Nominal Interest Rate & Effective Interest Rate

 Nominal Interest Rate & Effective Interest Rate

Nominal interest: The nominal interest rate is periodic interest rate times the number of periods per year. For example, a nominal annual interest rate of 12% based on monthly compounding means 1% interest rate per month.

If a financial institution uses a unit of time other than a year. A month or quarter (eg: when calculating interest payments), the institution usually quotes the interest rate on annual basis. Commonly this rate is stated as r% compounded M – ly

Where, r = nominal interest rate per year

         M = compounding frequency or number of interest periods per year         

         r/M = interest rate per compounding period

Effective interest: The actual rate of interest earned during one year is known effective rate and it is also expressed on the annual basis unless specifically stated otherwise; Effective interest rate is represented by 'i'

                                   Then i = (1+r/m)^m – 1

Where, m = compounding period per year

An interest rate takes two forms: nominal interest rate and effective interest rate. The nominal interest rate does not take into account the compounding period. The effective interest rate does take the compounding period into account and thus is a more accurate measure of interest charges. A statement that the "interest rate is 10%" means that interest is 10% per year, compounded annually. In this case, the nominal annual interest rate is 10%, and the effective annual interest rate is also 10%. However, if compounding is more frequent than once per year, then the effective interest rate will be greater than 10%. The more often compounding occurs, the higher the effective interest rate.

All of the formulas used in making time value calculations are based on effective interest rates. Therefore, whenever the interest rate that is provided is a nominal rate, it is necessary to convert it to an effective interest rate. As shown below, an effective interest rate, i, can be calculated for any time period longer than the compounding period.

The most common way that nominal interest rates are stated is in the form 'x% per year compounded y' where x = interest rate and y = compounding period. An example is 18% per year compounded monthly. When interest rates are stated this way, the simplest effective rate to get is the one over the compounding period because all that is required is a simple division. For example, from the interest rate of 18% per year compounded monthly, a monthly interest rate of 1.5% is obtained (i.e., 18% per year/12 compounding periods per year) and this is an effective rate because it is the rate per compounding period. To get an effective rate for any period longer than the compounding period use the effective interest rate formula.

                                             i = (1+r/m)^m – 1

The types of calculations used to obtain effective interest rates are summarized in Table below

Table:  Summary of Calculations Involved in Finding Effective Rates
Interest Statement	To Find i for Compounding Period	To Find i for any Period Longer than Compounding Period
i = 1% per month	i is already expressed over compounding period	Use effective interest rate equation
i = 12% per year compounded quarterly	Divide 12% by 4	Use effective interestrate equation
i = nominal 16% per year compounded semiannually	Divide 16% by 2	Use effective interest rate equation
i = effective 14% per year compounded monthly	Use effective interest rate equation and solve for r/m	For effective i values other than yearly, solve for r in effective interest rate equation and then proceed