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 6% based on monthly compounding means a 0.5% interest rate per month (compounded 6/12).
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 their 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 6% = 0.6%), 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% 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 R10,000 (paid at the end of the year in a single lump sum), the borrower would pay R51.56 more than one who was charged 10% interest, compounded annually
