THE VALUATION Of BONDS 133 50. The amortization of the premium on a bond bought above par. When a bond which is to be redeemed at par is bought at a premium, some provision must be made for restoring to the original capital the amount of the premium; otherwise the capital will be impaired when the bond is redeemed. To illustrate, sup- pose the guardian of a minor buys a bond with par value $1000 at a premium of $500, intending to use the income for the main- tenance of his ward. He has invested $1500 belonging to his ward, and if the annual income from the bond has all been used for living expenses, there will be only $1000 to reinvest, instead of the original $1500, when the bond is redeemed at par. In other words, $500 of the capital has disappeared as effectually as if it had been stolen. Indeed, the guardian should be held responsible for the disappearance of the $500, just as though it had been stolen. To remedy this difficulty, the premium should be considered as a debt to be repaid out of the surplus interest received. The gradual extinction of the premium through the application of the surplus interest is called the amortization of the premium. The value of the bond will diminish with each successive reduction of the premium until the date of redemption, when it should stand exactly at par. The value of a bond at any given date, when purchased to yield a given rate of interest, is termed the book value. An amortization schedule should be prepared exactly as in §§ 45, 46, and 47. Such a schedule should show the book value, the net income, and the amount of amortiza- tion at the end of every dividend period until the bond is redeemed. ILLUSTRATIVE EXAMPLE. Consider the amortization of the premium on a bond for $100, with interest at 6% (payable-January 1 and July 1), and redeemable at par January 1, 1916, bought January 1, 1911, to yield 5% nominal, convertible semiannnally. Solution. By (6) of § 49 the premium is found to be $4.376, and conse- quently the purchase price is $104.376. At the end of each half year $3 will be received, while 5% nominal on $104.376 for a half year is only $2.609 ; so that there is a surplus of $0.391 available for amortization. Applying this surplus to the reduction of the premium, we see that the value of the bond is reduced