In finance, the word interest refers to a fee which is charged in exchange for access to capital. Interest is paid by a borrower, such as an individual, a company, a bank or an insurance provider, to lenders for the use of their capital.
Borrowed capital is known as a loan. The capital making up the loan is the loan principal. Interest may be paid as a fixed amount (5 Swiss francs per 100 francs of principal, for example) or as an interest rate (5% of principal, for example).
Typically, interest is charged based on the amount of time for which the capital is borrowed. Interest rates are normally calculated on an annual basis, with the annual rate being used to calculate loan terms which are shorter or longer than one year.
If a bank were to pay a customer 1% interest per year for 1000 francs of capital lent to the bank (through a deposit into a bank account), that customer would receive 10 francs (1% of 1000) as an interest payment every year.
If the customer withdrew their money from their account after 6 months, they would receive half the amount of interest, or 5 francs (0.5% of 1000 francs). The annual interest rate of 1% would only be applied in full if the capital were lent to the bank for a full year.
The same applies when a borrower gets a personal loan, credit card loan, business loan or mortgage from a lender. The amount of interest which the borrower must pay for the use of the capital is normally based on the length of time for which they use the capital.
Interest compounding occurs when interest is applied, but is not withdrawn by the lender. Instead, the interest is added to the loan principal. Interest is then charged based on the full amount owed (loan principal + interest added). This is known as the compounding interest effect.
Example: Using the example above, lets say the bank customer were to lend their money to the bank for 3 years and not withdraw the interest paid to them. At the end of the first year, the bank would pay interest equal to 1% of the borrowed 1000 francs, bringing the full amount owed to the customer to 1010 francs. At the end of the second year, the bank would pay the customer 1% of 1010 francs, or 10.10 francs, bringing the total amount owed to 1020.10 francs. At the end of the third year the bank would pay interest equal to 1% of 1021, or 10.21 francs. So the bank would pay the customer a total of 30.31 francs in interest over the 3 year term, rather than the just 30 francs.
If the interest were applied on a monthly basis or a daily basis, the compounding interest effect would be stronger, and the increase in interest would be more significant.
An effective annual interest rate accounts for interest compounding and communicates the actual amount of interest which must be paid for a loan.
A nominal interest rate or simple interest rate does not account for interest compounding or inflation.
A real interest rate accounts for the effects of inflation. Because capital normally loses value over time, the longer the loan term is, the less the capital is worth by the time it is repaid to the lender. Real interest rates account for these losses in the value of capital over time (inflation) based on an inflation rate.