The price of money; rental payment upon money; a charge made to the borrower by the lender for the use of money. Interest is expressed in terms of an annual rate of percentage upon the principal. Thus, if $6.00 is paid for the annual use of $100, the rate is 6%; the (annual) rate is also 6% if $0.50 is paid for one month's use of $100. Interest is often payable at intervals shorter than one year but rarely at longer intervals. Interest on modern amortized mortgages, for example, is paid in monthly installments including as a portion thereof amortization payment on principal. Interest on bonds is usually paid semi-annually. Interest on commercial loans may be paid quarterly, while the charge for federal funds (See MONEY MARKET) is computed on an actual day basis (360-day year).
Simple interest is that computed upon the principal without reference to the interest period, on the assumption (for exact simple interest) that 1/365th of a year's interest accrues each day. It is equivalent to compounding at the day of calculation; if the interest period lent to compounding at the day of calculation; if the interest period is less than one year, the nominal simple interest rate is greater than the true interest rate compounded annually. Practically, however, this difference is disregarded.
Ordinary simple interest is based on the assumption that each day is 1/360th of a year. Ordinary interest for one day is slightly more than exact interest for one day.
Compound interest is computed upon the principal plus the interest that has accrued and is payable on the agreed interest date. Interest is usually compounded monthly, quarterly, semi-annually, or annually.
When interest is compounded more frequently than once a year, it produces an "effective" rate in excess of the nominal or quoted rate. For example, if the nominal interest rate on a $1,000 bond is $4 payable annually, the effective interest rate is the same, i.e., $4 if payable semi-annually, it is 4.04%; if payable quarterly, it is 4.0604%; if payable monthly, it is 4.0742%; and if payable daily, it is 4.0811%. The interest on a $1,000 4% bond compounded annually is therefore quarterly; $40.742 if compounded monthly; and $40.811 if compounded daily. Effective savings, therefore, are obtainable by compounding annually instead of more frequently.
In corporate bond practice, there is no compounding of interest. A $1,000 corporate bond bearing 4% interest, payable semi-annually, will pay $20 interest on the semi-annual interest payment dates specified. The interest on registered bonds is paid by check to the registered owners; in the case of coupon bonds, it is paid upon presentation of properly dated coupon to the payment agent. There is no interest on interest; if coupons are not presented promptly for payment, there will not be any interest on the interest since the specified payment date.
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