Aggregate interest rates take into account the impact of compounding. They are higher than the nominal or stated interest rate for this reason.

## The Basics

The interest rate for a particular type of debt is generally given in terms of annual numbers. If, however, there is compounding, then the aggregate rate is actually higher. This is due to the fact that compounding takes into account the cash created by the interest rate, thereby increasing the amount of money that is used to determine interest expense.

## Significance

Aggregate interest rates are significant because many different types of debt, including credit card debt and some types of mortgage financing, take into account compounding effects. This means many consumers are exposed to aggregate interest rates.

## Function

The best way to illustrate the function of compounding and aggregation is to use Excel. The “Effect” function in Excel determines the actual, aggregate interest rate when given two inputs. The first is the stated or nominal annual interest rate. The second input is the number of periods that this is calculated in a given year. For example, a loan that has an interest rate of 13 percent that is compounded quarterly, or four times a year, would have the function “=Effect(.13,4).” The answer given by this command is 13.65 percent, which is the aggregate, or real rate, and is higher than the 13 percent nominal rate. For the same annual rate compounded monthly, the formula would be “=Effect(.13,12), and the result would be 13.80 percent.

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## Identification

The way to identify situations in which the aggregate rate is used would be to read the fine print. In any loan document, if there is a stated annual interest rate, any impact of compounding by quarter or month should be clearly described in the agreement.

## Considerations

Aggregation is beneficial to an investor, as it increases the returns received by compounding. For the borrower, the aggregate rate illustrates the higher cost of borrowing money when compounding is involved. Understanding this concept is essential to being able to compare a wide variety of interest-bearing securities and instruments that have different aggregate rates. By solving each of them using the "Effect" function, it becomes very clear which rates are higher than others in terms of annual, real returns.

#### References

- "The Money Market"; Marcia Stigum; 1990

#### Photo Credits

- Image by Flickr.com, courtesy of Paul Stocker