NOMINAL INTEREST RATE AND EFFECTIVE INTEREST RATE
The nominal interest rate is the annual interest rate (per year) for a certain compounding period. A nominal interest rate can be applied to the advertised or stated interest rate on a loan, without taking into account any fees or compounding of interest. The nominal interest rate can be calculated using the formula:
j=im
where:
- i is the periodic interest rate
- j is the nominal/stated rate
- m is the number of compounding periods
The effective interest rate (f), (or simply effective rate) is the annual interest rate compounded annually. It may be seen on a loan or financial product restated from the nominal interest rate and expressed as the equivalent interest rate if compound interest was payable annually in arrears. It can be calculated with the following formula:
f=(1+i)m−1
where:
- i is the periodic interest rate
- f is the effective rate
- m is the number of compounding periods
An interest rate takes two forms: nominal interest rate and effective interest rate. The nominal interest rate does not take into account the compounding period. The effective interest rate does take the compounding period into account and thus is a more accurate measure of interest charges.
A statement that the “interest rate is 10%” means that interest is 10% per year, compounded annually. In this case, the nominal annual interest rate is 10%, and the effective annual interest rate is also 10%. However, if compounding is more frequent than once per year, then the effective interest rate will be greater than 10%. The more often compounding occurs, the higher the effective interest rate.
The relationship between nominal annual and effective annual interest rates is: ia = [ 1 + (r / m) ] m – 1
where “ia” is the effective annual interest rate, “r” is the nominal annual interest rate, and “m” is the number of compounding periods per year.
