# Nominal annual rate

The rate of return - or cost of borrowing - per conventional year named or quoted in a market, under the quoting convention for the given market.

Market quotations are usually given per annum, and for this reason the term nominal rate is sometimes used interchangeably with nominal annual rate.

Different conventional market bases for expressing nominal annual rates have arisen in different markets over time.

Often this was originally for local or domestic convenience, but it can lead to difficulties of comparability between different markets. For this reason it is essential to know and understand the basis on which any given nominal annual rate is being quoted. It is always best to be explicit about conventions when dealing, rather than assuming and hoping for the best.

## Illustration

Most rates in wholesale financial markets are quoted as nominal annual rates.

Example 1: Overnight interest

GBP overnight interest payable at the periodic rate of 0.014% per day, would conventionally be quoted on a nominal annual basis as:

= number of times the period fits into a conventional year x periodic rate

= 365 x 0.014%

= 5.11%.

## Other names for Nominal annual rates

The nominal annual rate is sometimes also known as a 'quoted rate', 'market rate, or 'nominal rate'.

The nominal annual rate should not be confused with the effective annual rate, which is usually different.

## Notation

Nominal annual interest rates and yields are often denoted by 'R'.

This distinguishes them from periodic interest rates and yields (r), and from effective annual rates (EAR).

## Conversion

Using the notation above:

R = nominal annual interest rate or yield

r = periodic interest rate or yield

n = number of times the period fits into a conventional year

#### To convert from a periodic rate (r) to a nominal annual rate (R)

R = r x n

Example 2: Calculating the nominal annual rate

The periodic rate for GBP interest is 0.01% per day.

Calculate the nominal annual rate.

R = r x 365

= 0.01% x 365

= 3.65%

#### To convert from a nominal annual rate (R) to a periodic rate (r)

r = R / n

Example 3: Calculating periodic rate

GBP interest is quoted at a nominal annual rate of 5.11% for daily interest calculation.

Calculate the periodic rate per day.

r = R / n

= 5.11% / 365

= 0.014%