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Interest Rates (Ch. 4)

Interest Rates (Ch. 4). 04/17/06. 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.

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Interest Rates (Ch. 4)

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  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 (1+r) = (1+r*) x (1+h) 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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