Nominal interest rate
From Wikipedia, the free encyclopedia
The term nominal interest rate is used in two distinct senses:
- To distinguish between the stated rate and the real interest rate (after adjustment for inflation).
- For interest rates that are stated without adjustment for the full effect of compounding; this may be referred to as the nominal annual rate.
The nominal interest rate (unadjusted for inflation) includes compensation for the lender's lost value due to inflation, whereas the real interest rate excludes inflation. The relationship between real and nominal interest rates can be described in the equation:
- (1 + r)(1 + i) = (1 + R) where r is the real interest rate, i is the inflation rate, and R is the nominal interest rate.[1]
- A common approximation for the nominal interest rate is: real interest rate + expected inflation = nominal interest rate rate.
A nominal interest rate is also the interest rate "as stated" - that is, not adjusted to reflect the full effect of compounding. 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). 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).[2] A nominal interest rate for compounding periods less than a year is always higher 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 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 the compounding periods are the same; effective interest rates 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). Simple interest is interest that is not compounded.
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[edit] Nominal and effective interest rates: calculations
The effective interest rate 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, and n the number of compounding periods per year (for example, 12 for monthly compounding):
[edit] Examples
[edit] Monthly compounding
A nominal interest rate of 6% compounded monthly is equivalent to an effective interest rate 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.
[edit] 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.
[edit] See also
- Time value of money
- Interest
- Compound interest
- Effective interest rate
- List of finance topics
- Real interest rate
- Real versus nominal value
