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**THE LEVEL OF INTEREST RATES**

CHAPTER 4 THE LEVEL OF INTEREST RATES

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**Copyright© 2006 John Wiley & Sons, Inc.**

Learning Objectives Define the concept of an interest rate and explain the role of interest rates in the economy. Define the concept of real interest rates and explain what causes the real interest rate to change. Explain how inflation affects interest rates. Calculate the realized real rate of return. Copyright© 2006 John Wiley & Sons, Inc.

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**What are Interest Rates?**

The cost of borrowing money for the use of its purchasing power (rental price for money). To a borrower, it is penalty for consuming before earning. To a lender, it is reward for postponing consumption. Expressed in terms of annual rates. As with any price, interest rates serve to allocate resources allocative function. SSU wants to buy financial claims with the highest returns ,whereas DSUs want to sell financial claims at the lowest possible interest rates.

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**The Real Rate of Interest**

The main determinants of interest rate are: Production opportunities. Time preferences for consumption. Copyright© 2006 John Wiley & Sons, Inc.

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**The Real Rate of Interest**

Production opportunities: Producers (investors in capital projects) seek financing for real assets. Expected ROI is upper limit on interest rate producers can pay for financing. Time preferences for consumption: Most people prefer to consume today rather than tomorrow (positive time preference for consumption). Savers require compensation for deferring consumption. Time value of consumption is lower limit on interest rate at which savers will provide financing. Real interest rate occurs at equilibrium between desired real investment (demand for funds) and desired saving (supply of funds). Copyright© 2006 John Wiley & Sons, Inc.

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**The Real Rate of Interest**

The determination of market interest rates occurs in demand and supply framework. The supply side is saving curve. At low rates, most people postpone very little consumption for the sake of saving(i.e. they save less) and at high rates, consumers tend to save more. Hence, the supply curve is upward sloped. Copyright© 2006 John Wiley & Sons, Inc.

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**The Real Rate of Interest**

The demand is the Investment curve. At high rates, fewer businesses can earn an expected return high enough to cover this high interest costs. Therefore, they borrow less. On the other hand, at low rates, they tend to borrow more. Hence, the demand curve is downward sloped. The equilibrium rate of interest is called the real rate of interest(r*). Copyright© 2006 John Wiley & Sons, Inc.

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**Determinants of the Real Rate of Interest**

Copyright© 2006 John Wiley & Sons, Inc.

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**Economic Forces change interest rates**

Factors that shift the investment curve either to the right or to the left: Productivity Technology taxes, expected risk expected sales Factor that shift the saving curve either to the right or to the left: Consumer attitude (propensity to save) personal Income, personal income tax Copyright© 2006 John Wiley & Sons, Inc.

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**Copyright© 2006 John Wiley & Sons, Inc.**

Loanable Funds Theory It is difficult to use the desired savings and investment framework to explain short-run changes in the interest rate. Therefore, in the short run, interest rate depends on the supply of and the demand for loanable funds. Supply of loanable funds— All sources of funds available to invest in (purchase) financial claims Demand for loanable funds— All uses of funds raised from issuing financial claims Copyright© 2006 John Wiley & Sons, Inc.

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**Supply of loanable funds**

All sources of funds available to invest in financial claims: Consumer savings Business savings Government budget surpluses Central Bank Action Copyright© 2006 John Wiley & Sons, Inc.

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**Demand for Loanable Funds**

All uses of funds raised from issuing financial claims: Consumer credit purchases Business investment Government budget deficits Copyright© 2006 John Wiley & Sons, Inc.

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**Copyright© 2006 John Wiley & Sons, Inc.**

Loanable Funds Theory Copyright© 2006 John Wiley & Sons, Inc.

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**Equilibrium Interest Rate**

Equilibrium interest rate occurs when supply of loanable funds = demand for loanable funds Equilibrium is temporary or dynamic: Any force that shifts supply or demand will tend to change interest rates. Copyright© 2006 John Wiley & Sons, Inc.

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**Copyright© 2006 John Wiley & Sons, Inc.**

Loanable Funds Theory Factors effect on Supply of Loanable Funds 1. Change in GOV. Budget (from Deficit to Surplus Position) 2. Change in Consumer Saving 3. Change in Business Savings Copyright© 2006 John Wiley & Sons, Inc.

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**Copyright© 2006 John Wiley & Sons, Inc.**

Loanable Funds Theory Factors effect on Demand for Loanable Funds 1. Change in Business investment 2. Change in GOV. Budget (from surplus to deficit position) 3. Change in consumer credit purchases Copyright© 2006 John Wiley & Sons, Inc.

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**Price Expectations and Interest Rates**

Unanticipated inflation benefits borrowers at expense of lenders during the life of a loan contract, because the borrower pay the lender money with less purchasing power. Therefore, lenders charge additional interest to offset anticipated decreases in purchasing power. Expected inflation is embodied in nominal interest rates: The Fisher Effect. The Fisher Effect Theory states that the nominal interest rate includes real interest rate (interest rate without inflation) and expected annual inflation rate. Copyright© 2006 John Wiley & Sons, Inc.

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**Copyright© 2006 John Wiley & Sons, Inc.**

Fisher Effect The exact Fisher equation is: Copyright© 2006 John Wiley & Sons, Inc.

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**Copyright© 2006 John Wiley & Sons, Inc.**

Fisher Effect, cont. From the Fisher equation, we derive the nominal (contract) rate: We see that a lender gets compensated for: rental of purchasing power anticipated loss of purchasing power on the principal anticipated loss of purchasing power on the interest Copyright© 2006 John Wiley & Sons, Inc.

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**Fisher Effect: Example**

1-year $1000 loan Parties agree on 3% rental rate for money and 5% expected rate of inflation. Items to pay Calculation Amount Principal $1,000.00 Rent on money $1,000 x 3% PP loss on principal $1,000 x 5% PP loss on interest $1,000 x 3% x 5% Total Compensation $1,081.50 Copyright© 2006 John Wiley & Sons, Inc.

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**Simplified Fisher Equation**

The third term in the Fisher equation is negligible, so it is commonly dropped. The resulting equation is Copyright© 2006 John Wiley & Sons, Inc.

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**Copyright© 2006 John Wiley & Sons, Inc.**

Fisher Equation Example 1: If real interest rate is 5%, actual inflation last year was 7%, and expected inflation for the coming year is 9%. What is the current level of nominal interest rate? Example 2: What is the total compensation required by an investor for lending a U.S. Treasury $1000 for 1 year if the real rate of interest is 4%, actual inflation last year was 6%, and expected inflation for the coming year is 7%? Copyright© 2006 John Wiley & Sons, Inc.

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**Copyright© 2006 John Wiley & Sons, Inc.**

The Realized Real Rate The Fisher equation is based on expected inflation rate. The actual rate of inflation may be different from the anticipated rate. This may lead to the realized rate of return on a loan to be different from the nominal interest rate agreed on at the time of the loan contract. The realized (actual) real rate is calculated as : r = i - ΔPa, Where; r = is the realized real rate of return, i = the nominal interest rate, and ΔPa = is the actual rate of inflation Copyright© 2006 John Wiley & Sons, Inc.

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**The Realized Real Rate-continued**

If the actual inflation turns out to be higher than the expected inflation, then the lender will have a lower realized real rate of return i.e. there was an unintended transfer of purchasing power to borrower from lender. If the actual inflation turns out to be less than the expected inflation, then the lender will have a higher realized real rate of return i.e. there was an unintended transfer of purchasing power to lender from borrower. Copyright© 2006 John Wiley & Sons, Inc.

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**The Realized Real Rate-continued**

The realized real rate may be Positive, Zero or Negative. If nominal interest rate (i) > actual inflation, then realized real rate is positive If nominal interest rate (i) = actual inflation then realized real rate is zero if nominal interest rate (i) ˂ actual inflation then realized real rate is negative Copyright© 2006 John Wiley & Sons, Inc.

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**The Realized Real Rate-continued**

Example: An investor buys a 1 –year Treasury security with a promised yield of 10%. The investor expected the annual rate of inflation to be 6%; however, the actual rate turned out to be 10%. What were the expected and the realized real rates of return for the investor? The expected real rate = The realized real rate = Copyright© 2006 John Wiley & Sons, Inc.

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**Interest Rate Movements and Inflation**

Historically, interest rates tend to change with changes in the rate of inflation, substantiating the Fisher equation. Short-term rates are more responsive to changes in inflation than long-term rates. Copyright© 2006 John Wiley & Sons, Inc.

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