Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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. • 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. 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) 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) m APR EAR 1 1 m where m is the compounding frequency (or C/Y) – For continuously compounded interest, EAR e APR 1 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. 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 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 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 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 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. 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 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.