Simple interest: simple interest does not take compounding into account, and is determined by multiplying the principal by the interest rate (per period) by the number of time periods.
To calculate: Add up all the interest payable/paid in a period. Divide that by the principal at the beginning of the period. Example on a $100 (principal):
a) Credit card debt where one dollar a day is charged. 1/100 = 1% a day.
b) Corporate bond where three dollars is due after 6 months, and another three dollars is due at year end. (3+3)/100 = 6% a year.
c) Certificate of deposit (GIC) where six dollars is paid at the end of the year. 6/100 = 6% a year.
There are 3 problems with simple interest.
The time periods used for measurement can be different, this can make comparisons wrong. You can't say the one percent a day credit card interest is 'equal' to a three hundred sixt five percent a year GIC. The time value of money means that three dollars paid every mo6nths hurts more than six dollars paid only at the end of the year. So you can't 'equate' the six percent bond to the six percent GIC. When interest not paid, but due, it must be clear what happens. Does it remain 'interest payable', like the bond's three dollar payment after 6 months? Or does it get added to the original principal, like the one percent a day on the credit card? Each time it is added to the principal it 'compounds'. The interest from that time forward is calculated on that (now larger) principal. The more frequent the compounding, the faster the principal grows, and the greater the interest amount is.
Compound interest: In order to solve these 3 problems, there is a convention in economics that interest rates will be disclosed as if the term is 1 year and the compounding is yearly, otherwise known as the effective interest rate. The discussion at compound interest shows how to convert to and from the different measures of interest. Interest rates in lending are often quoted as nominal interest rates (compounding interest uncorrected for the frequency of compounding. Loans often include various fees and non-interest charges (such as points on a mortgage loan in the United States; many jurisdictions require lenders to provide information on the 'true' cost of finance, often expressed as a APR or annual percentage rate, which expresses the total cost of a loan as an interest rate after including the additional expenses and added fees (the details, however, vary). In economics, continuous compounding is often used due to specific mathematical properties.
Fixed and floating rates
Loans don't always have a single interest rate over the life of the loan (although they generally still use compound interest). Loans for which the interest rate does not change are referred to as fixed rate loans. Loans may also have a changeable rate over the life of the loan based on some reference rate (such as LIBOR), usually plus (or minus) a fixed margin. These are known as floating rate, adjustable rate, or variable rate loans. Combinations of floating-rate and fixed-rate loans are possible and frequently used. Less frequently, loans may have different interest rates applied over the life of the loan, where the changes to the interest rate are not tied to an underlying interest rate (for example, a loan may have a rate of five percent in the 1st year, six percent in the 2nd, and seven percent in the 3rd).
The formula to calculate CI is = [P(1+R/100)^n] - P where P = Amount deposited