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Nominal versus real interest rate
The real interest rate includes compensation for the lender's lost value due to inflation, 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:
- (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 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).2 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 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.
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 (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 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
- Interest
- Compound interest
- Effective interest rate
- List of finance topics
- Real interest rate
- Real versus nominal value
References
- ^ Richard A. Brealey and Steward C. Meyer. Principles of Corporate Finance, Sixth Edition. Irwin McGraw-Hill, London, 2000. p. 49.
- ^ [1] Contemporary Financial Management (with Thomson One - Business School Edition and Infotrac) By R. Charles Moyer, James R. McGuigan, William J. Kretlow, pg. 163]
