Nominal and Effective Interest Rates

The interest period can be a day, week, month, year, etc. However, it is commonly defined in fractions of a year, for example, 1 yr, yr. 1/m yr, where m is the number of periods p year. When the interest period is not 1 yr, it is common to use the concepts of nominal interest rate and effective interest rate for compound interest, both based on 1 yr. The use of these two concepts permits the calculations to be carried out on an annual basis. 

Given the value of m, the number of times per year to calculate interest at i, the interest rate per period of 1/m yr (m times per year), the nominal interest rate per year, r, is 

If the interest rate is 3%/quarter, then with four quarters per year, the nominal interest rate, r, is 0.03(4) = 0.12 or 12%/yr. In the case of simple interest (no compounding), 1,000 at the beginning of a year would yield 1,000(1.12) = 1,200. But, more commonly, nominal interest rates are stated on an annual basis with a compounding period, for example, 12% compounded quarterly. 

To handle compound interest when the interest period is some fraction of a year, (1/m), an effective interest rate per year, 4ff, is defined by 

Based on i, the actual interest rate per 1/m yr, we can also write 

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It is desirable to express the exact interest rate based on the original principal and the convenient time unit of 1 year. A rate of this type is known as the effective interest rate. In common engineering practice, it is usually preferable to deal with effective interest rates rather than with nominal interest rates. The only time that nominal and effective interest rates are equal is when the interest is compounded annually. 

An interest rate is reported as 3% compounded quarterly. Determine the nominal and effective interest rates per year. 

Most of you have credit cards, so you already know that if you do not p the balance on time, the credit card issuer will charge you a certain interest rate each month. Assuming that you are charged 1.25% interest each month on your unpaid balance, what are the nominal and effective interest rates Also, determine the effective interest rate that your own credit card issuer charges you. 

A comparison of Eqs. (9-32) and (9-39) shows that the nominal interest rate i on a continuous basis is related to the effective interest rate i on an annual basis by... 

Nominal interest rates should always include a qualifying statement indicating the compounding period. For example, using the common annual basis, 100 invested at a nominal interest rate of 20 percent compounded annually would amount to 120.00 after 1 year if compounded semiannually, the amount would be 121.00 and, if compounded continuously, the amount would be 122.14. The corresponding effective interest rates are 20.00 percent, 21.00 percent, and 22.14 percent, respectively. 

By equating Eqs. (6) and (7), the following equation can be obtained for the effective interest rate in terms of the nominal interest rate and the number of periods per year ... 

Define the market interest rate i as the rate of interest that can be expected to be earned on investments in the marketplace. It is a function of the investments available on the market and their associated risks. Additionally, this rate includes the effect of inflation such that if there is an upward movement in prices (inflation), there is an upward movement in the market interest rate. Other terms that may be commonly used to refer to the market rate include the minimum attractive rate of return (MARR), nominal MARR, actual interest rate, effective rate, and inflated interest rate. 

Let us suppose that 100 is invested at a nominal interest rate of 5 percent. We then compute the future worth of the investment after 2 years and also compute the effective annual interest rate for the following lands of interest (I) simple, (2) annual compound, (3) monthly compound, (4) daily compound, and (5) continuous compound. The following tabulation shows the results of the calculations, along with the appropriate equation to be used ... 

Equation (9-113) shows that Eq. (9-114) is only approximately true and should be used, if at all, solely for low interest rates. Let us consider the case of a nominal (DCFRR) of 5 percent and an inflation rate of 3 percent. Equation (9-14) yields an approximate effective return rate of 2 percent, compared with the real effective rate of 1.94 percent given by Eq. (9-113) i.e., there is an error of 3.1 percent. Now let us consider the case of a nominal (DCFRR) of 2.5 percent and an inflation rate of 23 percent. Equation (9-114) yields an approximate effective return rate of 2 percent, compared with 1.63 percent from Eq. (9-113) in this case, the error that results is 22.7 percent. 

The EURIBOR futures contract provides the buyer with the theoretical commitment to place 1 million on deposit at a fixed interest rate for a nominal 90-day period starting on the futures expiry date, the third Wednesday of the delivery month. The fixed interest rate is not quoted directly, but is defined as 100 minus the quoted futures price. So if an investor buys a future at a price of 97, he or she is theoretically committed to deposit 1 million at 3% for 90 days. We have twice used the word theoretically because, in practice, these futures contracts are always cash settled, which means that buyers and sellers effectively pay or receive the difference between ... 

If you deposit 100.00 in a savings account, at 6% compounding monthly, then, using Equation (20.3), at the end of one year you -will have 106.16 in your account. The 6.16 earned during the first year is higher than the stated 6% interest, which could be understood as 6.00 for a 100.00 deposit over a period of one year. In order to avoid confusion, the stated or the quoted interest rate is called the nominal interest rate, and the actual earned interest rate is called the (ffietive interest rate. The relationship between the nominal rate, i, and the effective rate, is given by... 

The concept of the time value of money is discussed. The following topics are presented sinple and conpound interest, effective and nominal interest rates, annuities, cash flow diagrams, and discount factors. In addition, the concepts of depreciation, inflation, and taxation are covered. 

In comparing alternatives, the effective annual rate, and not the nominal annual rate of interest, must be used. 

What is the difference between the nominal annual interest rate and the effective annual interest rate When are these two rates equal ... 

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