Nominal and Effective Interest Rate Statements

In Chapter 1, we learned that the primary difference between simple interest and compound interest is that compound interest includes interest on the interest earned in the previous period, while simple interest does not. Here we discuss nominal and effective interest rates, which have the same basic relationship. The difference here is that the concepts of nominal and effective are used when interest is compounded more than once each year. For example, if an interest rate is expressed as 1% per month, the terms nominal and effective interest rates must be considered. Every nominal interest rate must be converted into an effective rate before it can be used in formulas, factor tables, calculator, or spreadsheet functions because they are all derived using effective rates.

The term APR (Annual Percentage Rate) is often stated as the annual interest rate for credit cards, loans, and house mortgages. This is the same as the nominal rate. An APR of 15% is the same as nominal 15% per year or a nominal 1.25% per month.

Also, the term APY (Annual Percentage Yield) is a commonly stated annual rate of return for investments, certificates of deposit, and savings accounts. This is the same as an effective rate. As we will discover, the nominal rate never exceeds the effective rate, and similarly                 APR < APY.

Before discussing the conversion from nominal to effective rates, it is important to identify a stated rate as either nominal or effective. There are three general ways of expressing interest rates as shown by the three groups of statements in Table (3-1). The three statements in the top third of the table show that an interest rate can be stated over some designated time period without specifying the compounding period. Such interest rates are assumed to be effective rates with the compounding period (CP) the same as that of the stated interest rate.

For the interest statements presented in the middle of Table (3-1), three conditions prevail: (1) The compounding period is identified, (2) this compounding period is shorter than the time period over which the interest is stated, and (3) the interest rate is designated neither as nominal nor as effective. In such cases, the interest rate is assumed to be nominal and the compounding period is equal to that which is stated. (We learn how to get effective interest rates from these in the next section).

For the third group of interest-rate statements in Table (3-1), the word effective precedes or follows the specified interest rate, and the compounding period is also given. These interest rates are obviously effective rates over the respective time periods stated.

The importance of being able to recognize whether a given interest rate is nominal or effective cannot be overstated with respect to the reader’s understanding of the remainder of the material in this chapter and indeed the rest of the book. Table (3-2) contains a listing of several interest statements (column 1) along with their interpretations (columns 2 and 3).

Table (3-1): Various Interest Statements and Their Interpretations

Table (3-2): Specific Examples of Interest Statements and Interpretations