DISCOUNT, a sum of money deducted from a debt in consideration of its being paid before the usual or stipulated time. The circumstance on which its fairness is founded is, that the creditor, by receiving his money before it comes due, has the interest of the money during the interval. Consequently he should only receive so much as, pat out to interest during the period in question, will realize the amount of his debt at the time when it would have become due. For instance, 100/. is to be paid at the end of three years ; what should be paid now, interest being 4 per cent. ? Here it is evident that if we divide the whole debt into 112 ( or 100-1-3X4) parts, 100 of these parts will make the other 12 in three years (at simple interest), whence the payment now due is the 112th part of 10,0001., or 89/. 5s. 9d. The rule is, a being the number of years (a fraction or number and fraction), r the rate per cent., and D the sum due, Present value = 100 D 100 r D n r • Discount = 1001-sr In practice, it is usual not to find the real discount, but to allow interest on the whole lebt in the shape of abatement.
Thus it would be considered that, in the preceding example, three years' discount upon 1001. at 4 per cent. is 12/., or 88l. would be considered as the present value.
In transactions which usually proceed on compound interest, as in valuing leases, annuities, &c., the principle of discount is strictly preserved. The present value in the preceding case is, in its most usual and the discount D — (I + )"; where e is the rater pound (not : thus it is •04 for 4 per cent.). But recourse is usually had to the tables of present values which accompany all works on annuities or compound interest.
The name of discount is also applied to certain trade allowances upon the nomi nal prices of goods. In some branches
of trade these allowances vary according to the circumstances which affect the markets, and what is called discount is in fact occasioned by fluctuations in prices which it is thought convenient to main tain nominally at unvarying rates. This system is practised in some branches of wholesale haberdashery business, and we have now before us a list of prices fur nished to his customers by a manufac turer of tools at Sheffield, in which the nominal price of each article is continued the same at which it has stood for many years, while to every different species of tool there is applied a different and a fluctuating rate of discount, this fluctua tion constituting in fact a difference of price between one period and another : the rates of discount in this list vary from 5 to 40 per cent. upon the nominal prices of the different articles.
The term discount is also employed to signify other mercantile allowances, such for example as the abatement of 12 per cent, made upon the balances which un derwriters, or insurers of sea risks, re ceive at the end of the year from the brokers by whom the insurances have been effected. The word discount is further used, in contradistinction to pre mium, to denote the diminution in value of securities which are sold according to a nominal value, or according to the price they may have originally cost.
If, for example, a share in a canal com pany upon which 100/. has been paid is sold in the market for 981., the value of the share is stated to be at 2 per cent. discount.