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Source: Encyclopedia of Banking & Finance (9h Edition) by Charles J Woelfel
(We recommend this as work of authority.)

This term has two meanings:

1.   Literally, "killing off" or wiping out, a term applied to (1) the gradual reduction of a debt by   equal periodic payments sufficient to pay current interest and to extinguish the principal completely by final maturity (see AMORTIZED LOANS); (2) the periodic writing off of an asset over a specific term, such as capitalized expenses (deferred charges) and intangibles (such as goodwill, patents, trademarks, and copyrights).  Depreciation is a process of regular amortization of the depreciable cost, including accelerated amortization of defense-essential facilities.

2.   The process of periodically reducing or writing off the premium on a bond brought above par, in order to bring its investment or basis value into coincidence with par (face amount of denomination of the bond) on the maturity date.  The premium paid for a bond at the time of purchase represents a part of the investment which will not be returned at maturity.  Consequently, a part of the cash interest paid periodically on the bond should not be regarded as income but as an amount to be applied to the reduction of the premium.  This is accomplished by a charge at each bond interest date to the cash interest account and a corresponding credit to the cost basis on the bond or to valuation reserve, amortization of premium.

To illustrate the mathematical history of a bond bought at a premium and carried currently on an investment basis, suppose a 6.0% tax-exempt bond, paying interest semiannually March 1 and September 1, with a four-year maturity, is bought March 1, 1978, to yield 4.5%, or a cost of $1,054.40.  The appended table (Mathematics of Amortization) shows what portion of the cash interest is to be regarded as net interest income or yield and how much as reduction of the principal of the investment (amortization of the premium).

The yield is determined by multiplying the book value, which in the first instance is the purchase price, by the predetermined yield or basis rate, 4.5%.  The net income for September 1, 1978, therefore, is determined by multiplying $1,054.40 by 2.25% (the semiannual rate).  This is $23.70.  The difference between $23.70 (y8ield or net income) and $30.00 (cash interest) is $6.30, which is the first amortization installment to be applied in the reduction of the book value of the investment.  The new book value for September 1, 1978, is the difference between $1,054.40 and $6.30, or $1,048.10.  Since the book value is constantly being reduced, the net income for such subsequent interest periods declines.  It will be seen that the total of the amortization is equal to the premium and that provision has been made to extinguish it completely.

The entry on the book for the first interest period should be as follows:   

Dr. Cash     $30.00
Total   $30.00  
Cr. Interest Income  $23.70
Amortization of Bond Premium $6.30  
Total $30.00  

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