Contents
Time Value of Money
Annuities
Perpetuities
Kinds of Interest Rates
Future Value of an Uneven Cash flow
Probability Distribution
Standard Deviation
CAPM
Security Market Line
Bond Valuation
Stock Valuation
Cost of Capital
The Balance Sheet
Financial Terms
Scientific Terms
Disclaimer Kinds of Interest Rates

Let's say I give you a credit card and the interest rate on the card is 3% per month. What is the annual rate that you are actually charged?? 36%?? Well, no. It's actually 42.57%.

 Nominal Rate Nominal means "in name only". This is sometimes called the quoted rate. Periodic Rate The amount of interest you are charged each period, like every month. Effective Annual Rate The rate that you actually get charged on an annual basis. Remember you are paying interest on interest.

In the example
• The Nominal Rate is 36%.
• The Periodic Rate is 3% (you are charged 3% interest on your balance every month)
• The Effective Annual Rate is 42.57%
 Nominal Rate = Periodic Rate X Number of Compounding Periods
 Effective Annual Rate = (1+ i / m)m -1
• m = the number of compounding periods
• i = the nominal interest rate

O.K., so let's try the example again.

• Effective Annual Rate = (1+ i / m)m -1
• Effective Annual Rate = ( 1 + .36 / 12 )12 -1
• Effective Annual Rate = (1.03)12 - 1
• Effective Annual Rate = (1.4257) -1
• Effective Annual Rate = .4257
• Effective Annual Rate = 42.57 %

Detailed Explanation

The Nominal Rate - The nominal rate is one of the most basic concepts in finance and is a key component in understanding the cost of borrowing and the return on investment. It is the stated interest rate on a loan or investment, and represents the annual percentage rate (APR) that the lender or investor charges for the use of their money.

The nominal rate is also sometimes referred to as the “quoted” rate or “stated” rate. This rate does not take into account any compounding, which is the process of earning interest on both the initial principal and any accumulated interest. The nominal rate only reflects the simple interest rate, which is calculated on the principal amount only. As such, it is not always an accurate representation of the true cost of borrowing or the return on investment.

One example of the use of nominal rates is in the calculation of the interest expense on a loan. For example, if a borrower takes out a \$10,000 loan with a 10% nominal rate for one year, the total interest expense would be \$1,000 (\$10,000 x 10%). However, this calculation assumes that the interest is only charged once at the end of the year, and that there is no compounding of interest during the year.

It is important to note that the nominal rate can be expressed in different time periods, such as monthly, quarterly, or semi-annually. The periodic rate is the interest rate charged per compounding period, and is calculated by dividing the nominal rate by the number of compounding periods in a year. For example, if the nominal rate is 12% per year and interest is compounded monthly, the periodic rate would be 1% per month (12% divided by 12 months).

The Periodic Rate - The periodic rate refers to the interest rate applied to a loan or investment over a specific period of time, such as a month, quarter, or year. Understanding the periodic rate is essential for calculating the total interest paid or earned over the life of a loan or investment.

One common use of the periodic rate is in the calculation of the annual percentage rate (APR) on a loan. The APR is the annualized interest rate charged on a loan, including any fees or other costs associated with borrowing. To calculate the APR, the periodic rate is first determined by dividing the annual interest rate by the number of periods in a year. For example, if the annual interest rate on a loan is 10%, and the loan is paid monthly, the periodic rate would be 10% / 12 = 0.833%.

Another use of the periodic rate is in the calculation of interest earned on an investment. For example, if an investment earns 5% interest per year, the periodic rate would be 5% / 12 = 0.417% per month. By multiplying the periodic rate by the principal investment, the amount of interest earned in a specific period of time can be calculated.

It's important to note that the periodic rate may not always be constant over the life of a loan or investment. In some cases, the rate may be variable and change periodically based on market conditions or other factors. When this occurs, it is important to recalculate the interest or payment schedule to ensure accuracy.

The Effective Annual Rate - The Effective Annual Rate (EAR) is an important concept in finance that allows investors to compare the interest rates of different investments with different compounding periods. The EAR is the actual rate of return that an investor receives after taking into account the effect of compounding over the course of a year. It is also referred to as the annual percentage yield (APY) or the annual equivalent rate (AER).

The EAR takes into account the compounding of interest, which is the process of earning interest on both the principal amount and the interest that has already been earned. The more frequently interest is compounded, the higher the effective rate of interest will be. For example, an investment with a nominal interest rate of 5% per year compounded quarterly will have a higher EAR than an investment with a nominal interest rate of 5% per year compounded annually.

Calculating the EAR is important because it allows investors to compare the true returns of different investments. If an investor is considering two investments with different compounding periods and nominal interest rates, they cannot simply compare the nominal interest rates to determine which investment will provide the higher return. Instead, they must calculate the EAR of each investment to compare the true returns.

Understanding the concept of EAR is important not only for comparing the returns of different investments, but also for understanding the impact of fees and expenses on investment returns. Fees and expenses can significantly reduce the effective rate of return on an investment, and investors must take these costs into account when making investment decisions.

In addition to comparing the returns of different investments and understanding the impact of fees and expenses, the concept of EAR can also be useful in financial planning. By understanding the true rate of return on investments, investors can better plan for their financial goals and make more informed investment decisions.

Bibliography

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Gitman, L. J., & Joehnk, M. D. (2019). Fundamentals of investing. Pearson.

Hillier, D., Ross, S. A., Ross, W. T., Jaffe, J., & Jordan, B. D. (2017). The theory and practice of corporate finance: evidence from the field. Cengage Learning.

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Mishkin, F. S. (2016). The economics of money, banking, and financial markets. Pearson.

Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2016). Essentials of Corporate Finance. McGraw-Hill Education.

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Van Horne, J. C., & Wachowicz, J. M. (2014). Fundamentals of financial management. Pearson. Author: Mark McCracken is a corporate trainer and author living in Higashi Osaka, Japan. He is the author of thousands of online articles as well as the Business English textbook, "25 Business Skills in English".