## Formula

i = m x ((1 + r)^{1/m}- 1)

**Where**

r = Effective annual rate of interest

i = Annual nominal rate of interest

m = Number of compounding periods in a year

## 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).

## Excel Function

The Excel NOMINAL function can be used instead of the nominal interest rate formula, and has the syntax shown below.

i = NOMINAL(r,m)

## Nominal Interest Rate Formula Example

If the effective rate is given as 5.116%, what is the annual nominal interest rate if compounding takes place monthly?

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 = 5.116% m = compounding periods in a year = 12 Nominal interest rate = 12 x ((1 + 5.116%)^{1/12}- 1) Nominal interest rate = 5.000%

The same answer can be obtained using the Excel NOMINAL function as follows:

Effective annual rate = NOMINAL(r,m) r = 5.116% m = 12 Nominal interest rate = NOMINAL(5.116%, 12) Nominal interest rate = 5.000%

The nominal interest rate formula is one of many annuity formulas used in time value of money calculations, discover another at the links below.