Nominal Interest Rate

4 Key excerpts on "Nominal Interest Rate"

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  eBook - ePub

  Money and Banking

  An International Text

  • Robert Eyler(Author)
  • 2009(Publication Date)
  • Routledge

    (Publisher)

  Interest rates come in many forms, all with the same basic set-up. An interest rate includes measures of risk, both general and very specific. When you borrow money, the rate at which you borrow is the nominal rate. This rate is the stated interest cost or return of a financial investment. There is also a real rate, but what separates the two? The difference between nominal and real variables in economics has to do initially with inflation, or purchasing power erosion, and other risks. In its most basic form, a Nominal Interest Rate has the following equation:

  R = r + P

  (2.1)

  where R is a nominal rate, r is the associated real rate and P is the expected inflation rate. Equation 2.1 assumes the only risk to be inflation. The best way to think of the real rate of interest is what the lender wants to receive as revenue, less the calculated risks. The nominal rate is the sum of the real rate and the “expected” inflation rate, which is a calculated guess and not the actual inflation rate. When a lender provides a loan, the lender must make conjectures concerning what the risk of future inflation may be. Unless the interest rate is allowed to adjust with new inflation information, the lender bears that risk directly; when inflation rises without the nominal rate changing, the real value of her loan gets smaller. Both the borrower and lender make decisions based on their individual assessment of the real rate of interest. Even though the borrower writes a check every month to the credit card company based on a nominal rate, the lender is seeking protection of the real rate as the driving force behind providing credit. If all the expected risks play themselves out as predicted, the borrower and lender pay and receive the real rate respectively.

  We will discuss later the difference between fixed and variable rates of interest, but keep in mind that few assets, real or financial, can circumvent the risk of inflation. Inflation is also a representation of time in financial markets, specifically eroding nominal income and wealth.

  Defining interest rates

  The cost of borrowing

  This is the classic role we think of interest rates playing in finance, an explicit cost of consuming beyond one’s income or wealth by choice. As a corollary, it is also the opportunity cost of consuming, regardless of the entity being a net consumer or not. A net consumer is a household that both consumes and saves, but consumes more than its income in net. If one consumes anything, there is lost interest revenue from saving the resources otherwise; however, financial leverage may be a decision because the cost of debt is less than the return to savings. Households are willing to bear this cost, however, at some level because of necessity and because of satisfaction or utility otherwise, an issue discussed in more detail in Chapter 9

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  eBook - PDF

  Financial Institutions, Markets, and Money

  • David S. Kidwell, David W. Blackwell, David A. Whidbee, Richard W. Sias(Authors)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  The interest rate is the price of “renting” an amount of money over a given period of time. Interest rates are similar to other prices in the economy in that they allocate funds bet- ween SSUs and DSUs. 2 Define the concept of the real interest rate and explain what causes the real interest rate to rise and fall. The real rate of interest is the fundamental long‐run interest rate in the economy. It is the market equilibrium interest rate at which desired lending by savers equals desired borrowing by producers. It is the rate of interest that prevails under the assumption that there is no inflation in the economy. 3 Explain how inflation affects interest rates. To pro- tect borrowers and lenders from unwarranted transfers in purchasing power, the nominal (or stated) interest rate on a loan equals the real rate of interest plus compensation for changes in the purchasing power of money caused by price‐level changes. This relationship is shown in the Fisher equation, which states that the Nominal Interest Rate equals the real rate of interest plus the expected inflation rate. 4 Calculate the realized real rate of return on an investment. The return from a loan stated in terms of purchasing power of money is the realized real rate of return, which equals the Nominal Interest Rate minus the actual rate of inflation. The realized real rate of return can be positive, zero, or negative, depending on how differ- ent actual inflation is from expected inflation. 5 Explain how economists and financial decision makers forecast interest rates. Investors and financial institutions have a keen interest in forecasting the move- ments of interest rates because of the potential impact on their wealth. Interest rate forecasting models use expected economic activity and inflation expectations to predict interest rates.

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  Money, Enterprise and Income Distribution

  Towards a macroeconomic theory of capitalism

  • John Smithin(Author)
  • 2008(Publication Date)
  • Routledge

    (Publisher)

  In fact, he goes on to point out that in many cases the real rate in the above sense is actually more variable than the nominal rate. This is simply because the nominal rate is not always adjusted promptly when the inflation rate changes. It seems clear also, that in such a case it will be the variable real rate that will affect economic decision-making rather than the “sticky” nominal rate. It is implicit in these observations, however, that the real interest rate could be made more stable (for example, by central bank policy) if the nominal rate was so adjusted. These ideas do militate against the idea that there is any such thing as a “natural” real rate, but not against the notion of a real rate of interest as a definitional concept – simply the difference between nominal rates and expected inflation. The Chicago-trained economist Burstein has similarly distinguished between a natural rate theory of real interest rate determination, and the definition of the real (inflation-adjusted) interest rate. According to Burstein (1995, 1), in a phrase that neatly ties together the two alternative meanings of the term, there can be both a “real theory of the real rate of interest” and also a “monetary theory of the real rate of interest”. The former is an accurate description of the classical theory, whereas the latter is what Burstein would attribute to Keynes and others. 1 The term structure of interest rates The concept in theoretical finance of the “term structure of interest rates”, illustrated empirically by a graph of the “yield curve”, refers to the relationship between interest rates on debt instruments with different terms to maturity. The annualized yields on instruments with (say) less than one year to run, are generically referred to as short rates, and those with several years to run as long rates

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  Mathematical Interest Theory

  Third Edition

  • Leslie Jane Federer Vaaler, Shinko Kojima Harper, James W. Daniel(Authors)
  • 2019(Publication Date)
  • American Mathematical Society

    (Publisher)

  He would like to borrow money in order to completely pay for a $3,000 used piano. Ezra wishes to repay the loan with a payment in exactly five years. How much money must he ask to borrow at 8% discount? Section 1.10 Nominal rates of interest and discount 47 Solution Let $ K denote the amount Ezra requests to borrow for five years at 8% discount. Then the amount he receives is $ K (1 − . 08) 5 = $ K ( . 92) 5 . In order for this amount to be $3,000, it is necessary that K = 3 , 000( . 92) − 5 ≈ $4 , 551 . 79. Since $4 , 551 . 79( . 92) 5 ≈ $3 , 000 . 000686, if Ezra borrows $4,551.79 for five years at 8% discount, he receives exactly $3,000. 1.10 NOMINAL RATES OF INTEREST AND DISCOUNT Suppose that we have an investment governed by compound interest. This means that if i is the applicable effective interest rate for the investment, then the growth of the money is governed by the compound accumulation function a ( t ) = (1 + i ) t = 1 + [(1 + i ) t − 1]. Therefore, 1 invested for a period of length T earns (1 + i ) T − 1 interest. The quantity [(1 + i ) T − 1] may be thought of as the effective interest rate for a period of length T . In particular, the effective interest rate for a period of length T = 1 m is [(1 + i ) 1 m − 1]. Banks commonly credit interest more than once per year, say m times per year. They advertise a nominal (annual) interest rate of i ( m ) convertible or compounded or payable m times per year . 6 The word “nominal” means “in name only,” and this is indeed the case. The bank pays interest at a rate of i ( m ) m per m -th of a year. But we just observed that the rate for such an interval is [(1 + i ) 1 m − 1]. We therefore have the following important statement. IMPORTANT FACT 1.10.1 If an account is governed by a Nominal Interest Rate of i ( m ) payable m times per year, the bank pays interest at a rate of i ( m ) m = [(1 + i ) 1 m − 1] per m -th of a year.

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