not
    necessarily paid) more than once during the
    period.
  • We examine here what the effect of the frequency
    of compounding has on interest rates.

3
Quoting conventions
  • Annual Percentage Rate (APR)
  • a.k.a. nominal, stated or quoted rate
  • Rate required to be disclosed in lending
    agreements (Truth-in-lending laws)
  • Does not reflect the actual interest earned/paid
  • APR periodic interest rate compounding
    periods per year (C/Y)

4
Quoting conventions
  • Effective Annual Rate (EAR)
  • The annual rate of interest actually paid or
    earned.
  • Incorporates the effect of compounding
  • The EAR is equal to the annual percentage yield
    (APY) which is the rate required to be disclosed
    in savings products (Truth-in-savings laws)
  • where m is the compounding frequency (or C/Y)
  • For continuously compounded interest,

5
Employing compounded interest in PV/FV
calculations (rules to follow)
  • For lending (savings) products, assume that the
    interest rate stated is the APR (APY) unless
    otherwise specified.
  • Ensure that the frequency of cash flows and
    interest rate used is consistent.
  • If APR is compounded and the compounding
    frequency (C/Y) is the same as the cash flow
    frequency, use APR/ (C/Y) for the interest rate.

6
Employing compounded interest in PV/FV
calculations (rules to follow)
  • Ensure that the frequency of cash flows and
    interest rate used is consistent. (contd.)
  • If cash flows are annual, use EAR regardless of
    the compounding frequency
  • For simple (single cash flow) PV/FV problems, use
    EAR
  • If you are provided with an interest rate over
    the same period as the cash flow period, no
    adjustments need to be made

7
Nominal and Real Interest Rates
  • APR and Periodic Rates are nominal rates
  • Nominal Rates have two components
  • Real Rate
  • Expected Inflation Rate
  • Real Rate is the reward for saving
  • Expected Inflation is the rising price of a good

8
Nominal and Real Interest Rates
  • Fisher Effect
  • Relationship between real rate, expected
    inflation, and nominal rate
  • (1r) (1r) x (1h)
  • where r is the nominal rate, r is the real rate,
    and h is expected inflation
  • We can get an approximate value for r r r
    h

9
Risk-free Rate and Premiums
  • Nominal interest rates (of return) associated
    with a particular investment or asset are based
    on four components.
  • Risk-free rate
  • Default Risk
  • Maturity
  • Liquidity

10
Risk-free Rate and Premiums
  • Risk-free rate (rf)
  • a guaranteed rate available to investors
  • 3-month U.S. Treasury Bill rate
  • Default Risk
  • Different Investments have different default risk
    based on the issuers ability to meet future
    promised payments
  • Credit ratings (by Standard and Poors, etc.)
    evaluate the default risk of public companies.

11
Risk-free Rate and Premiums
  • Maturity Premium
  • Investors demand more compensation for investing
    in longer-maturity investments
  • The term structure of interest rates and yield
    curve reflects the difference in rates as the
    borrowing time increases and provides an estimate
    of the maturity premium
  • Liquidity Premium Different investments can be
    converted back to cash at different speeds and
    ease

12
Risk-free Rate and Premiums
  • Summary of Interest Rates
  • The nominal interest rate can be summarized as
    follows
  • r rf h dp mp lp
  • where dp, mp and lp represent the premiums
    required by investors for default risk, maturity
    and liquidity of the investment.
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