Interest in finance, is a surcharge on the repayment of debt (borrowed money). Interest is justified in capitalist countries by one or more of the following:

• the time value of money
• the opportunity cost of money
• macroeconomic price changes (inflation)

Mathematically, interest generally falls in one of the following two categories:

• simple interest, in which outstanding balances grow linearly with time. In each period, the total balance grows by some fraction of the principal (that is, of the original investment).
• compound interest, in which outstanding balances grow geometrically with time and exponentially with time in the limit as the rate of compounding becomes instantaneous. In each period, the total balance grows by some fraction of the sum of the principal and the interest paid on all previous periods.

In either case, the fraction by which the balances grow is called the interest rate.

Simple interest is seldom used in practice. In most cases this is because the interest earned in previous periods is assumed to remain in the account. Only when the interest earned is immediately withdrawn from the account should simple interest be used. When interest is not collected as it is accrued (as with a certificate of deposit, where the payment is in a lump sum), the interest increases the amount of money subject to interest. In this case simple interest would produce mathematically inconsistent results. In compound interest, how often it is compounded changes the amount of interest.

Economists sometimes referred to interest as rent on money. As with any rental, the market price (or rate) is subject to change to reflect market conditions. Interest rates are very closely watched market indicators, and have a dramatic impact on finance and economics.

Interest involves the future, which is uncertain. Some interest bearing investments are riskier than others. The greater the risk of the security, the more interest investors expect to receive.

Different parties will be offered different rates on debt obligations (such as loans). The measure of credit worthiness of an individual is called a credit rating or credit score. Other entities (such as governments and companies) will acquire a bond rating if they are active in bond markets.