What is the difference between nominal interest and effective interest?
Nominal interest, also referred to as the Annual Percentage Rate (APR), is the rate quoted on an annual basis and is usually followed by the compunding frequency. The effective interest is the exact rate of interest earned during some period. Usually, effective interest rates are found over a one year period but they may be found for shorter periods, such as the effective interest per month or the effective interest per quarter. To find a period rate given the nominal rate use: iM = r/M, where r is the nominal rate and M is the number of compounding periods per year (i.e. M=12 if interest is compounded monthly.) To find the effective annual rate given the nominal rate use: ieff = (1 + r/M)^M – 1 For example, a bank may advertise a loan interest rate of 12% compounded monthly. The monthly (M=12) interest rate is: i/month = 12%/12 = 1% per month. The effective annual rate is: ieff = (1 + 0.12/12)^12 – 1 = 12.68% per year If the bank charged interest on a quarterly bases then: The quarter
