Nominal interest rate

# Nominal interest rate

Discussion
 Ask a question about 'Nominal interest rate' Start a new discussion about 'Nominal interest rate' Answer questions from other users Full Discussion Forum

Encyclopedia
In finance and economics nominal interest rate or nominal rate of interest refers to the rate of interest
Interest
Interest is a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets. It is most commonly the price paid for the use of borrowed money, or money earned by deposited funds....

Inflation
In economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time.When the general price level rises, each unit of currency buys fewer goods and services. Consequently, inflation also reflects an erosion in the purchasing power of money – a...

(in contrast with the real interest rate
Real interest rate
The "real interest rate" is the rate of interest an investor expects to receive after allowing for inflation. It can be described more formally by the Fisher equation, which states that the real interest rate is approximately the nominal interest rate minus the inflation rate...

); or, for interest rates "as stated" without adjustment for the full effect of compounding
Compound interest
Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding...

(also referred to as the nominal annual rate). An interest rate is called nominal if the frequency of compounding (e.g. a month) is not identical to the basic time unit (normally a year).

## Nominal versus real interest rate

The real interest rate is the nominal rate of interest minus inflation
Inflation
In economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time.When the general price level rises, each unit of currency buys fewer goods and services. Consequently, inflation also reflects an erosion in the purchasing power of money – a...

. In the case of a loan, it is this real interest that the lender receives as income. If the lender is receiving 8 percent from a loan and inflation is 8 percent, then the real rate of interest is zero because nominal interest and inflation are equal. A lender would have no net benefit from such a loan because inflation fully diminishes the value of the loan's profit.

The relationship between real and nominal interest rates can be described in the equation:
where r is the real interest rate, i is the inflation rate, and R is the nominal interest rate.
• A common approximation for the real interest rate is:
real interest rate = nominal interest rate - expected inflation

In this analysis, the nominal rate is the stated rate, and the real interest rate is the interest after the expected losses due to inflation. Since the future inflation rate can only be estimated, the ex ante and ex post (before and after the fact) real interest rates may be different; the premium paid to actual inflation may be higher or lower. In contrast, the nominal interest rate is known in advance.

## Nominal versus effective interest rate

The nominal interest rate is the periodic interest rate times the number of periods per year. For example, a nominal annual interest rate of 12% based on monthly compounding means a 1% interest rate per month (compounded). A nominal interest rate for compounding periods less than a year is always lower than the equivalent rate with annual compounding. A nominal rate without the compounding frequency is not fully defined: for any interest rate, the effective interest rate
Effective interest rate
The effective interest rate, effective annual interest rate, annual equivalent rate or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears.It is used to compare the...

cannot be specified without knowing the compounding frequency and the rate. Although some conventions are used where the compounding frequency is understood, consumers in particular may fail to understand the importance of knowing the effective rate.

Nominal interest rates are not comparable unless their compounding periods are the same; effective interest rate
Effective interest rate
The effective interest rate, effective annual interest rate, annual equivalent rate or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears.It is used to compare the...

s correct for this by "converting" nominal rates into annual compound interest. In many cases, depending on local regulations, interest rates as quoted by lenders and in advertisements are based on nominal, not effective interest rates, and hence may understate the interest rate compared to the equivalent effective annual rate.

The term should not be confused with simple interest (as opposed to compound interest
Compound interest
Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding...

). Simple interest is interest that is not compounded.

The effective interest rate
Effective interest rate
The effective interest rate, effective annual interest rate, annual equivalent rate or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears.It is used to compare the...

is always calculated as if compounded annually. The effective rate is calculated in the following way, where r is the effective rate, i the nominal rate (as a decimal, e.g. 12% = 0.12), and n the number of compounding periods per year (for example, 12 for monthly compounding):

### Monthly compounding

Example 1: A nominal interest rate of 6% compounded monthly is equivalent to an effective interest rate
Effective interest rate
The effective interest rate, effective annual interest rate, annual equivalent rate or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears.It is used to compare the...

of 6.17%.

Example 2: 6% annually is credited as 6%/12 = 0.5% every month. After one year, the initial capital is increased by the factor (1+0.005)12 ≈ 1.0617.

### Daily compounding

A loan with daily compounding will have a substantially higher rate in effective annual terms. For a loan with a 10% nominal annual rate and daily compounding, the effective annual rate is 10.516%. For a loan of \$10,000 (paid at the end of the year in a single lump sum
Lump sum
A lump sum is a single payment of money, as opposed to a series of payments made over time .The United States Department of Housing and Urban Development distinguishes between "price analysis" and "cost analysis" by whether the decision maker compares lump sum amounts, or subjects contract prices...

), the borrower would pay \$51.56 more than one who was charged 10% interest, compounded annually.

• Time value of money
Time value of money
The time value of money is the value of money figuring in a given amount of interest earned over a given amount of time. The time value of money is the central concept in finance theory....

• Interest
Interest
Interest is a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets. It is most commonly the price paid for the use of borrowed money, or money earned by deposited funds....

• Compound interest
Compound interest
Compound interest arises when interest is added to the principal, so that from that moment on, the interest that has been added also itself earns interest. This addition of interest to the principal is called compounding...

• Effective interest rate
Effective interest rate
The effective interest rate, effective annual interest rate, annual equivalent rate or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest payable in arrears.It is used to compare the...

• Real interest rate
Real interest rate
The "real interest rate" is the rate of interest an investor expects to receive after allowing for inflation. It can be described more formally by the Fisher equation, which states that the real interest rate is approximately the nominal interest rate minus the inflation rate...

• Real versus nominal value (economics)
• Zero interest rate policy
Zero interest rate policy
The zero interest rate policy is a macroeconomic concept describing conditions with a very low interest rate, such as contemporary Japan and, since December 16, 2008, the United States. It can be associated with slow economic growth....