

piscorxT. 



DISl 



in the and. And it U not fair to 

 litioo of simple interact, and then to com- 



' 



iU ?! K H no equ 

 ye* 1 interest + 

 on making Urtii 



_j of tho*e rule* to reprewnt tin remit* of 

 lining by simple interent, N-t ui *M how the 

 the end of the term you*, upon the different 



of parment* be made, he will Jure KXtf. + four 

 jut received, 42W. in all. with which ho U to go 

 4001. only. 



8. If he receive by the ftnt rule 4001. at the end of six yean, he 

 will at the end of the Mrenth year hare 42(V., .if which 4001. it to go 

 on at interest a* before. 



3. If he rewire by the Moond rule ho will hare at the and of the 

 erenth year (100/. + 2-901.. year*' interest) which he received + 1-088... 

 yean' interest which he make* on the 1(XV. (the other part not making 

 interect) + the sum which will in 1-038... yean yield SOW. I'JS.VIW...)* 

 the intcrot on thi. That U, 4-201. altogether, of which 2W. is interest 

 only : for the I a-t mentioned item, though gained in the manner of 

 interest, U diaoount intended to make up a prinfi/ml. Or, it any one 

 will not admit this Lust distinction, thon tlie most approved nile puta 

 the receiver in a worse position than the old rule. 



The fact in, that if equation of payment* were ever made, it ought 

 to be supposed that all money, principal and interest, becomes pro- 

 ductive money to the receiver from the moment it is received : or 

 compound interest should be supposed. This puta the parties into a 

 state of equity at all times, both during the longest term of debt and 

 after. To show this, suppose that A is due at the end of a years and 

 B at the end of I yean, interest being r per pound. To satisfy this 

 debt by a sum A + B paid at x yean from this time, the equation to 

 determine jc is 



and the receiver of the equated sum, m years after its receipt, or .> + w 

 years from the present time, will have (A + B) (1 + r)" which is 



A (! + >)- 



Or 



And this is precisely what he would have had from the payments 

 themselves. And the accumulations or present value of the equated 

 sum are at all times equal to the accumulations or present values of 

 the payment*. 



There is another remarkable case of the name kind, in which dis- 

 count at simple interest is compared with notions derived from com- 

 pound interest, and a rule is consequently said to be false which is, 

 upon its own hypothesis, perfectly true. The value of an Interminable 

 annuity, calculated at simple interest, comes out infinitely great : or 

 no sum is large enough to pay it. Now it in clear that 20/. will pay 

 an annuity of I/, a year at five per cent, for ever. And this may even 

 be called simple interest, for at the end of a year the interest of the 

 SOL is paid away, and the original principal only remains : so that there 

 is no interest upon interest But the truth is, that in the construction 

 of all rules at simple interest, the money is arbitrarily divided into two 

 part*, productive and unproductive, and a rule which expressly re- 

 quires payment to be made from time to tune out of the productive 

 part, may produce very different results from another in which the 

 unproductive part is paid away first. Now take the case of an annuity 

 for three yean, of M., money making r per pound. The ordinary rule 

 gives 



(1 + r)- 1 + (1 + 2r)-> + (1 + 3r)~ 



At the end of a year, this becomes 



l+2r 



1+r 

 l+3r 



The first term 1 partly principal, partly interest: and I?, of 

 annuity has become due. But the manner in which the rule was 

 framed doe* not allow us to pay away the r(l + 2r)-> and r(l + 3r)-', 

 which are never to make interest again, in part of the first year's 

 annuity, but requires that the 1, part of whi.-h will make interest, 

 should all be so paid. And, when the productive money i broki-n in 

 upon before the unproductive U all gone, it is per- that no 



sum is large enough to pay a perpetual annuity : and, if this be done, 

 not only may the rule for n per|><-tual annuity be objected to, but with 

 a* much justice that for a finite term of years. For instance, at 10 

 percent., an annuity of II for five yean is worth, according to the 

 usual simple-interest mipponitiunt. :t y.iUBU A year's interest is 

 M9201/. ; let this all bo paid away, and the balance of II. made up 

 linoijnl, and wi n. and it will IK> found tli.il there U a sum 

 in band at the end of the ten years: in fact S7!">7!'/. will in this wav 



all demand*. Hut the manner in wlii.-h tin 

 i mippnM* the annual demands to be made up out of prin- 

 cipal and interest in the following way, the mini* before the line- 



showing how the pound yearly accruing due is rated, partly 

 principal, partly out of interest : 



Principal. Interest 



8-89261 -88920 



Pay -90909 -r -09091 = 1. 



: - J 



29885 

 Pay -88888 + -1M67 = 1. 



2-16019 -48008 



21502 

 Pjy -76923 + -23077 = 1. 



1-38096 -41428 



13810 

 Pay -711-29 + -28571 = 1. 



;87 

 Pay -66667 + -38333 = 1. 







1 001 



While if interest were made to go as far aa it could, we should 

 have 



3-89261 

 MMM 



3-28187 after paying 1. 

 32S19 



2-61006 

 2C101 



1-87107 

 18711 



1-05818 

 10582 



16400 



to that there would remain -111/. 



The truth is, that the rule for annuities by discounting at mingle 

 interest it wrong except upon the condition that principal and interest 

 are to be rated in a specified way (which those who understand the 

 formula will easily collect) to meet the accruing demands. And more- 

 over, when interest is to be all disposed of first, before any principal is 

 touched, the rule* for simple and compound inttretl are i<!i utind. 



It is, however, necessary to distinguish between true discount and 

 the discount^of commerce. When a bill of exchange for 1001., having 

 three months to run, is presented by the holder for discount ; the 

 discounter calculates the simple interest on lOOf. for three months, 

 with three days of grace added, deducts this from the amount 

 of the bill and pays over the difference to the holder. Thus it 

 will be found on consideration, that the discounter always obtains 

 something more than the usual and current rate of interest for the 

 money that he thus employs. Bills of exchange, on which are the 

 best name*, are discounted on the lowest or most liberal terms ; 

 because the rate of discount must, of course, rise as the character of 

 the parties to the bill appears to be lower in point of solvency : the 

 rate of discount also has a tendency to rise, when money is scarce, 

 which tendency not (infrequently grows into an effect almost inde- 

 pendently of the character of the paper offered for discount. [See 

 examples under BANK ; where also see lie-discount, vol. i., col. 858. 

 The usual course of the Bank of England in .regard to discounting 

 will be found fully explained in the article BANK, BANKER, BASKING J 

 Also, under other circumstances, when confidence is interrupted, the 

 discounting of bills is only done at very high rates, and in some 

 extreme cases it is altogether refused by the ordinary bill discounters. 

 (' Rep. of Committee on Bank Acts' 1853, p. viii.) 



Discount is also said to take place on merchandise, when a buyer 

 having agreed with the seller to pay for the goods so much on such a 

 day which is to come, before that day arrives finds that he is in cash 

 MithViently to pay, and claims and gets from the seller a deduction 

 from the price so settled, in consideration of his anticipating the day 

 of payment. This discount is in practice made at a rate which usually 

 exceeds the current interest of the day. 



DISO'VKCY IN I..UV. [KyriTY.] 



DISCOVERY. [INVF.XTION AND DISCOVERT.] 



IHSCUS (t'urxat, ditcot), a quoit of stone, brass, or iron, 10 or 12 

 inches in diameter, with which the Greeks and KomaiiH diverted them- 

 selves in the public games. The discus, when perforated like our 

 modern quoit, was thrown l.y the help of a thong, put through the 

 middle of it. It was at other times of a solid piece, and was then 

 hurled directly from the h and. The object was to throw it to as great 

 a distance as possible. This last method is illustrated by the celebrated 

 ntAtue of the Discobolus, or quoit thrower, attributed to Myron. Of 



