Compound interest

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. It is the result of reinvesting interest, rather than paying it out, so that interest in the next period is then earned on the principal sum plus previously-accumulated interest. Compound interest is standard in finance and economics.

Compound interest may be contrasted with simple interest, where interest is not added to the principal, so there is no compounding. The simple annual interest rate is the interest amount per period, multiplied by the number of periods per year. The simple annual interest rate is also known as the nominal interest rate (not to be confused with nominal as opposed to real interest rates).

The compounding frequency is the number of times per year (or other unit of time) the accumulated interest is paid out, or capitalized (credited to the account), on a regular basis. The frequency could be yearly, half-yearly, quarterly, monthly, weekly, daily (or not at all, until maturity).

For example, monthly capitalization with annual rate of interest means that the compounding frequency is 12, with time periods measured in months.

The effect of compounding depends on:

The nominal rate cannot be directly compared between loans with different compounding frequencies. Both the nominal interest rate and the compounding frequency are required in order to compare interest-bearing financial instruments.

To assist consumers compare retail financial products more fairly and easily, many countries require financial institutions to disclose the annual compound interest rate on deposits or advances on a comparable basis. The interest rate on an annual equivalent basis may be referred to variously in different markets as annual percentage rate (APR), annual equivalent rate (AER), effective interest rate, effective annual rate, annual percentage yield and other terms. The effective annual rate is the total accumulated interest that would be payable up to the end of one year, divided by the principal sum.

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