Formula and Use
The nominal interest rate formula calculates the annual nominal rate of interest (i), based on an effective annual rate (r). and a number of compounding periods in a year (m). The nominal rate does not allow for the effect of compounding whereas the effective rate does. An example of a nominal rate is the coupon rate on a bond.
Excel Nominal Interest Rate Function
The Excel NOMINAL function can be used instead of the nominal rate formula, and has the syntax shown below. The examples below demonstrate the use of the Excel function.
i = NOMINAL(r,m)
Nominal Interest Rate Formula Examples
Monthly Compounding
If the effective rate is given as 6%, what is the annual nominal interest rate if compounding takes place monthly?
The calculation of the nominal interest rate for the year using the nominal interest rate formula is as follows:
Nominal interest rate = i = m x ((1 + r)1/m - 1) r = effective annual rate = 6% m = compounding periods in a year = 12 Nominal interest rate = 12 x ((1 + 6%)1/12 - 1) Nominal interest rate = 5.841%
Similarly the Excel NOMINAL function provides the same answer as follows:
Effective annual rate = NOMINAL(r,m) r = 6% m = 12 Nominal interest rate = NOMINAL(6%, 12) Nominal interest rate = 5.841%
Quarterly Compounding
Again if the effective rate is given as 6%, what is the annual nominal interest rate if compounding takes place quarterly?
The nominal interest rate for the year is calculated using the nominal interest rate formula as follows:
Nominal interest rate = i = m x ((1 + r)1/m - 1) r = effective annual rate = 6% m = compounding periods in a year = 4 Nominal interest rate = 4 x ((1 + 6%)1/4 - 1) Nominal interest rate = 5.870%
Similarly the same answer can be obtained using the Excel NOMINAL function as follows:
Effective annual rate = NOMINAL(r,m) r = 6% m = 4 Nominal interest rate = NOMINAL(6%, 4) Nominal interest rate = 5.870%
Annualized Percent Rate
The nominal interest rate is often referred to as the annualized percentage rate as it represents the effective rate when interest is compounded once per year. It can be seen for the formula above that if the number of compounding periods (m) is 1 then the nominal rate (i) is equal to the effective annual rate. To demonstrate using the same details as in the example above.
Nominal interest rate = i = m x ((1 + r)1/m - 1) r = effective annual rate = 6% m = compounding periods in a year = 1 Nominal interest rate = 1 x ((1 + 6%)1/1 - 1) Nominal interest rate = 6% = Annualized percent rate
In this instance as the compounding is annual the effective interest rate is the same as the nominal interest rate.
Nominal Interest Rate vs Real Interest Rate
The nominal interest rate also forms the basis of the calculation of the real interest rate. The real interest rate adjusts the nominal interest rate for inflation. The calculation of the real interest rate is discussed in more detail here.
The nominal interest rate formula is one of many annuity formulas used in time value of money calculations, discover another at the links below.
About the Author
Chartered accountant Michael Brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a degree from Loughborough University.