£. s. d. qr. 210: 7: 6:0

210: 7:6 Principal firft Year

5 Intereft first Year 10:10: 4:2

10 51: 176 Principal fecond Year 220:17:10:2

Principal for the third Year 231 18: 9:1

d. gr.

Principal for the third Year 231:18: 9:1 Intereft for the third Year 11:11:11: I nearly

Anfw. The whole Amount is 243: 10: 8: 2

Note, Thefe Interests might have been found more compendiously by Art. 306.

342. Scholium. Though the Law does not allow compound Intereft to those Persons who lend Money, yet it is used in purchafing Annuities, freehold Estates,

c. which we intend to explain hereafter in its proper Place; and fhall here only obferve with Mr. Malcolm, that," abftracting from the Reafon of the Law

(which may be the Encouraging of Trade, by employing Money that Way rather than upon Intereft) "if taking Intereft be at all juft, compound Intereft "cannot be unreasonable. For, if I can demand my

Interest, when it is due, I may take that Interest"Money, and lend it out again upon Interest to

any other Perfon; why then may I not lend it out "alfo to the Perfon who has my principal Sum? "And, in Point of Right and Juftice, it is the fame "Thing if I continue or leave that Intereft in his "Hands: Therefore, there is the fame Reason that it fhould bear Interest after it becomes due, as that "the original Sum fhould do fo."

343. R

CHA P. XXIII.

Of REBATE, or DISCOUNT.

EBATE, OF DISCOUNT, is the Rule by which we find either what prefent Money will pay a Debt, which cannot be demanded till fome Time to come, or what must be deducted or abated

out

out of the Debt, at a given Rate of Interest per Cent. per Annum.

344. The ready Money that will fatisfy the Debt, is called the prefent Worth; because, if it was put our to Intereft at the given Rate, for the Time the Dif count is computed, it would amount to the given Debt.

345. The Rebate, or Difcount, is the Money which is abated, or deducted, in Confideration of paying the Money before it is due.

346. Axioms. The given Debt less the present Worth is equal to the Rebate, or Discount; and the given Debt lefs, the Discount is equal to the prefent Worth; fo that, one being known, the other becomes known alfo by a bare Subtraction.

1

ཨི ཙྪཱ

347. Scholium. That an Allowance ought to be made for paying Money before it falls due (which is fuppofed to bear no Intereft till after it is due) is very reasonable; for, if I keep the Money in my own Hand till the Debt becomes due, I may, in the mean Time, put it to Intereft, and receive an Increase of it; but, if I pay the Whole in ready Money, it is giv. ing that Benefit to him; therefore, we have only to enquire what Difcount ought to be allowed. And here fome Debtors will be ready to fay, that fince, by not paying the Money till it becomes due, they may employ it at Intereft, they think, by paying it before due they fhall lofe that Intereft, and, for that Reason, all fuch Intereft ought to be discounted: But here we may reply, that they cannot be properly faid, to lofe that Intereft till the Time the Debt becomes due arrives; whereas we are now to confider, what would properly be loft at prefent by paying the whole Debt, before it falls due; and this can, in Point of Equity or Juftice, be no other than what, being put out to Intereft till the Debt becomes due, would amount to the Intereft of the Debt for the fame Time. Whence this Rule: Find the Amount of Hool for the given Time, and then fay, as that Amount is to the Intereft of 100/. for the given

E

Time,

Fime, fo is the whole Debt to the Difcounturenonreach rach

Question 1. What Discount ought there to be allowed on paying, in ready Money, a Debt of 210%. Tos. due at the End of two Years, Rebate being made "at-1. per Cent. per Annum fimple Intereft a nos

༄། ༤

Solution. Say first, If 1 Year: 5! :: 2 Yearscről. the Intereft of 100%. for 2 Years; hence 100%. + 310%=110 the Amount of 100% in z Years; whence, by the above Rule, we have, as rroM: 10%.

216. 10. 19l. 2s. 8d. 3grs. very near, = the Rebate, or Difcount; confequently, if the prefent Worth had been demanded, then 2 rol. 103. 197. 2 3. 8 d. 3 qrs. = 1911. 75. 3 d. 1 gr. prefent Worth.

the *

349. Corollary. Hence the above Rule may be otherwife written thus: As 1 Year, 12 Months, or 365 Days the Rate propofed :: the Time propofed a fourth Number. Then as 100that fourth Number that fourth Number:: the given Debt the required Difcount, or Rebate.og smiT 14350. The present Worth may be found independent of the Rebate, by confidering, that the prefent Worth must be fuch a Sum, as, being put out to Intereft the given Time, would amount to the whole Debt for in fuch Cafe, and fuch only, neither Party is wrongyed;

* Demonstration Let the Rate per Cent. per Annum set — the Time; d the Debt; x the required Discount then as 1 Year: rt the Intereft of 100. in the Time t, and 100 += the Amount of 100l. in the Time ; alfo 100: 2:

rid

100

འལ འར

the Intereft of the Debt in the Time ; whence

rtd

as

100 + 1000 (the Sum which in the Time ? would

rtd

amount to Juts: 407 01100

up 1 to talo“. the Intereft of the Debt in the Time, which, **erintrame bluow

346.

by: the above Reasoning, is) xarid 100 +&£X*, * 185.

'which divided by +x gives 100+

asvig ads, tot, door to t

rt

Third: x, that is, as the Amount of 100%

the given Time :: the whole Debt: the Rebate.

+ 108.

its firteret for 2.E. D.

ed; because, if either the Perfon who is to receive. or he who is to pay the Money, was to put it to Intereft for fo long a Time, he would have just as much to receive as the Debt. Whence it is evident the following Rule will find the prefent Worth, viz. Find the Amount of 100l. for the given Time; then fay, as that Sum: 100%: the given Debt to the prefent Worth. Or, in other Words, as 1 Year, 12 Months, or 365 Days: the Rate propofed :: the Time propofed a fourth Number: Then as 100 + that fourth Number: 100l. :: given Debt: the prefent Worth.

351. Let it be here required, for Example, to find the prefent Worth (or what ready Money will pay the Debt mentioned in Question the firft, viz.) of 210l. 10s. due at the End of 2 Years, Rebate being made at the Rate of 51. per Cent. per Annum?

Solution. Say firft, if 1 Year 5. 2 Years: 10%. the Intereft of 100l, for 2 Years; hence 100%. で is the prefent Worth (or which is the fame Thing, would difcharge a Debt) of 100l.+ 107.110l. payable at 2 Years End. Confequently, as 110: its prefent Worth 100l.: 210/. 105.: 1911. 75. 3 d. Lgs. nearly its prefentWorth. Q. E. I. And, if the Dif count be required, 210l., 105, 1911. 75. 3 d. 3 grs.— 191. 2s. 8 d. 3 grs. very near, the Discount as before, 352. Scholium. As this Rule is of Ufe in difcounting Bills paid before they are due, it may not be improper to obferve in this Place, (though fomething foreign to our prefent Defign) that, according to Mr. Clare, in his Youth's Introduction to Trade and Bu Jinefs," the Ufance or Usage of Merchants, with Re, fpect to foreign Bills of Exchange, to and from "London to Rotterdam, Antwerp, or any Part of the Low Countries, is one Calendar Month after the Date of the Bill; double Ufance two Months, &c. Ufance from Hamburgh, Copenhagen, StockΔέσ holm, Lubeck, Strasburgh to London, and contra, is "alfo one Month; tho' Bills from thofe and other diftant Places are commonly drawn payable after

66

ἐσ

"Sight,