# Nominal Interest Rate Formula

## 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.

Nominal Interest Rate Formula November 6th, 2016

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