Banking basics: Nominal and effective interest rates and their application

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The distinction between nominal and effective interest rates is not just academic knowledge; it has useful applications for the average Joe. Perhaps the greatest benefit of understanding the distinction is being able to work out your interest returns on savings. The knowledge can also come in handy for those who wish to do financial calculations for their personal benefit (For example, goal-based investing or retirement planning).

Nominal rate: The rate of interest for a specific compounding period.

Effective rate: The interest rate per annum (also known as the effective annual yield or annualized interest rate).

Financial institutions may apply interest at different periods. The basic modes are: daily, monthly, quarterly, semi-annually and annually. The nominal rate will change depending on the compounding period used. This is because, by definition, the nominal rate corresponds to the period. Technically, it can be calculated for compounding periods that exceed one year, but this is not common practice.

For example, assume that the annualized interest rate is 8%. The following are the nominal interest rates for certain compounding periods:

Daily: 7.6969%

Monthly: 7.7208%

Quarterly: 7.7706%

Semi-annually: 7.8461%

Annually: 8%

Biennially: 8.32%

This can help persons to accurately calculate how much interest would be credited to their savings depending on the compounding period and annualized yield. For instance, suppose you have $100,000 in savings at 8% per annum. However, interest is applied quarterly and the person is wishes to withdraw the interest each quarter.

Mathematics for Finance: An Introduction to Financial Engineering (Springer Undergraduate Mathematics Series)
Mathematics for Finance: An Introduction to Financial Engineering (Springer Undergraduate Mathematics Series)

As with the first edition, Mathematics for Finance: An Introduction to Financial Engineering combines financial motivation with mathematical style. Assuming only basic knowledge of probability and calculus, it presents three major areas of mathematical finance.

 

The compounding period would be quarterly, which equals 7.7706% per quarter. Therefore $1,942.65 should be the interest available for withdrawal every quarter. At the end of the year, the individual would have withdrawn $7,770.60. If they waited to withdraw the amount at the end of the year, they’d have received $8,000; a difference of $229.40.

It is possible to do these conversions using a table or a financial calculator. The financial calculator is more robust and efficient when used properly. It has a conversion workbook embedded and a Future Value (FV) schedule that you can program by setting the compounding period and entering the corresponding interest rate in the FV schedule. For example, if your compounding period is set to 12 on the calculator, any interest rate entered in the FV schedule would be considered effective. If you intend to input the nominal rate for the period, it is necessary to re-program the compounding periods as well.

The concepts of nominal and effective rates are critical and interrelated components of the compound interest concept. Understanding them would help you to avoid inaccuracies in financial calculations, especially where larger figures are involved and material errors would be more significant.

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