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In finance and economics nominal interest rate or nominal rate of interest refers to the rate of interest
Interest

Interest is a fee paid on borrowed assets. It is the price paid for the use of borrowed money , or, money earned by deposited funds .Assets that are sometimes lent with interest include money, shares, consumer goods through hire purchase, major assets such as aircraft finance, and even entire factories in finance lease arrangements....
 before adjustment for inflation (in contrast with the real interest rate
Real interest rate

The "real interest rate" is approximately the nominal interest rate minus the inflation rate . Since the inflation rate over the course of a loan is not known initially, Volatility_ in inflation represents a risk to both the lender and the borrower....
); or, for interest rates "as stated" without adjustment for the full effect of compounding
Compound interest

Compound interest is the concept of adding accumulated interest back to the principal, so that interest is earned on interest from that moment on....
 (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).

real interest rate includes compensation for the lender's lost value due to inflation
Inflation

In economics, inflation is a rise in the general price level of goods and services in an economy over a period of time. The term "inflation" once referred to increases in the money supply ; however, economic debates about the relationship between money supply and price levels have led to its primary use today in describing price inflatio...
, whereas the nominal interest rate excludes inflation.






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In finance and economics nominal interest rate or nominal rate of interest refers to the rate of interest
Interest

Interest is a fee paid on borrowed assets. It is the price paid for the use of borrowed money , or, money earned by deposited funds .Assets that are sometimes lent with interest include money, shares, consumer goods through hire purchase, major assets such as aircraft finance, and even entire factories in finance lease arrangements....
 before adjustment for inflation (in contrast with the real interest rate
Real interest rate

The "real interest rate" is approximately the nominal interest rate minus the inflation rate . Since the inflation rate over the course of a loan is not known initially, Volatility_ in inflation represents a risk to both the lender and the borrower....
); or, for interest rates "as stated" without adjustment for the full effect of compounding
Compound interest

Compound interest is the concept of adding accumulated interest back to the principal, so that interest is earned on interest from that moment on....
 (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 includes compensation for the lender's lost value due to inflation
Inflation

In economics, inflation is a rise in the general price level of goods and services in an economy over a period of time. The term "inflation" once referred to increases in the money supply ; however, economic debates about the relationship between money supply and price levels have led to its primary use today in describing price inflatio...
, whereas the nominal interest rate excludes inflation. The real interest rate therefore expresses the cost of borrowed funds after the expected erosion of the value of those funds due to the rise in the general price level.

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

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....
 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 they are 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....
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 is the concept of adding accumulated interest back to the principal, so that interest is earned on interest from that moment on....
). 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....
 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 fraction, eg 12% = 0.12), and n the number of compounding periods per year (for example, 12 for monthly compounding):

Examples


Monthly compounding

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....
 of 6.17%. 6% monthly 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), the borrower would pay $51.56 more than one who was charged 10% interest, compounded annually.

See also

  • Time value of money
    Time value of money

    The concepts of present and future value hinge upon the premise that an investor prefers to receive a payment of a fixed amount of money today, rather than an equal amount in the future, all else being equal....
  • Interest
    Interest

    Interest is a fee paid on borrowed assets. It is the price paid for the use of borrowed money , or, money earned by deposited funds .Assets that are sometimes lent with interest include money, shares, consumer goods through hire purchase, major assets such as aircraft finance, and even entire factories in finance lease arrangements....
  • Compound interest
    Compound interest

    Compound interest is the concept of adding accumulated interest back to the principal, so that interest is earned on interest from that moment on....
  • 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....
  • List of finance topics
    List of finance topics

    Topics in finance include:...
  • Real interest rate
    Real interest rate

    The "real interest rate" is approximately the nominal interest rate minus the inflation rate . Since the inflation rate over the course of a loan is not known initially, Volatility_ in inflation represents a risk to both the lender and the borrower....
  • Real versus nominal value
    Real versus nominal value

    In economics, nominal value refers to any price or value expressed in money of the day, as opposed to real value, which adjusts for the effect of inflation....
  • Zero interest rate policy
    Zero interest rate policy

    The zero interest rate policy is a Keynesian macroeconomics scheme for economies exhibiting slow growth with a very low interest rate, such as contemporary Japan and since December 16, 2008 the United States....