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Compound interest is interest added to the principal of a deposit or loan so that the added interest also earns interest from then on. This addition of interest to the principal is called ''compounding''. A bank account, for example, may have its interest compounded every year: in this case, an account with $1000 initial principal and 20% interest per year would have a balance of $1200 at the end of the first year, $1440 at the end of the second year, $1728 at the end of the third year, and so on. To define an interest rate fully, allowing comparisons with other interest rates, both the interest rate and the compounding frequency must be disclosed. Since most people prefer to think of rates as a yearly percentage, many governments require financial institutions to disclose the equivalent yearly compounded interest rate on deposits or advances. For instance, the yearly rate for a loan with 1% interest per month is approximately 12.68% per annum (1.0112 − 1). This equivalent yearly rate may be referred to as ''annual percentage rate'' (APR), ''annual equivalent rate'' (AER), ''effective interest rate'', ''effective annual rate'', and other terms. When a fee is charged up front to obtain a loan, APR usually counts that cost as well as the compound interest in converting to the equivalent rate. These government requirements assist consumers in comparing the actual costs of borrowing more easily. For any given interest rate and compounding frequency, an equivalent rate for any different compounding frequency exists. Compound interest may be contrasted with simple interest, where interest is not added to the principal (there is no compounding). Compound interest is standard in finance and economics, and simple interest is used infrequently (although certain financial products may contain elements of simple interest). ==Terminology== The effect of compounding depends on the frequency with which interest is compounded and the periodic interest rate which is applied. Therefore, to accurately define the amount to be paid under a legal contract with interest, the frequency of compounding (yearly, half-yearly, quarterly, monthly, daily, etc.) ''and'' the interest rate must be specified. Different conventions may be used from country to country, but in finance and economics the following usages are common: The ''periodic rate'' is the amount of interest that is charged (and subsequently compounded) for each period divided by the amount of the principal. The periodic rate is used primarily for calculations and is rarely used for comparison. The ''nominal annual rate'' or ''nominal interest rate'' is defined as the periodic rate multiplied by the number of compounding periods per year. For example, a monthly rate of 1% is equivalent to an annual nominal interest rate of 12%. The ''effective annual rate'' is the total accumulated interest that would be payable up to the end of one year divided by the principal. Economists generally prefer to use effective annual rates to simplify comparisons, but in finance and commerce the nominal annual rate may be quoted. When quoted together with the compounding frequency, a loan with a given nominal annual rate is fully specified (the amount of interest for a given loan scenario can be precisely determined), but the nominal rate cannot be directly compared with that of loans that have a different compounding frequency. Loans and financing may have charges other than interest, and the terms above do not attempt to capture these differences. Other terms such as annual percentage rate and annual percentage yield may have specific legal definitions and may or may not be comparable, depending on the jurisdiction. The use of the terms above (and other similar terms) may be inconsistent and vary according to local custom or marketing demands, for simplicity or for other reasons. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「compound interest」の詳細全文を読む スポンサード リンク
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