Interest means the fee paid on borrowed money. This fee is a compensation to the lender for foregoing other useful investments that could have been made with that money. The amount lent is called the principal. The percentage of the principal which is paid as fee (the interest), over a certain period of time, is called the interest rate.

Types of interest

Simple interest

Simple interest: Simple Interest is simply the product of the principal, the interest rate (per period) and the number of time periods.

To calculate: Add up all the interest paid/payable in a period. Divide that by the principal at the beginning of the period. E.g. on $100 (principal):

• Credit card debt where $1/day is charged. 1/100 = 1%/day.
• Corporate bond where $3 is due after six months, and another $3 is due at year end. (3+3)/100 = 6%/year.
  
• Certificate of deposit (GIC) where $6 is paid at year end. 6/100 = 6%/year.
  There are three problems with simple interest.
  
• The time periods used for measurement can be different, making comparisons wrong. You cannot say the 1%/day credit card interest is 'equal' to a 365%/year GIC.
  
• The time value of money means that $3 paid every six months hurts more than $6 paid only at year end. So you cannot 'equate' the 6% bond to the 6% GIC.
  
• When interest is due, but not paid, it must be clear what happens. Does it remain 'interest payable', like the bond's $3 payment after six months? Or does it get added to the original principal, like the 1%/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

Compound interest: Compound Interest is much similar to Simple Interest; the principal changes with every time period unlike simple interest where the principal is the same. The new principal at the end of every time period is essentially the simple interest on the principal at the beginning of the time period. Suppose P is the principal and R and T have their usual meanings, then the principal at the end of the first period will be P*R (T=1 period). Similarly, the principal at the end of the second period will be (P*R)*R. Thus we can land upon a general formula: Compound Interest= P*(R)^T Compounded amount= P*(1+R)^T In order to solve these three problems, there is a convention in economics that interest rates will be disclosed as if the term is one 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 non-interest charges and fees (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 an annual percentage rate, which expresses the total cost of a loan as an interest rate after including the additional fees and expenses (the details, however, vary). In economics, continuous compounding is often used due to specific mathematical properties.

Fixed and floating rates

Loans may not 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, variable rate or adjustable rate loans. Combinations of fixed-rate and floating-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 5% in the first year, 6% in the second, and 7% in the third).