DISCOUNT, the difference between a sum of money due at a future period and its present value; or the deduction made from the amount of a debt that is paid before it is due. It is usually ascertained—in the case of bills of exchange, promissory notes, and the like—by subtracting from the principal amount its interest, calculated from the date of payment until the date when the amount is due; but this, although sanctioned by usage, leads to an excess of charge, time interest being thus advanced to the lender before it has actually accrued. True discount is computed as follows: Suppose that £100 is advanced for one year at, say 5 per cent, the sum repayable at the end of the year in respect of this advance will be £105; therefore, £100 is the present value of £105 due a year hence; and from this conclusion it is easily deduced by proportion, that the value of £100 due a year hence is £95 4s. 9id. Hence the true discount on £100 due in a year at 5 per cent, is £4 his. 21d-. The usual formulas are—for the present value, 100 100-F Ar • • r for the discount, ; where " A" is the principal sum due; " n " the fi time, in years or fractions of a year; and "r" the rate per cent, simple interest being assumed. For example, let it be required to find the discount on £97 7s, Gd., due seven months hence, at 4+ per cent. Here A=£97 7s. 6d.=97.375, r=4+; nr=f1X:=
Anr= 97.375 100-1.-nr=100-K-= 204.4875 = 2.491= £2 9s. 10d.
Hence the discount is 821 821 But it is easier first to determine the present value, and hence, by subtraction from the amount due, the discount.
An extension of the above formulas is necessary in computations connected with leases, reversions, etc., to be valued on the stricter principle of compound interest, for which see INTEREST.
By discount is likewise understood the depreciation in value of a fixed investment; as when a railway share, on which say £100 has been paid, can be sold for £90 only, the " discount" being thus 10 per cent.
The allowance made to a trader, under the name of discount, for prepayment of a debt, is usually greater than the current rate of interest, as the creditor receiving the money before it becomes due, secures himself against the insolvency of the debtor.
The rates of discount vary according to the demand for money and the nature of the security. The range in Britain is from 3 to 10 per cent, except in the case of doubt. ful bills or post-obit bonds, when a much higher rate is exacted. Bills at and under three months' currency are usually charged a per cent less than those of a long date. In the colonies higher rates are allowed.