The scales of commerce and trade: ballancing betwixt the buyer and seller, artificer and manufacture, debitor and creditor, the most general questions, artificiall rules, and usefull conclusions incident to traffique: comprehended in two books. The first states the ponderates to equity and custome, all usuall rules, legall bargains and contracts, in wholesale ot [sic] retaile, with factorage, returnes, and exchanges of forraign coyn, of interest-money, both simple and compounded, with solutions from naturall and artificiall arithmetick. The second book treats of geometricall problems and arithmeticall solutions, in dimensions of lines, superficies and bodies, both solid and concave, viz. land, wainscot, hangings, board, timber, stone, gaging of casks, military propositions, merchants accounts by debitor and creditor; architectonice, or the art of building. / By Thomas Willsford Gent.

THE SECOND PART.

Definitions and Etymologies of Usury and Interest Money, with the several operation compendiously displayed.

USury is derived particularly from Usu∣ra, ab usu aeris, or generally from the use and occupation of any thing, as Money, the worth or estimate of it, upon some mutuall contract, where∣in the Debtor allows the Creditor a Loan in lieu of the money or goods borrowed; which in times past hath been at liberty as men could agree; but when the unsatiable avariciousness of rich misers attracted extortion from the indigency of borrow∣ers, the corroding use of money was by provident Lawes confined to a certain rate, as to 10 L per cent. per ann. afterwards to 8 L, and now of late to 6 L, that is, if a Creditor lends 100 L for a year, he may legally exact 6 L profit for the use of the mo∣ney lent.

These are divided into 3 parts, viz. Principall, Time, and Interest: the first signifies the summe, or value of the money or goods so lent: Time is the forbearance of it, as Dayes, Weeks, Moneths, or Years. Thirdly, Interest is the profit that arises from the other two, and is derived from two com∣pound Latin words, viz. inter and est, ab edo, to eat or devour, as it is the property of Use to do; they have these proportions, as the Principall to the Time, the Rate contracted for, and Interest to it self, and generally as commixt with one ano∣ther.

Interest resembles Janus with two faces, one looking upon the time past, the other on that to come: i•• this tract the Principall runs, like a snow-ball rising upon an even superficies, equally moving, but the encrease unequall, although pro∣portionall to the body, as it is magnified in the motion; and if continued, in time it will gather up all: this is called Forbearance. And Rebate or Discount of money is like the tract in which a snow-ball moved, and in its descent takes up all untill it is staid, leaving the ground bare from whence it takes a seeming originall, where Time hath not arrived, but beholds it, as sea-men an ob∣ject, which seems little at a great distance, and en∣creases to the Optick sense by unsensible approa∣ches.

Use or Interest hath in either Predicament two Species, viz. Simple or Compounded, the first is computed from the Principall and Time onely, up∣on a certain rate given or allowed, whether ascend∣ing or descending, as in Forbearance, or upon

discount, which are thus explained; if 100 L be continued for 2 years, at 6 L per cent. per ann. the creditor at that term of time is to receive but 112 l, that is 12 L for simple interest in lone of the mo∣ney forborn; here 100 L is the principal lent, the term 2 years, the use 6 L per ann. whereas in com∣pound interest, the first payment attracts a propor∣tional use: as admit in annual disbursements, in the second year there is an use required, or imposed on the 6 L due, if continued, and therefore it is called interest upon interest.

Discount or rebate of money is upon a legacy, or summe due to be paid at a time to come, yet satis∣fied or discharged with so much present money, as immediately put forth at an interest or rate allowed forborn untill the legacy should have been due, re∣turns again to its first principal or summe, the mo∣ney paid being computed at the same rate of inte∣rest for the forbearance, as was the discount made, as by following examples shall be illustrated, ob∣serving these proportions, viz.

The RULE.

As the principal and time for which a lone is al∣lowed,

Shall be in proportion unto the interest thereof,

So will any other summ of money to be borrowed

Be proportional to the interest for the same time.

PROPOSITION XXXVIII.

What comes the interest of 145 L unto, forborn a year at 6 L per cent, per ann?

An explanation of simple interest. Lib. 2. Parag. 8.

Any question of this nature 〈 math 〉〈 math 〉 is with facility performed by the common rule of Three, as if 100 L principall forborn a year requires 6 L interest, the 145 L for the same term of time will exact 8 7/10 L, as in the table, that is, 8 L 14 ss. the question answered.

PROPOSITION XXXIX.

A Money-Merchant employed at Use 250 L sterling for 5 moneths, at the rate of 8 L per cent. per ann. and the simple interest of it is here requi∣red.

An explanation of simple interest, lib. 2. par. 10.

All questions of this

	Prin. In. Prin.
1 Rule	100-8-250
	M—M
2 Rule	12-5
Product	1200. 8. 1500
Or as	3 to 1 so 25
Facit	8 L.. 6 ss 8 D

kind doe consist of 5 termes, viz. 100 L Principall, secondly, the rate for Use, as in this, 8 L. thirdly, the Principall lent, as in the first rule; in the second rule under 100 l is placed the time for which 8 L was due, as at a yeare, or 12 moneths: the fifth number is the term for the principall bor∣rowed, viz. 5 moneths, the products of those are 1200. 8 and 1250, and may be reduced (as in the 13 and 14 Axiom, lib. 1. parag. 7.) to 3.1. 25. the quotient here answers the question, viz. 8 L 6 ss 8 D, the proportionall interest, for the summe and time required.

PROPOSITION XL.

A Banker did lend 650 L. which principall was repayed at the term of 6 moneths 3 weeks and 3 days; what came the interest of it to at 6 L per cent. per ann.

An explanation of simple Interest. lib. 2. parag. 10.

In this double

	Princi. Inter. Princ.
1 Rule	100... 6... 650
	D — D
2 Rule	365 192
Prod. 36500. 6. 124800
Or as- 365 to 6. so 1248
facit 20 l 10 ss 3 d. 2 34/73 Q

rule the first term is 100 l. the second its interest for a yeare, the third is the prin∣ci••al lent: the first term of the second rule 365, the num∣ber of dayes in a vulgar year; the last term is 192, the number of dayes terminating the time, accoun∣ting 4 weeks to the moneth; the products of these are 36500, and 124800, and reduced will be 365 and 1248. which multi••lied by 6 l the interest is 7488, and divided by 365 the quotient will be (in a direct proportion) 20 l 10 ss 3 d 2 34/73, as in the table, the simple interest of 650 l. the time requi∣red.

PROPOSITION XLI.

A man received 8 l 6 s 8 d for 5 moneths interest of a summe unknown, but at the rate of 8 l per cent. per ann. and the principall is here the thing deman∣ded.

An explanation of this Proposition, lib. 2. parag. 10. quest. 4.

〈 math 〉〈 math 〉

In the first rule, as 8 l interest is to 100 l princi∣ple, what 8 ⅓ the interest received: in the second rule stands the terms of time, viz. 12 mo. and 5 m. which multipliers and the 2 dividers encreased re∣ciprocally by one another, they will produce these 3 numbers, viz. 40. 100. 100. all questions of this nature are made either direct or reverse, according∣ly as the products are placed; but by either way the quotient will be discovered, 250 l the princi∣pal lent, as in the table; the proposition solved ac∣cording to demand.

PROPOSITION XLII.

What shall the simple interest of a mixt principall, as 265 l 13 ss 4 d 1 q. amount unto at 6 l per cent. per ann.

An explanation of interest money by the rules of practise: Lib 2. Parag. 9. Que••t. 4, 5, & 6.

The encrease

100 L. 6 In. 265 L. 13 ss. 4 ¼ D.
Products L 15	94. 00. 1 ½ 20
100 L divid. 6 L multipl.	S 18	80
	12
D 9	61/4
Q 2	46
26/100	or 23/50

of any mixed summe will be thus discover'd; first place your proposition ac∣cording to the demand made, as here viz. if 100 L requires 6 L interest, what shall the principall given, as 265 L 13 ss 4 ¼ D in this, 6 is the multiplier, with which encrease the principall, as in lib. 1. sect. 1. parag. 4. exam. 9. and the product will prove 1594 L 0 ss 1 ½ D. here draw a line as in the ta¦ble, cutting off two places on the right hand, a•• 94, because 100 is the divisor, the quotient 15 L secondly, the remainder 94 or 94/100 reduce into. shillings, by the multiplication of 20 the product will be 1880, and being no shilling left in the last operation, sever 2 places with the line, the quoti∣ent is 18 ss, the remainder 80, which by 12 reduce into pence, and adde to it 1 D remaining in the first product, cut off 2 figures on the right hand, viz. 61, so on the left hand there will be 9 D. the 61 reduced into farthings by 4, produceth 244, to which adde the ½ D remaining yet in the first pro∣duct, the summe is 246, that is 2 Q. and 46/100. so

the totall interest for a year of 265 L 13 ss 4 ¼ D at 6 L per cent. comes unto 15 L 18 ss 9 D 2 2••/50 Q, as by the operation in the table is conspicu∣ous.

PROPOSITION XLIII.

To finde the Use-money of any summe, whose prin∣cipal and interest are of severall denominations; as 956 L 7 ss 6 D, at 5 L 17 ss 6 D per cent. per ann.

An Explanation.

To solve any que∣stion

Prin.	Inter.	L	ss	D
100	5. 17. 6.	956	7	6
				5
The products	4781	17	6
478	3	9
239	1	10 ½
119	10	11 ¼
The in∣terest money	L 56	18	14	0 ¾
ss 3	74	17	6
D 8	88	〈 math 〉〈 math 〉
Q 3	55/••00

of this kinde, state the propositi∣on as in the head of the table, then take the greatest deno∣mination of the in∣terest allowed, as in this example, 5 L. which multiply through all the de∣nominations of the principall here sta∣ted, according to sect. 1. parag. 4. examp. 9. the product will prove 4781 L 17 ss 6 D. had the in∣terest been 6 L, the product would have contained

the principal once more; but being 17 ss 6 d, di∣vide it into proportional parts, lib. 2. parag. 9. quest. 4. as in the table at A, viz. 10 ss. 5 ss. and 2 ss 6 d. for the 10 ss take ½ the principal, that is half of 956 l 7 ss 6 d, which will be 478 l 3 ss 9 d. next for 5 s take ¼ part of the principal, or ½ the last, which is 239 l 1 s 10 ½ d, and the half of that again is 119 l 10 s 11 ¼ d. the total of all these is 5618 l 14 s 0 ¾ d. this done, divide the greatest denomination by 100 l, or cut off two places on the right hand, and you will find 56 l and 81 remaining, with which proceed as before, and you will discover (as in the table) the interest to prove 56 l 3 s 8 d 3 5••/100 q. the simple use for a year, as was required: and thus may all other propositions be expeditely solved by this operation, and the rules of practise.

PROPOSITION XLIV.

What amounts the interest money unto upon a mixt principall, for a time lesse or greater then a yeare, as 645 l 6 s 8 d, lent for 11 moneths, at 5 l per cent. per ann.

An Explanation.

State the question

Prin. Inter.	L	S	D
100 L 5	645	6	8
Product	3226	13	4
Products	1613	6	8
806	13	4
537	15	6 ⅔
The interest	L 29	57	15	6 ⅔
	20
S 11	55	Months 11
D 6	66	6
Q 2	66	A 3
		2

as in the head of the table; that multipli∣ed by the interest al∣lowed in this 5 l, the product is 3226 l 13 s 4 d. now being the money is to be continued but 11 moneths, take pro∣portional parts, as in the table at A, 6 M. 3 M. and 2 M. for the 6 M. take halfe the first product, then ¼ and ⅙. or thus, ½ of 3226 l 13 s 4 d. is 1613 l 6 s 8 d for 3 Months, the ½ of that is 806 l 13 s 4 d. lastly. 2 moneths ⅓ part of the former, which is 537 l 15 s 6 ⅔ d. this done, proceed as in the last, or by 42 proposition, and you will discover the interest money to be 29 l 11 s 6 d 2 66/100 q. the demand performed, and if it had been required for any longer forbearance, finde the interest for the term of years by the former propositions, and the parts of a year by this.

PROPOSITION XLV.

What shall the Use-money come unto of any summe, whose Principall, Interest, and Time, are all com∣pounded numbers, viz. 543 L 13 ss 4 D, to be conti∣nued for 9 moneths, at 5 L 12 ss 6 D per cent. per ann.

An Explanation.

The propositi∣on

Princip.	Interest	L	S	D
100	5. 12. 6	543	13	4
Products of in∣terests per cent. per ann.	2718	6	8
271	16	8
67	19	2
The totall is	3058	2	6
Interest in respect of time	1529	1	3
764	10	7 ½
(A)	L 22	93	11	10 ½
5 l 12 s 6 d		20
5 L	S 18	71	months 9
½	10 ss	D 8	62	B 6	½
¼	2 ss 6 D	Q 2	½	B 3	½

being stated (as in the head of the table) multi∣ply the principal by the greatest denomination of interest, viz. 5 L, as in the table at A, according to the prescribed rules of practise, lib. 2. paragr. 9. quest. 4. for the 10 ss take half the principall, and for the 2 ss 6 D ⅛ or ¼ part of the last, so you will produce these 3 numbers 2718 L 6 ss 8 D. secondly, 271 L 16 ss 8 D. and thirdly, 67 L 19 ss 2 D. the totall is 3058 L 2 ss 6 D to be divided by 100 L, if forborn a year; but the term of time here is but 9 moneths, as in the table at B, which I divide into two parts, viz. 6 M.

and 3 M. then take half the totall, that is, 1529 L 1 ss 3 D, and for 3 moneths the half of that 764 L 10 ss 7 ½ D. the totall is 2293 L 11 S 10 ½ D, to be divided by 100 L. now proceed according to the former examples, and you will find the interest de∣manded 22 L 18 S 8 D 2 ½ Q. the proposition solved.

If this question had depended on moneths, weeks, and dayes, you must have taken proportio∣nall parts, and proceed, as before is specified; so there needs no more examples for the ingenious, to whom all other questions (in the rules of pra∣ctise) will be direct, and indirect for others, to in∣cumber their understandings with multiplicity of wayes in this kind, therefore I will onely shew you the discount of money, and proceed to Decimall Tables of compounded Interest.

PROPOSITION XLVI.

Upon any interest per cent. and the summe of mo∣ney that shall be due at the term of a year, to find the worth of it in ready money, or present pay, the inte∣rest deducted from the summe.

The RULE.

If 102 L and the annual interest due at a years end

Be worth a 100 L at one entire and present pay∣ment,

What shall any other summe due at that term

Be worth in ready money, the interest deducted?

An explanation of this rule in discount, or rebate of money, lib 2. parag. 8.

Admit the interest were 〈 math 〉〈 math 〉 6 l per cent. per ann. which added to 100 l makes the summe 106 l to be rebated: for if this principal were due at the term of 12 mo∣neths, it were worth 100 l present pay, because at 6 l per cent. it would encrease in a years space unto 106 l again: from hence this rule of antepayment is framed, and all questions of this condition (if terminated by a year) are solved, as in this example; suppose 546 l shall be due at the term of a year, and desired presently, rebating at 6 l per cent. per ann. the proportion is evident, viz. as 106 is unto 100, so shall 546 be to 515 09••/1000 l, which decimal fra∣ction is 1 s 10 ½ d. so 546 l, which should have been due at a yeares end, is worth upon discount present pay 515 l 1 s 10 ½ d, as in the table is de∣monstrated by a decimal, and in a natural fraction, it will be 515 5/53 l.

PROPOSITION XLVII.

A Legacy, or any summe of money not presently due, and to be discharged at two severall payments, as the first at 6 moneths end. the other at the term of a year, how much money will discharge it at one pay∣ment, discounting 10 l interest per cent. per ann.

The RULE.

As 12 moneths, or the true term of a year

Is in proportion to the annual interest allowed,

So the moneths, or term for day of payment

Shall be proportional to the interest for the time.

An explanation of discount or rebate of money, for dayes, weeks, moneths, &c.

In all questions upon re∣bate 〈 math 〉〈 math 〉 of mony at simple inter∣est for the space of a year, ob∣serve the last proposition: but if for a greater or shorter term of time, viz. moneths, weeks, dayes, &c. or dayes, weeks and moneths; in all such cases you ought to find a proportional interest for those annual parts, because the money due at several payments is terminated therein,

as the other in a year. As for example: there is a Le∣gacy of 1000 l bequeathed to T. W. at equall pay∣ments, viz. 500 l to be paid at the end of 6 months, and the other 500 l at the period of a year: what is it worth present pay, rebating at 10 L interest per cent. per ann. as for the last payment, form the rule of Three according to the last proposition, viz. as 110 L is to 100 L, so 500 L will be in proportion to 454 L 6/11 L. now for that due at 6 moneths end, find a proportionall intere t for the time (ac∣cording to the rate allowed) as by the first of these tables in the margent, which is 5 L. and by the se∣cond tables operation you will find for the fourth proportionall number 476 4/21 L, the value of the first 500 L present pay: the summe of both pay∣ments 930 170/231 L, 930 L 14 sh 8 48/77 D. the Legacy as valued present pay upon rebate at 10 L per cent. per ann. simple interest, which in the first table re∣quired no rule to discover it, but many other pro∣positions may, therefore it was inserted by me, and made plain as it is generall; if the respite of time had been for more or fewer moneths, with weeks and dayes, the manner of operation is the same in effect, therefore to write ane more of this would prove superfluous unto the ingenious Arith∣metition; so of simple interest I will here con∣clude.

Many rules do seem originally derived from Truth, or extracted from Art, but if well observed, they are easily detected, being erroneously reered upon falacious grounds, and their derivations from imaginary principles, viz. as in interest, dis∣count of money, Equation in payments relating to

Time and Interest, &c. These I have inserted to please some, but not to delude any, the wayes be∣ing common in generall received customes, plain, easie, and of good use, the errours not being great or considerable in small summes, or in a short for∣bearance, as in Bonds, they rarely pleading pre∣scription of years, or exeeding an annual revoluti∣on, upon forfeiture in transgressing a penal Law; whereas rebate or discount of Mony often depends upon long terms, involv'd with multiplicity of ante∣dated years, as in purchasing of Leases, Pensions, An∣nuities, Reversions, &c. therefore these were com∣posed so compendious as I could, since there be better rules extracted from Artificial numbers, and Decimal Arithmetick in compound Interest, as those following.

A Decimal Table of Interest money forborn any num∣ber of dayes, weeks, moneths, or years, to 25 inclu∣sive, accurately calculated at 6 l per cent. per ann.

Dayes	Decimall numbers	Yeares	Decimall numbers
I	1.000160	I	1.060000
II	1.000319	II	1.123600
III	1.000479	III	1.191016
IV	1.000639	IV	1.261477
V	1.000798	V	1.338226
VI	1.000958	VI	1.418519
		VII	1.503630
Weeks		VIII	1.593848
		IX	1.689479
I	1.001118	X	1.790848
II	1.002237	XI	1.898298
III	1.003358	XII	2.012196
Moneths		XIII	2.132928
		XIV	2.260904
I	1.004867	XV	2.396558
II	1.009760	XVI	2.540352
III	1.014674	XVII	2.692773
IV	1.019613	XVIII	2.854339
V	1.024576	XIX	3.025599
VI	1.029563	XX	3.207136
VII	1.034574	XXI	3.399564
VIII	1.039610	XXII	3.603537
IX	1.044671	XXIII	3.819750
X	1.049756	XXIV	4.048936
XI	1.054865	XXV	4.291871

The second Table of compound Interest money dis∣counted for dayes, weeks, moneths, or yeares, unto 25 inclusive, exactly calculated at 6 l per cent. per ann.

Dayes	Decimall numbers	Yeares	Decimall numbers
I	.999840	I	.943396
II	.999681	II	.889996
III	.999521	III	.839619
IV	.999361	IV	.792093
V	.999202	V	.747258
VI	.999042	VI	.704960
		VII	.665057
Weeks		VIII	.627412
		IX	.591898
I	.998883	X	.558394
II	.997767	XI	.526787
III	.996653	XII	.496969
Moneths	XIII	.468839
XIV	.442301
I	.995156	XV	.417265
II	.990335	XVI	.393646
III	.985538	XVII	.371364
IV	.980764	XVIII	.350343
V	.976013	XIX	.330513
VI	.971286	XX	.311804
VII	.966581	XXI	.294155
VIII	.961859	XXII	.277505
IX	.957239	XXIII	.261797
X	.952643	XXIV	.246978
XI	.947988	XXV	.232998

Table 3. Forbearance of annuities, rents, or pensions from 1 year to 25, at 6 l per cent. per ann.	Table 4. Discount of an∣nuities, rents, or pensions, from 1 year unto 25, a•• 6 l per cent. per ann.	Table 5. Purchase of an∣nuities, rents, or pensions from 1 year unto 25, at 6 l per cent. per ann.
Years	Deci. N.	Years	Deci. N.	Years	Deci. N.
I	1.00000	I	.94340	I	1.06000
II	2.06000	II	1.83339	II	.54544
III	3.18360	III	2.67301	III	.37411
IV	4.37462	IV	3.46510	IV	.28859
V	5.63709	V	4.21236	V	.23740
VI	6.97532	VI	4.91732	VI	.20336
VII	8.39384	VII	5.58238	VII	.17914
VIII	9.89747	VIII	6.20979	VIII	.16104
IX	11.4913••	IX	6.80169	IX	.1470••
X	13.18079	X	7.36009	X	.13587
XI	14.97164	XI	7.88687	XI	.12679
XII	16.86994	XII	8.38384	XII	.11928
XIII	18.88214	XIII	8.85268	XIII	.11296
XIV	21.01506	XIV	9.29498	XIV	.10758
XV	23.27597	XV	9.71225	XV	.10296
XVI	25.67253	XVI	10.10589	XVI	.09895
XVII	28.21••88	XVII	10.477••6	XVII	.09544
XVIII	30.90565	XVIII	10.82760	XVIII	.09236
XIX	33.75999	XIX	11.15811	XIX	.08962
XX	36.78559	XX	11.46992	XX	.08718
XXI	39.99272	XXI	11.76407	XXI	.08500
XXII	43.39229	XXII	12.04158	XXII	.08305
XXIII	46.99583	XXIII	12.30338	XXIII	.08128
XXIV	50.81557	XXIV	12.55036	XXIV	.07968
XXV	54.86451	XXV	12.78335	XXV	.07823

The construction of Decimal Tables for Use money, made proportional for any interest, time, or terme of years required, with the applications of these il∣lustrated with usefull and compendious examples.

All questions of compound interest money may be comprehended and solved by one of the 5 pre∣cedent Tables, calculated (without sensible errour) and extracted from the former prescribed rules, as in the 38 and following Propositions of simple in∣terest: And first, here observe that these Tables are composed upon the worth or interest of 1 L princi∣pal per ann. after the rate of 6 L per cent. yearly payments, as the Law now commands, with a pro∣hibition of any greater interest, upon the penalty of a forfeiture, excepting such cases wherein there depends some apparent hazard, as in Exchanges, Cambio Maritimo, or in Bonds and Obligations not satisfied, that antedate the Act, &c. and upon this foundation are erected these tables, whose cal∣culations I will first exhibit to your view, both for farther satisfaction, & the composing of any others upon other rates or proportions; and then proceed unto the use and explication of these.

The proportions of compound Interest Money, in Decimall numbers, due upon the lone of 1 L Principall.

RULE 1.

As 100 L sterling lent for term of a year

To the summe of the Principal and interest allowed,

So shall 1 or an unite of the first denomination

Be unto the principal and interest in a Decimal.

RULE 2.

As 100 L sterling forborn the term of a year

Shall be in proportion to the last years Decimal,

So will the summe of the principal and interest

Be unto a Decimal for the succeeding year.

An illustration.

		Prin.	Decimal	Principal	Decim.
I		100 l	is to 106	so wil 1 l be to	1.060000
II		100 l	is to 1060000	so 106 l is to	1.123600
III	as	100 l	is to 1123600	so 106 l unto	1.191016
IV		100 l	is to 1191016	so 106 l unto	1.262477
V		100 l	is to 1262477	so 106 l unto	1.338226

In the construction of these tables, take an unite with what number of ciphers you please for the Radius, one place more then you intend to in∣scribe,

but of no necessity, as here 1,000,000, the seventh place being an integer, all the other to∣wards the right hand are fractions, or representing their places according to my third book of Artifici∣all Arithmetick: now for framing the first table (wherein the principal is forborn) adde the princi∣pal and interest together; the summe is here 106, annex 4 ciphers or points to it, equal to the Radi∣us, and it is a decimal fraction for the 1 L forborn a year; or by the first rule, as 100 L is to 106, the principal and interest allowed, so shall 1 L princi∣pal be in proportion to 1.060000, which is a mixt decimal fraction, and comprehends the 1 L princi∣pal, with the interest 06/100, and reduced is 1 ss 2 d 1 ⅗ q. but leaving it involved, as the encrease of the first year, all the rest will be discovered by the second rule successively, viz. as 100 L to 1.060000, so 106 the principal and interest to 1.123600, the decimal for the second year; then for the third year, as 100 L is to 1123600, so 106 in proportion to 1.191016 in the same manner of operation, you will find 1,262477 for the fourth year, and 1,338226, a proportional decimal fra∣ction comprehending 1 l principal forborn 5 years, with the compound interest of it, which is 6 ss 9 d, and not one farthing more: thus you may proceed to what number of years occasion shall require.

To finde Decimal Numbers for any parts of a year, as moneths, weeks, dayes, or for half years and quarterly payments.

Take the Decimall for a yeares interest, viz. 1.060000, whose Quadrat Root extracted as in lib. 2. parag. 1. examp. 5. you will find 102956, a proportional decimal, for the interest of 1 l forborn 6 moneths, in money 7 0••44/10000 d. the mean proporti∣onal betwixt 1.02956 and 1.06000 will be the de∣cimal for 9 moneths, viz. 1.04467, and be∣tween an unite or 1, and 102956 will be .1.01467, a decimal mixt number (according to compound interest for 3 moneths) equal in value to 1 L 0 ss 3 ½ d. and thus you may with facility discover all the other numbers: if the annual table had been for half yearly or quarterly payments, you must find 1 or 3 mediums between every continued and suc∣ceeding year; which to effect, I refer the Reader to lib. 2. parag. 6. prop. 1. and 4. and observe to an∣nex ciphers to the Decimal (whose Root is requi∣red) in such a number as to equal the places in the table, and point them from the left hand to the right, so that the first prick of your pen may be o∣ver the radius or integer. In other things observe lib. 2. parag. 1. exam. 5.

The framing of the second Table for discount or rebate of money.

RULE 1.

As 100 L with the interest due at a yeares end

Is unto the principall 100 L present pay∣ment,

So an unite or 1 L due at the same terme of time

Shall be to a Decimal fraction interest dedu∣cted.

RULE 2.

As 106 L upon discount for the terme of a year

Shall be in proportion to the Decimall last found,

So will 100 L Sterling, or its value, present pay∣ment

Be proportional to a Decimal for the time re∣quired.

An illustration.

		Prin.	Decimal	Principal	Decim.
I		106 l	is to 100 L	so wil 1 l be to	.9433962
II	as	106 l	is to .9433962	so 100 l is to	.8899964
III		106 l	is to .8899964	so 100 l unto	.8396192

The second Table for discount or rebate of mo∣ney at 6 L per cent. per ann. is thus composed for the first year and Rule 1. as 106 L due at a years end shall be worth 100 L present pay, so will 1 L principal (according to the rule of Three in Decimals) be in proportion unto 9.433962; which fraction is in money 18 ss 10 d 1 66/100 q. the value of 1 L due at a years end, and presently paid upon discount: but if not due until 2 years shall be expi∣red: say as 10 6 L is in proportion to the first years decimal fraction, viz. 9.433962, what shall 100 L produce? 8.899964. then for the third year, as 106 L is to the last decimal found, viz. 8.899964, so will 100 L present pay be in proportion unto 8396192. which fraction of 1 L reduced is 16 sh 9 ½ d. and thus you may continue it to what num∣ber of years you please, and inscribe what places of decimals you think fit, but make them all to one Radius, and one place less upon discount, being but fractions or parts of 1 L principall, viz. 943396/1000000 as in the first year.

How to find Decimal numbers for parts of a year upon discount, or for half years and quarterly payments.

These are composed after the same manner as the table of money forborn, excepting onely in pointing the numbers for the Roots extraction, the first Decimals being all mixt numbers, and those of

discount are every one proper fractions, having onely a point prefixt for the Radius or integer; therefore in these make the first point under the second figure on the left hand. As for example, 943396 is the decimal for the years rebate of 1 L, put the first point under the figure of 4, and so in order to the right hand, the root thus extracted will be .971286 in 6 places for the discount of 1 L, 6 moneths as 6 L percent. the square root of that again will be .985538 for 3 moneths; and thus proceed with mean proportionals until the places are all compleat between the radius and the decimal last found; as for half yearly and quarter∣ly payments, they are discovered as were those be∣fore in the forbearance of money, to which I re∣ferre you, and Lib. 2. Paragr. 6. Proposition 1. and 4. observe the 2 Tables, for out of these grounds the other 3 are framed and erected as followeth.

The invention of Decimall Fractions, or proportionall numbers for the third Table.

Here are two tables

Forbearance of money at 6 l per cen. (1)	Forbearance of Rents at 6 l per cen. (2)
1	1. 060000	1	1.000000
2	1. 123600	2	2.060000
3	1. 191016	3	3.183600
4	1.262477	4	4.374616
5	1.338226	5	5.637093
6	1.418519	6	6.975318
7	1.503630	7	8.393837

inscribed for 7 years, whereof the one is the transcription of the first breviat, out of which the third table is composed, & thus: an Annuity, Rent, or Pension of 1 L per ann. is but so much mony due at the term of a year, therefore on the head of the table I place the Radius, against the interest and principal of 1 L forborn a year, viz. in the first table 1.060000, in the second 1.000000. the summe of these two numbers is 2.060000, the rent which will be due at the two years end: in which time there will be 2 L in arrears, and the annual interest of 1 L, to which adde the second yeares forbearance, viz. 1.123600, the summe will be 3.183600 for the rents 3 years forborn, and thus in order, the 6 years added together will make the seventh as 8.393837, and the seven years the 8, viz. 9.897467, which reduced is in money 9 L 17 ss 11 d 1 ½ q. and so much 1 L yearly rent or annui∣ty forborn 8 years does amount unto at 6 L per cont. per ann. annual payments and compound inte∣rest: in this manner you may proceed, according to what number of years the first table comprehends.

The construction of Decimal Fractions, or proportio∣nal numbers for the fourth table.

The first of these 2

Discount of money at 6 l per cen. (1)	Discount of rents at 6 l ••er cent. (2)
1	.943396	1	.943396
2	.889996	2	1833392
3	.839619	3	2673012
4	.792093	4	3465105
5	.747258	5	4212363
6	.704960	6	4917323
7	.665057	7	5582380

tables is transcribed out of the second breviat, from whence the the 4th is framed after the man∣ner of the last, for 1 L Pension, Rent or An∣nuity due at a yeares end is worth but so much upon discount as the interest rebated, which at 6 L per cent. is included by this Decimal 943396. and the second years number must be encreased by the Annuity, Rent, or Pension discounted for: therefore adde 889996 unto 943396, the summ will be 1833392 the decimal fraction for the second year, and so proceed to the seventh year of the first table, by ad∣ding that number, 665057 unto 4917323, the sixth years discount in this second table, the summe will be 5582380. the Decimal for 7 years rebate of rent at 6 L per cent, and in this manner continue on the tables to what number of years you please. Here 1 L Annuity discounted for 7 years, is worth in ready money 5 L 11 ss 7 d 3 q. compound in∣terest rebated.

How to find the Decimal Fractions, or proportionall Numbers for the fifth table.

RULE 1.

As the Decimal for 2 years rent rebated

Is equal in value to 1 L annuity for 2 years,

So is 1 L of annuall annuity the same terme of time

In proportion to the Decimal purchased by 1 L:

Or,

As 1.833392- to 1 L- so 1.000000 unto .54544.

Or thus,

As 1 L 16Purchase sh 8 d- is toAnnuity 1 L, so will 1Purchase L be to 10 shAnnuity 10 9/10 d.

An Illustration.

The Annuity, Rent, or Pension, which 1 l will pur∣chase for a year, lies involved in the decimal of 1.060000, according to the first table, there being onely one years forbearance of 1 L, then for the se∣cond year take the decimal fraction of 1 L rent dis∣counted for the term of 2 years, which is 1.833392, in money 1 L 16 sh 8 d. and it is evident how this summe is equal unto 1 L annuity purchased for 2 years, and consequently the proportion will be as in the rule before: if 1 L 16 sh 8 d, or 1.833392 (the decimal for two years rent rebated) be equal to 1 L annuity to continue 2 years; what annuall

rent or pension will 1 L purchase for the same term of 2 years? which fourth proportional num∣ber discovered, will prove .54544, as in the second year of the fifth table, and reduced, is in money 10 sh 10 9/10 d. the annuity or annual pension pur∣chased by 1 L for 2 years, which at 6 L per cent. in the term of 2 years returns to its first principal, the interest considered: now for the third years deci∣mal, as 2.673012 is unto an unite with ciphers, so will 1 L for a purchase be in proportion to 37411, in money 7 sh 5 d 3 q. an annuity to continue 3 years; and thus proceed to what number of years you please, since by the third, fourth and fifth &c. are framed out of the 3, 4, 5 years, &c. respective∣ly answering the years of discount or rebate of rent, as in the fourth table; the fifth being thus finish∣ed, if the half years and quarterly payments be re∣quired, they may be extracted by finding mean proportional numbers, as hath been declared in the calculation of the former table of Decimals; and as for parts of a pound sterling, I refer you to lib. 3. sect. 1. cap. 7. but here note that the precedent tables be continued to one or two places more, otherwise er∣rours will creep in at the root or end of these num∣bers by annexing of ciphers; for which cause (as it is the common custome) these 3 last tables were framed on a lesser Radius (as by one place or de∣gree of figures and ciphers) then are the two first.

The description, use and explantion of these Decimal Tables, accommodated to the compound interest al∣lowed, at 6 L per cent. per ann. calculated with∣out sensible errour in the forbearance or discount of Money, Annuities, Rents, Pensions, and Reversi∣ons, with the purchase of them due upon yearly pay∣ments.

The first Table is divided into 4 columns, and begins with one comprehending the parts of a year, ascending by dayes, weeks and moneths; the third row contains the years from 1 to 25 inclu∣sive, both noted with numeral letters; upon the right hand of these are placed (in Arithmetical cha∣racters) the Decimal numbers made proportional for 1 L forborn, respectively answering the times included, calculated u••on the Radius of a million 1000000. the second table is for discount of 1 L principal, after the rate of 6 L per cent. per ann. made by the former Radius, viz. 1000000, for the same parts and term of time as was the last. This discount or rebate of money is by some termed In∣terest damageable, by reason it is ever lesse then the Principal, although upon a dayes discount, or any shorter time, as you may see in the head of the table, with a title to each column; the first hath the Radius prefixt to the Decimals, the second of Discount have onely points to denote their places, as Primes, they being all proper fractions, and parts of 1 L. the third, fourth and fifth Tables have each 2 columns onely, the first numbring the years from 1 to 25 in numeral letters, and against

those annual computations are placed the Decimal numbers depending on those years, as by their titles do appear: the third and fourth encreases, the fifth declines the Radius; which prolix numbers in these the three last Tables, extends to 100000, and so much for the model and form of them.

The first Tables use illustrated.

QUESTION I. If 1000 L be forborn 1 day, what shall be the inte∣rest of it, after the rate of 6 L per centum per an∣num?

Look in the first Table for 1 day; against which (under the title of Decimal numbers I find 1000160, which multiplied by the principal 1000 l, or annex 3 ciphers to it, the product is 1000, 160000, from whence sever the Radius by cutting off 6 places from the right hand, you will find 1000 L for integers struck off, and the remain∣ing fraction .160000, which reduce, as in lib. 1. sect. 2. parag. 1. paradig. 10. or multiply it by 20, and from the product cut off 6 places, and so pro∣ceed; you will find the loan of 1000 L to be 3 ss 2 d 1 ⅗ q.

QUESTION II. What will the interest of 300 L amount unto, if for∣born 3 weeks, after the rate of 6 L per centum per annum?

The decimal for 3 weeks is 1.003358. which multiplied by the principal 300 L produceth 301, 007, 400. from whence cut off 6 places and reduce them, you will find 301 L 0 ss 1 D 3 q. the encrease of 300 L for the time required, viz. 1 L 0 ss 1 d 3 q.

QUEST. III. What will the interest of 200 L rise unto, if for∣born 6 moneths, after the rate of 6 L per centum per annum?

The Decimal for 6 moneths forbearance of 1 L is 1.029563, so the rule is in this and all the rest; as 1 L, or the decimal 1,000,000 is in proportion unto 200 L, the principal propounded; so the de∣cimal of 1 L forborn the same term of time shall be proportional to 205.912.600. from which com∣pound fraction sever 6 places numbred from the right hand, the integers are 205 L, the fraction 912600 reduced, will be in money 18 ss 3 d, so here the interest of 200 L for 6 moneths proves

but 5 L 18 sh 3 D, whereas, according to cu∣stome, you may discover amongst the vulgar errors the loan of this principal forbo••n half a year comes to 6 L, that is, 1 sh 9 D too much.

QUESTION IV. How much comes the interest of 150 L unto, if for∣born 7 years, at the rate of 6 L per centum per an∣num?

The Decimal against 7 years is 1503630. which multiplied by 150 L produceth 225, 544, 500, and reduced, is in money 225 L 10 sh 10 68/100 D, so the encrease of 150 L, all interest forborn 7 years, swel•• to the summe in clear profit 75 L 10 sh 10 68/100 D, which by the common current of simple interest does multiply in the seven years apprenti∣ship (when the Principal shall be discharged the Indenture) but 63 L, which is less (I conceive) then the intention of the English Laws allow by 12 L 10 sh 10 d. for if any loan upon a principal can be legally exacted in equity, use upon the interest (so often as due) may be as justly claimed by the same prerogative, according to Humane institutions, not warrantable by the Divine Law.

QUESTION V. If 210 L be forborn the term of 3 years, 3 mo∣neths, 3 weeks, and 3 dayes, what will be the encrease at 6 L per centum per annum?

The Products	I	Decimals 1191016 2382032
II	25011336	Yeare:
III	25378356	Moneths
IV	25463576	Weeks
V	25475773	Dayes
The totall is— 254 L 15 ss 1 ¼ d.

In all questions of this kind, seek the Decimal for the longest term of time allowed, as here 3 years, whose artificial number is 1191016, which multi••lied by 210 L (the principal lent) or by 21, lib. 1. sect. 1. parag, 4. exam. 7. as in this table and first row: in the second stands the product, viz. 25011336. to which you may annex the cipher in 210 L. it is not material, the number being one place greater then is the Radius, & yet the product one cipher defective; therefore strike off but 5 places from the right hand, and the fraction redu∣ced, the summe would prove at 3 years end 250 L 2 ss 3 d. But to proceed, the second row for the term of years multiplied by 10.14674 (the Deci∣mal

for 3 moneths) produceth in the third row of the table 25378356, the number for 3 years and 3 moneths, as noted on the right hand of the Ta∣ble; which multiplied by the Decimal 1003358 for 3 weeks, the product will be in the fourth row 25463576, the artificial number for 3 years, 3 moneths, and 3 week; and lastly, multiplied by 1000479 (the decimal for 3 dayes) the fifth row will specifie in the product 25475773, the artifi∣cial number for the whole time, viz. 3 years, 3 moneths, 3 weeks, and 3 dayes; from wh••nce se∣ver the integers, and reduce the fraction, the total appears (as in the table) 254 L 15 ss 1 ¾ d. the true compound interest for the summ and time re∣quired.

The second Table of compound Interest illustrated by Examples.

QUESTION VI. At the term of 6 moneths A is to pay unto B 500 l, but do agree in receiving it presently upon discount, af∣ter the rate of 6 L per cent. per ann. what summe of money will discharge it?

In the second table (for discount of money) I find the decimal for 6 moneths .971286, which fra∣ction of 1 L Sterling multiplied by 500 L, or 5 the product will be 4856430, to which annex 2 ci∣phers, the number will be 485,643,000; from the

right hand cut off 6 places, and reduce the fracti∣on, there will appear 485 L 12 sh 10 ¼ d, the true summe upon rebate, that will discharge 500 L 6 moneths before tis due, which according to the best vulgar custom comes near the truth, as by Pro. 47 of this book (the discount being but for a short time) viz. 485 L 8 sh 8 d 3 q.

QUESTION VII. A had a Lease in reversion, which at the expiration of 7 years was valued worth 1200 L. which Lease B would purchase present pay, rebating at 6 L per cent. per ann. what will be the value of i••?

This differs not essentially from the last, for it is no more but to find the present value of 1200 L not due until 7 annual revolutions be completed. Look in the second Table for discount of money, and in the column against 7 years you will discover 665057, which Decimal multiplied by 1200 L, produceth 798,068,400, from the right hand se∣ver 6 places and reduce the fraction, the summe will appear in money 798 L 1 sh 4 ½ d very near; and so much money present pay B must disburse to A for his Lease in reversion, commencing at 7 years expiration, the thing required.

QUESTION VIII. A is to pay unto B a Legacy of 1800 L, which is to be discharged at 3 several and equal payments, viz. at the end of 6 moneths 600 L, at the term of a year 600 more, and the last payment 6 moneths after that: B desire, it presently, and A is willing upon discount at 6 L per cent. per ann. what summe will discharge it at one present and entire payment?

The summe here

	The decimals		L S d
1	582771600	1	582. 15. 5
2	566037600	2	566. 0. 9
3	549784200	3	549. 15. 8
1698. 593400	1698. 11. 10

propounded is 1800 L at 3 equall pay∣ments: the Decimal for discount of 6 moneths is 971286. which multiplied by 600 L (the first payment to be due at the half yeares end) the product is 582771600, which reduced does prove 582 l 15 s 5 d, then is there 600 l upon a years rebate: the de∣cimal for that term of time is 943396. which mul∣tiplied by 600 L will produce 566,037,600. which reduced into money is 566 L o sh 9 d due upon the years rebate, as in the second row of the table: now the last payment is 600 L upon a year and a halfs discount, to find an artificial number for this; the Decimal for a years discount is 943396, and for 2 yeares 889996. the product of these will be 83.96.18.66.64.16. the Quadrat ex∣tracted as it is pointed will be 916307, a meane proportionall number betwixt the first and second yeare, according unto the construction

of these tables before delivered, and if multiplied by 600 L the last payment (due at that time) the product will be 549784200, as in the third row of the table, and is in money 549 L 15 ss 8 d. the total 1698 L 11 ss 10 d. which summe will dis∣charge all the 3 payments at one time, and present upon discount; and the 3 several Decimals (whose total is 1698593400, and reduced, will prove the same total summe: the money deducted is 101 L 8 ss 2 d.

The third Tables use of compound interest demonstrated by examples.

QUESTION IX. If an Annuity of 60 L per ann. be all forborn 7 yeares, how much will it amount unto when that terme expires.

Look in the third table for Annuities forborn the time specified, where against 7 years you will finde the Decimals 8.39384. which multiplied by 60 L (the annual rent) the product proves 503.63040. cut off 5 places, whereby to sever the integers from the fractions, which reduce into money, and you shall find 503 L 12 ss 7 d. the true value of the 60 L annuity forborn 7 years; the question solved.

QUESTION X. A did owe unto B 186 L, and upon covenant to pay unto the said B a rent of 20 L 13 ss 4 d per an. untill the debt should be discharged; yet after this contract, they both agreed to respite the payments, un∣till the last were due, with this proviso, to pay it all in then, allowing interest for the forbearance, at 6 L per cent. per ann.

Find what number of yeares 〈 math 〉〈 math 〉 would have terminated the An∣nuitie first agreed upon betwixt A and B, for the payment of 186 L by 20 L 13 ss 4 d annual rent, which will be per∣formed by the example in the Table, viz. as 62/3 L is to 1 year, so will 186 L be unto 9 years: which rent is to be respited during the aforesaid term. Look in the Table of Rents forborn, where against 9 years you will find this 11.49132 to be multi∣plied by the decimal of 20 L 13 ss 4. the Deci∣mal of 13 ss 4 d is (as in lib. 3. sect. 1. chap. 7.) 66667, to which prefix the integer 20 L, the to∣tal is 2066667. this multiplied by 11.49132, the decimal for the term of years, the product will be 237-4873183044, according to the rules of Mul∣tiplication in Decimals, lib. 3. sect. 1. cap. 4. sever off 10 places for the fraction, the integer will be 237 L, reduce 5 or 6 places of the fraction, ma∣king the Radius one place more, you will find 9 ss 9 d very near: so A must be responsable to B, or their heirs at 9 years end for 237 L 9 ss 8 d 3 ••/10 q.

This exactnesse was not required, nor yet so great a number taken for the fraction of 13 sh 4 d. but these if understood, the ingenuous will ease them∣selves by my labours, to which end I will proceed.

QUESTION XI. A was to pay unto B 200 L at the full term of 5 years, for which debt A was contented to make B a Lease of a Farm to continue in force the same time, whose annual rent was 35 L. which of them gained by this contract, interest allowed at 6 L per cent. per annum?

In the Table of Rents forborn, under years look 5, the decimal number against it is 5.63709. which multiplied by 35 L (the Rent respited the term of 5 years) the product will be 197.29815, and re∣duced into money is 197 L 5 sh 11 ½ d. which subtracted from 200 L, the remainder is 2 L 14 sh 0 ½ d. and so much A did gain by the bargain or contract made with B.

The fourth Table exemplified in discount of Annui∣ties, Rents, Pensions, or Reversions, at 6 L per cent. per ann. compound interest.

QUESTION XII. What is the present worth of 80 L Rent or Annuity, to continue 25 years, rebating at 6 L per centum per annum?

Look in the fourth Table for 25 years, against

which I find 12.78335. This compound Deci∣mal multiplied by 80 L (the Annuity propounded) the product proves 1022.66800. which redu∣ced into money will be 1022 L 13 sh 4 ¼ d, the true value of 80 L per annum yearly pay∣ments, rebated for 25 years according to de∣mand.

QUESTION XIII. A man hath a Lease of Lands or Tenements worth 15 L per ann. more then the rent, and hath a Lease yet 4 years in being; the Tenant desires to take ano∣ther in reversion for 21 years at the same rent, what must the Lessee pay for a Fine, interest allowed at 6 L per centum per annum?

	for 4 years		for 25 years
	346510		1278335
1	1732550	5	6391675
2	51.97650	6	191.75025
3	51 L 19 sh 6 D	7	191 L 15 sh 0 D
4	139.77375	8	139 L 15 sh 6 D

First seek the Decimal for the term of four years 346510. which multiplied by 15 L, or by 5, as in the first Table in the margent, according to lib. 1. sect. 1. parag. 4. exam. 5. the product in the a row will be 51.97650, in money 51 L 19 sh 6 d.

and so much the old lease in being is worth, when the new for 21 years enters possession: now admit the term of the old Lease and the new added toge∣ther, the summe of years is 25, the profit or over∣plus of Rent is to continue all the time, therefore 1278335, the Decimal for 25 years, multiplied by 15 L, as in the fifth row of this table, produceth in the 6.119.75025, equal in value to 191 L 15 ss. the difference of the first Lease and the total time in the 8 row is 139 L 15 ss 6 d. and so the differ∣ence of decimals in 4 row reduced is very near, without a material error, being 139 L 15 ss 5 7/10 d.

QUESTION XIV. A Tenant hath a Lease of 21 years, the present thereof is 41 L per ann. during the term of 7 years, and after that time shall be expired, the Lessee is to pay 50 L rent per ann. for the residue of the term, what is the value of this Lease in ready money, interest discounted at 6 L per cent. per annum?

	for 21 years		for 7 years
1	11.76407	5	5.58238
	5		9
2	588.20350	6	50.24142
3	588 L 4 ss 0 ¼ d	7	50 L 4 sh 10 d
4	537 L 19 ss 2 ¾ d	8	537.96208

In the fourth table (of Rents rebated) the Deci∣mal

of 21 years is 11.76407. which multiplied by 50 L (the rent of 21 yeares) the product is 588.20350, as in the second row of this Table; which reduced is 588 L 4 ss 0 2/4 d, as in the third row, which had been the true value of it, at L per ann. for the whole term of time; but the first 7 yeares of this Lease was but 41 L annual rent, therefore the first Decimal was too great, by the difference of rent, which was 9 L per annum; then look into the fourth Table for 7 years, and against it you will find 5.58238. which multiplied by 9 L, as in the first row of this Table, the product in the sixth, is 50.24142, and reduced is 50 L 4 ss 10 d very near; which subtracted from the third row, the remainder, is 537 L 19 sh 2 ¾ d, as in the fourth row; or subtract the Decimals found in the sixth, from the second row; the dif∣ference will be 537.96208. which artificiall number reduced would be 537 L 19 sh 2 ¼ d, as before; the true value of the Lease requi∣red.

QUESTION XV. There is a Lease to be taken for 21 years at 30 L per ann. and 100 L Fine: the Lessee likes the bar∣gain, but not the condition, desiring the annual rent to be but 10 L yearly payments, and is willing to give such a Fine as shall be proportionable to the rent aba∣ted, during the aforesaid term of 21 yeares, and here the Fine is demanded.

In all questions of this kind

	The Decimal
1	11.76407
2	L 235.28140
3	S—5.628
	1256
4	D— 7.536

take the rent abated, which is here 20 L per ann. for 21 years, whose decimal (in the 4^th Ta∣ble of Rents rebated) is 11.76-407, as in the margent; which multiplied by 20 produceth 235.2814, that is, 235 L. reduce the fraction (neglecting the ciphers) the value of 20 L per ann. (the difference of Rent) for 21 years, is as in the 2, 3, and 4 row, in all 235 L 5 sh 7 ½ D. this ad∣ded unto the former Fine, 100 L, makes in all 335 L 5 sh 7 ½ D, the true summe to be paid for a Fine, in lieu of 20 L Rent per ann. abated during the Lease of 21 years; the thing required.

QUESTION XVI. A had a Lease of 130 L per ann. to continue 24 years; B had another of 210 L per ann. and 11 years to come; these 2 men mutually exchanged Leases; A (upon the contract) paid unto B 20 L in ready mo∣ney, which of these had the better bargain, and how much?

A		B
12.55036		788687
3765108	1	1577374
1631.54680	2	1656.24270
1631 L 10 sh 11 D.	3	1656 L 4 sh 10 D.
1651 L 10 sh 11 D.	4	4 L 13 sh 11 D.

Against the 24 year of the fourth Table, look and you will find the Decimal of it 1255036, for A. se∣condly, the lease of B 11 years, hath this decimal 7.88687. these 2 numbers multiplied by their re∣spective rents, as in the first row of this table, accor∣ding to lib. 1. sect. 1. par. 4. exam. 6 & 7. or by the vulgar way. In the second row of the margent A does produce 1631.5464, and B 1656.2427, neg∣lect the ciphers, and reduce the numbers: in the third row you may find the Lease which A exchan∣ged is worth in present money 1631 L 10 ss 11 d. and the lease which B was owner of being 210 L per ann. for the term of a 11 years, proves in cur∣rant coyn the summe of 1656 L 4 sh 10 D. and A mended his in the barter or exchange 20 L,

which makes the value of his lease, as in the fourth row, 1651 L 10 sh 11 D. which still is less worth by 4 L 13 sh 11 D, as in the fourth row (by sub∣traction) is evident, and that B lost so much money by the bargain.

The fifth Table does demonstrate in its use the pur∣chasing of Annuities, Rents, Pensions, or Rever∣sions, at 6 L per centum per annum compound Interest.

QUESTION XVII. What Annuity, Rent, or Pension, will 250 L in ready money purchase for a Lease of 7 yeares; interest allowed at 6 L per cent. per ann.

Seek the seventh year in the fifth Table (which is the terme of yeares that the Lease continues) whose Decimal number is .17914, and if mul∣tipled by 250 L, the product will be 44.78500, and reduced, is in money 44 L 15 sh 8 ¼ d. And this Annuity or Rent to continue the full terme of seven yeares, which the former summe of money will purchase as a yearely revenue du∣ring that time.

QUESTION XVIII. There was a man who purchased a Lease to conti∣nue 25 years, at 10 L per ann. for which the Lessee paid a Fine of 150 L. how much was the annual rent of this Lease valued at, when interest was rated at 6 L per cent. per annum?

This differs little from

	Decimals
1	07823
	39115
2	11.73450
3	11 L 14 ss 8 D

the last; for here you are to find what Annuity or Rent 150 L in ready money will purchase for the term, as in the fifth Table against 25 yeares stands this Decimal 07823. which multiplied by 15, as in the mar∣gent, in the first row of numbers, whose pro∣duct in the second row with the cipher annexed, is 11.73450. that reduced, is in money 11 L 14 ss 8 D (the farthing neglected as not mate∣rial) and this annual Annuity 150 L will pur∣chase for 25 years: therefore adde this unto the Rent paid, viz. 10 L per ann. the total is 21 L 14 ss 8 D. the question answered.

QUESTION XIX. There is a Lease of 25 years to come, set at 10 L rent per ann. and the Fine demanded is 150 L. the Tenant is willing to give 100 L, and a proportional annual revenue during the whole term, what wil be the rent required, the loan for money allowed at 6 L per centum per annum?

This does not vary essenti∣ally

	Decimals
1	07823
	5
2	3.91150
3	3 L 18 ss 2 ¾ D

from the former: for the Fine being diminished, the annual rent must be encrea∣sed: take the difference be∣twixt the two Fines, viz. 100 L, and 150 L, as 50 L the Decimal for the term of years 25 is .07823. which multiplied by 50, or by 5 (as in the first ta∣ble of the margent) the product in the second is 3. 91150. which reduced in the third row is 3 L 18 sh 2 ¾ D. the rent which 50 L will purchase for 25 year; which added to the former Annuity of 10 L per ann. makes the whole rent 13 L 18 sh 2 ¾ D, according to demand.

QUESTION XX. A Citizen giveth over his Trade unto a faith∣full servant, leaving him his shop ready furni∣shed, the Wares prized at 1408 L, the Lease of his house valued at 250 L, so in all 1638 L, which the Master was to receive by equall and annuall payments in the space of 7 yeares, the interest agreed upon at 6 L per centum per annum, what annuity will discharge this debt.

To discover this annual Rent, look in the first Table for the term of years specified, and against 7 you wil find .17914. This multiplyed by 1658 L produceth 297.01412. the Decimal•• reduced will prove in money 297 L o ss 3 ¼ D. Which Annui∣ty or Rent, for 7 years annual payments, discharges the whole debt with interest, at 6 L per cen∣tum.

QUESTION XXI. A Tenant took a Lease of a House and Land for a term of 21 years, paying 160 L Fine, and 16 L Rent per ann. at 7 yeares end the Lessee was resolved to put it off: What annual Rent or Annuity must he set the Tenement at, to with∣draw his former Fine, or reserving the same Rent, impose another proportionall for the years to come? Interest at the rate of 6 L per cent. per ann.

	Rent		Fine
1	.08500	5	9.2949••
51000	13.6
2	13.60000	6	5576988
		2788494
3	13 L 12 ss	929498
4	29 L 12 ss	7	126.411728

First to impose a proportional Rent, find by the first Table (of Annuities to be purchased) what 160 L will buy for the full term of 21 years, whose Decimal is .08500, which multiplied by 160 L, or 16, as in the first row of this marginal table, the product in the second is 13.60000. in the third is reduced to 13 L 12 ss. & this annual Pension 160 L will purchase for 21 years; which added to 16 L

per ann. (the Rent of the Tenement) does evident∣ly shew the nature of the Lease, as in the fourth row 29 L 12 sh. and setting of it at that rate the re∣maining years, the Tenant saves himself.

To discover what Fine must be imposed, the old Rent reserved, and yet a ••roportional part for the first Fine. The term of years remaining are 14, whose Decimal in the fourth table of Discount is 9.29498, which multiplied by the Decimal of 13 L 12 sh last found, viz. 13.6, as in the fifth row, in the s••xth stand their several products, and in the seventh row the totall summe, as 1••6.411728, from whence strike off 6 places, which are fractions (according to the Rules of Mul∣tiplication in Decimals) and reduce the test, the Fine will be discovered 126 L 8 sh 2 ¾ D, which saves the Tenant harmless, the old Rent still re∣served, without gain or loss; the thing required. As for the Decimal of 12 sh. find the fraction, or see lib. 3. ca••. 7. table 1.

Rules I have here delivered, equally ballanc'd betwixt the Buyer and Seller, Debitor and Cre∣ditor, whereby neither side might deceive, non yet be deceiv'd by falacious or ambiguous cont••••cts. As for Interest Money, here are composed rules both according to Custome, prescriptions of Art, and the precepts of humane Institutions, which tolerates Usury, confined to a Loan of 6 L per centum per annum. I cordially wish the frugality of the people would lessen the trade of money, and sink the Im∣post to a Land rate; yet there would be ma∣ny Money-corm••rants, and their pro••it great, because such Estates lye dormant in Banks,

obscured from the inquisition of a sax; and rare∣ly appea o•• wake but with the noyse of a Forfei∣ture o•• the Owners Land, or the liberty of his per∣son. The Interest, like a Monster, by an unlawfull conception, and a prodigious birth (grown greater then the Principal) makes appeal to the rigor of the Laws, against those who bore too prodigal a Saile, and now like to suffer wr••ck betwixt Scylla and Charybdis, or swallowed by those yawning waves.

Usury is like a Cancer, which by an unperce∣ptible Consumption ingratefully wasts that body where by Corruption it took a being; I wish none to adore the Golden Calf, nor yet slight the ma∣terials, their use being good and laudable, where Vertue is Treasurer, Discretion Controller, and Charity Purse-bea••er: but if abused by being cast in another mould, or the three adverse parties in office, it will as e•• ly catch those (who make worldly wealth their Mammon) as lime does Birds; so the danger is great, and the more, when usually the love of Money multi••lies, as their Stocks and Magazines encrease; and those who have most are often most miserable in want, ignorant in the use of temporall blessings, and glutted with ex∣cesse, become immedicable by those surfeits; like men in Dropsies, the more waterish they grow, the more they desire drink, with an unsatiable thirst, so feeds the humours, and that the di∣sease. And thus I will conclude with the ingenu∣ous Poet, Ovid.

Sic quibus in••umui suff••sa venter ab unda, Quò plus s••n potae, plus sitiuntur aquae.

In English thus,

Men s••ell'd with Dropsies grow excessive dry, And drinking, covet more untill they die.