The Doctrine OF INTEREST, BOTH SIMPLE & COMPOUND: EXPLAINED In a more exact and satisfactory Method then has hitherto been Published.

DISCOVERING The Errors of the Ordinary Tables of Rebate for Annuities at Simple Interest.

AND CONTAINING Tables for the Interest and Rebate of Money for Days, Months, and Years, both at Simple and Compound Interest: Also Tables for the Forbearance, Discompt, and Purchase of Annuities.

AS LIKEWISE, Equation of Payments made Practicable and useful for all Merchants and others.

Together with divers others useful Reflections.

Humbly Presented to His Most Sacred Majesty, CHARLES II. By Sir S. Morland, Knight and Baronet.

Printed at London, by A. Godbid and J. Playford. and are sold by Robert Boulter, at the Turks-Head, over against the Royal-Exchange in Cornhill, 1679.

[Page]

[coat of arms or blazon]

A necessary and useful INTRODUCTION.

THe Author of this little Book hopes he has served the Publick somewhat better than other Arithmeticians, who have gone before him, for the following Reasons.

1. In that his Method is more plain and easie than that of other Men; and those things which they have left intricate and difficult to be understood, are here made evident by clear Demonstrations, obvious to the meanest capacity.

[Page] 2. In that his Tables are Calcu­lated with greater care, and are much more correct than those that have been Published of late years. For instance, all those Tables in Mr. Newton's Book, Printed 1667, are full of Errors and mistakes; and which is very remarkable, the Tables which Mr. Dary has Pub­lished as his own, are only tran­scribed out of Mr. Newton's Book, and that with all the Errors, which are so many, that they must needs mislead and discourage either young or old Practitioners from trusting to, or making use of them.

In Mr. Clavel's Tables, which seem to be more correct than the others, there will be found many very considerable Errors. As for [Page] instance, if you would know what an Annuity of 600l. to con­tinue 21 years is worth in ready Money, you will find it there to be but 6058: 08: 11.034, which is too little by 1000l. also if you would know the Present Worth of 60 l. Annuity for the like time (in the same Page that re­solves the former Question) you will find but 605 : 16 : 10.703, which is less than the truth by 100 l.

Whereas in this little Book, by the more than ordinary care and diligence of Mr. John Playford, Printer, (whom I have found the most ingenious and dexterous of any of his Profession, in Printing of Tables, and all sorts of Mathe­matical Operations) it is presumed [Page] that there will hardly be found one false Figure; but if there should, the Tables are so framed, that what the one does by Multiplication, the other proves by Division, & vice versâ, what­ever the one performs by Division, the other makes out by Multiplica­tion to be a truth.

3. Because the Operations accor­ding to the Rules and Tables of this little Book, where the Sums are great, are much more easie, practi­cable, and satisfactory, than by Mr. Clavel's Tables; besides that those Tables do not answer very many useful Questions that will daily occur to Men of business.

For Example.

He has Tables for the Amount of any Sum to 10000 l. for 365 days, but he has no Tables of Rebate for so many days, which is full as useful as the other, not only in Simple, but also Compound Interest; so that the Practitioner must very often be forced to have recourse to the Logarithms, or other tedious Calculations.

4. Because all the Operations in this Book are performed by DECIMAL ARITHMETICK, which of all other is the most use­ful and Practicable, when well understood: And in order there­unto, the Author has here given several Examples, and explained [Page] the respective Operations in such a manner, that any person who does at all understand the Vulgar Arith­metick, may in one hours time throughly comprehend this.

Addition and Subtraction of Decimals.

AS for the Operations of Ad­dition and Subtraction, they are the very same with the Vulgar.

For Example.
To375.42
Add49.32
Sum424.74.

[Page] There must only care be had of setting Unites under Unites, and Fractions under Fractions, in their proper Ranks and Files; as likewise that there be as many places of Fractions in the Total, as are found in either of the Sums, before they are added together.

Thus:
To375.42
Add495.4
Sum870.82
Or thus:
To375.42
Add95.03
Sum470.45
[...]
[...]

[Page]

Again,
From870.82
Deduct495.4
Remainder375.42
Or,
From470.45
Deduct95.03
Remainder375.42

Multiplication of Decimals.
Rule.

SET one Number over ano­ther, (making only a Full­point to Distinguish between whole Numbers and Fracti­ons) in the very same manner as is none in ordinary Multi­plication, only when the Pro­duct is finished, look how many places of Fractions are found, both in the Multiplicand and Multiplicator jointly, just so many must be left in the Pro­duct.

For Example.

To multiply 342.34 by 3.123, place them thus: [...]

Explanation.

Because in the Multiplicand there are two places of Fractions, and in the Multiplicator three, in all [Page] five; therefore in the Product there must be also five places of Fractions.

Thus, [...]

Here the Practitioner is to ob­serve, that the Fraction which is in truth less, is set over the whole Number, which is really greater. But because the Fraction consists of more places, it is set uppermost, [Page] though it is a thing indifferent, for if they were set otherwise, the Product would still be the same.

For, [...]

Which is the very same as before.

[Page] By the same Reason, [...]

The Product must evermore be compleated, as to the number of places that are found in both Mul­tiplicand and Multiplicator.

An excellent Method of Con­tracting a Long Multipli­cation.

1. IN the first place, wherever a Multiplication consists of above three places, the Author does recommend to all Practitioners (as a thing which he has sufficiently experienced to be the most safe and easie) to make use of a Tariffa, or Table of Multiplication for the Multiplicand: And though it may and will seem at the first view to be more tedious, yet it will be found to be the shortest of all other ways whatsoever, being per­formed by Addition only, and less [Page] subject to error; and not only so, but whereas all other Operations of Multiplication do extreamly distort the Eyes by looking sted­fastly upon Figures placed Diago­nally, by this Tariffa the Eye looks on them always in a streight Line, and no otherwise.

For Example.

Suppose the two Sums to be multiplied one by another were 259879.890625, and 1.1173698, but the Product to consist of no more than Eleven places.

[Page]

Tariffa for the Mul­tiplicand.
1259879890625
2519759781250
3779639671875
41039519562500
51299399453125
61559279343750
71819159234375
82079039125000
92338919015625

Having made a Tariffa, and placed the Multiplicand and Multipli­cator as is before directed, because in the Multiplicand there are twelve places, and eight in the Multipli­cator, in all twenty places; and [Page] it is desired to contract them to eleven places. First let a Line be drawn, leaving eight places to the right hand; and then let all the imaginary places underneath be supplied with Points or Cyphers, decreasing in a Triangular Figure to nothing.

Then let the Multiplication be performed as follows.

Let the last Figure in the Multi­plicator be found in the Margin of the Tariffa, and the Product answering to it subscribed, only let eight places be imaginary ac­cording to the number of Points or Cyphers, and let the remain­ing Figures (viz. 20790) be transcribed on the other side of the Line.

[Page] Under the next Figure of the Multiplicator (9), are seven Points or Cyphers, therefore the Product answering to (9) in the Margin of the Tariffa being found, viz. 233891/9015625, let the first seven Figures to the right hand be left, and the other six in­scribed, as in the Example is better seen.

And thus must the Operation be performed, 'till all be finished; and considering that there are eight several Products, it may be well imagined, that at least (2) must be carried from the last place; and therefore (2) being added to (27) there must be set down (9), and (2) carried to the next place; and thus must be wrought the whole Multiplication, [Page] and at last it gives the Product, as is here-under exprest, viz. [...]

And after this manner may any Multiplication be contracted to any number of places, more or less.

Division of Decimals.

IN Division of Decimals, the greatest difficulty is to know of what nature the first Figure or Cypher in the Quotient ought to be, for that being once known, all other things are the very same as in the ordinary Operation of Di­vision.

And therefore I shall give this General Rule, for the finding of what nature or quality the first Figure or Cypher of any Quoti­ent in a Decimal Operation ought to be.

General Rule.

The first Figure in the Quo­tient must and will always be of the same nature and qua­lity with that Figure or Cy­pher in the Dividend, which at the first Question stands over the place of Vnites in the Divisor.

Example 1.

Let 7.4944 be given to be di­vided by 32.

By the foregoing Rule, because the Figure (4) of the Dividend stands over the Unite (2) of the Divisor, and the Figure (4) is [Page] a Fraction; therefore the first Fi­gure of the Quotient (viz. 2) must be a Fraction, and have a Point prefixed.

And then all the other Figures of the Quotient follow in course, as in the ordinary Method of Di­vision.

Tariffa.
132
264
396
4128
5160
6192
7224
8256
9288

[...]

Example 2.

[...]

Direction

In this last Example, because the Divisor may not be placed un­der the first Figure of the Dividend, nor indeed under the second, therefore are two Cyphers put first in the Quotient, but under the third Figure it may be set, and then .0204 is found three times in 0652, [Page] and 40 over; then bringing down (8), and adding it to 40, makes the Product (408), which is just the double of (204) which gives (2) for the last Figure of the Quotient.

And after this manner may any Division be wrought, without the least difficulty or uncertainty.

Example 3.

Let.0006258 be the Dividend, and.0032 the Divisor.

Here must be a remove before the Divisor will come under the the Dividend, which is the occa­sion of putting one Cypher in the Quotient, before the Figure (2).

[Page]

Tariffa.
10032
20064
30096
40128
50160
60192
70224
80256
90288

[...]

[...]
[...]

Again, Let the Numbers in the first Example be given thus: [...]

Tariffa.
174944
2149888
3224832
4299776
5374720
6449664
7524608
8599552
9674496

Explanation of the fore­going Examples.
Explanation of the first Example.

IN the first Example a less Number 7.4944 is divided by a greater, viz. 32.

The young Practitioner will presently object, and demand how this can be, for to divide one Number by another, is to demand how many times that other Num­ber is found in the first; that is, in this case, how many times 32 is found in 7 Integers, and a Fraction of .4944.

Explanation.

The Answer in plain English is this:

First, 32 is not found so much as once in 7, and that is the reason of the Full-point (.) in the Quo­tient, before the Figures of the Fraction, to signifie, that the whole Quotient consists of Deci­mal Parts.

Secondly, the first Figure of the Fraction being (2) denotes this, namely that 32 comes no nearer, being found in 7.49, &c. than [...]2/10, or two Tenths of once, or one time; that is to say, it comes no nearer than 2 is to 10.

And the second Figure of the Quotient (3) gives to under­stand, [Page] that 32 comes no nearer, being found in 7.49, &c. so much as once, or one time, than 23/100, or Twenty three Hundred parts; that is to say, no nearer than 23 is to 100.

And (4) the third Figure goes farther, and says, that 32 comes no nearer, being found once, or one time, in 7.49, &c. than 234/1000, or Two Hundred thirty four Thousand parts; that is to say, no nearer than 234 is to 1000.

And the last Figure determining the Question, yet somewhat more exactly; that is to say, denotes that 32 comes no nearer, being found so much as once in 7.4944, than 2342/10000; that is, no nearer than 2342 is to 10000.

Explanation of the second Example.

IN the second Example likewise a less Number seems to be divi­ded by a greater, viz. .0006528 by .0204, and also (in the third Example) by .0032; and an Explanation of one of these may serve for both.

And the true meaning is,

1. First .0032 cannot be found once in .0006528, therefore is a Point prefixed before the Quotient.

2. The first Cypher denotes that .0032 comes not so near, being found once in .0006528, as 1/10, or one Tenth; that is, not so near as 1 to 10.

[Page] 3. The second Cypher tells the Practitioner that it comes not so near as 1/100, or as 1 to 100.

4. The Figure (3) in the third place, acquaints him, that 32 is no nearer, being found once in .0006528, than 1/1000, that is, Three parts of a Thousand, or no nearer than 3 is to 1000.

And the last Figure in the Quo­tient, (viz. 2) signifies that 32 is no nearer, being found once in . 0006528, than 32/10000; that is to say, no nearer than 32 is to 10000.

And this Mystery being once throughly comprehended, and digested by the young Practitioner, there can be no farther difficulty, about a less Number being divided by a greater.

[Page] 5. In the fifth and last place, by this little Book may be com­pared together the Operations of Simple and Compound Interest, and so may be discovered how errone­ous and extravagant the one is, and how true and rational the other, and only fit to be made use of by all those who deal in matters of Money, or Purchases, which that the Reader may better comprehend, let him consider well the following Animadversions, or Reflections.

Reflections upon Simple and Compound Interest.

Reflection I.

LEt there be proposed an An­nuity of 100 l. to be conti­nued 10, 20, 30, 40, 50, 60, 70, 80, 90, or 100 Years, and let it be demanded, what the Present Worth of such an Annuity is for any of the following Terms, at the Rate of 6 per Cent. and that as well according to Simple as Com­pound Interest?

Answer.

An Annuity of 100l. to conti­nue for 10, 20, 30, 40, 50, 60, 70, 80, 90, or 100 Years, is worth in present Money so many Years Purchase as is hereafter exprest, viz.

Number of Years to be conti­nued.Years Purchase, at Simple Inte­rest.Years Purchase at Compound In­terest.
107.937.35
2014.2711.46
3020.0313.76
4025.5215.01
5030.8715.72
6036.1316.16
7041.3216.38
8046.4816.50
9051.6016.57
10056.7116.61

[Page] By which Table it is very ob­servable, what a small difference there is at Compound Interest, be­tween the Present Worth of 50 Years, and the Present Worth of 100 Years, (viz. 00. 89/100) in com­parison with the difference be­tween 50 and 100 Years, at Simple Interest, (viz. 25 Years Purchase, more by 84/100) the one not ex­ceeding 16 Years Purchase, more by 61/100; and the other still in­creasing as far as almost 57 Years Purchase; and if continued to a greater Number of Years, would still swell into an extravagant Sum, for the Purchase, Treble, or Qua­druple, to the usual Rate of Pur­chases in the Kingdom where wo live.

Reflection II.

FOr as much as it is a truth re­ceived by all, That the Pur­chase of an Estate or Revenue for ever, in most places of England, is not worth above 20 Years Pur­chase, and that to be computed according to Compound Interest, which is made up of so many Geometrical Proportional Numbers: What reason can there be given, why the Present Worth of any Payment, due at any time hereafter, should not be com­puted by the same proportion, although the Payment be but for a Year, nay, for a Day, or Hour, or Minute to come?

[Page] Thus, according to the Rate of Compound Interest, the Purchase of an Estate for 30 years to come, at 4 per Cent. is worth 17 years Purchase, and somewhat more; at 5 per Cent. is worth 15 years Purchase, more by [...]9/100; at 6 per Cent. is worth 13 years Purchase, more by 76/100. The same Estate for 20 years to come, at 4 per Cent. is worth 13 years and a half Pur­chase, and somewhat more; and for 10 years to come, is worth above 8 years Purchase; and for two years to come, is worth one years Purchase, more by 88/100; and all these Numbers are Calcu­lated as Geometrical Proportionals: Why then should the same Estate, for a Year, or 6 Months to come, be Calculated by any other Pro­portion? [Page] Or indeed, how can it be rightly Calculated by any other Proportion, without doing wrong to either Buyer or Seller?

Reflection III.

COmpound Interest being made up of Geometrical Proportio­nals, the Debtor ought not really to pay after the Rate of 30s. a Quarter for 100l. let out to him at 6 per Cent. because, if 100l. be put out to Interest, and the Interest come to 1l. 10s. the first Quar­ter, that 101l. 10s. by the end of the next Quarter (keeping to Geometrical Proportion) will become 103l. 5d. 1q. more by 6 [...]/100 of a Farthing; that is to say, 100l. [Page] after this manner, would amount in a years time to 106l. 2s. 8d. 2q. more by Ninety Hundred parts of a Farthing, as may be seen by the following Calculation.

[...]

Which in a great Sum is more considerable.

For suppose the Crown to be indebted 1 Million, or (1000000l.) and it were agreed to pay at the Rate of 30s. for each 100l. the first Quarter, and it were not paid 'till the Twelve Months end; the Amount would be as follows.

[Page] [...] Which at the years end amounts to 60000l. (which ought to be the Total Sum of the Interest for 12 Months, at 6 per Cent.) and over and above the said 60000l. there is 1363l. 11s. which 1 Million according to such an Accompt, if put out for a year, would amount to: So that in effect this is not 6 per Cent. but 6l. 2s. 8d. 2q. Ninety Hundred parts of a Farthing per Cent. For he who lends Money, if so soon as the first Quarters Inte­rest grows due, and the Creditor pay it not at the just time, (if he so please) obliges the Creditor to [Page] acknowledge so much Principal, and then it increases as aforesaid.

Divers other Reflections of this kind might be made, and applied to the manifold abuses that may be committed, by Selling according to one Rate of Interest, and Buying by another, and so confounding together Simple and Compound Inte­rest, as it makes most for the ad­vantage of the Money Merchant, there being very few so well versed in Numbers as to contradict them. The truth is, it is as great pity that there should be two so different Calculations of Interest, as that there should be so many different Weights and Measures, and those divided and subdivided into so many Heterogeneous Fractions, which must of necessity create to [Page] all Dealers innumerable difficul­ties; whereas if Coyns, Weights, and Measures, were divided and subdivided by Decimals, all Cal­culations would be performed with ease and pleasure.

For Instance,

If a Pound were divided into 10 Shillings, a Shilling into 10 Pence, and a Peny into 10 Farthings, and only a Point to distinguish Inte­gers from Fractions; then the fol­lowing Sum would easily be added together, viz.

l.s.d.q.
15961
39830
48721

[Page] For they might be set down thus: [...]

That is to say, the Sum would be 104 Pound, 5 Shillings, 1 Peny, and 2 Farthings.

Or if these were Weights, they might be,

104 Pound-weight, 5 Ounces, 1 Dram, 2 Scruples.

And after this manner might all Calculations be abbreviated, [Page] and made much more practicable than now they are, especially the Operations of Multiplication and Division.

For to multiply 48 l. 7 s. 2 d. 2 q. as they are now divided, by 124, is very troublesom, and re­quires many Operations, both of Multiplication and Division; but in a Decimal way, it would be plain and easie by one single Multipli­cation, viz. [...]

[Page] That is to say, 6041 Pound, 5 Shillings, 2 Pence, and 8 Far­things.

The convenience and expedi­tion would yet be greater in Long and Square Measures; and all for­mer Accompts by unequal Divi­sions, might for the present be re­conciled and reduced to Decimals, and in a few years utterly for­gotten, and become altogether useless.

But for as much as a private Person can only give hints of what he conceives to be of publick use and benefit, and that it is a thing wholly in the Power of those who are Law-makers, to inspect and rectifie [Page] what they in their great Wisdom shall judge amiss; the AUTHOR does in all Humility lay by his Pen, and puts a period to his Discourse upon this Subject.

The CONTENTS of the First Book.
  • OF Interest in general, Page 1
  • The Reduction of Shillings, Pence, and Farthings, into Decimal Fractions, 3
  • The Interest of One Pound for a Year, at any Rate of Simple Interest, from 1 to 12 per Cent. 4
  • The Interest of One Pound for half a Year, at any Rate of Simple Interest, from 1 to 12 per Cent. 5
  • The Interest of One Pound for a Quarter of a Year, at any Rate of Simple Interest, from 1 to 12 per Cent. 6
  • The Interest of One Pound for a Month, at any Rate of Simple Interest, from 1 to 12 per Cent. 7
  • The Interest of One Pound for a Day, at any Rate of Simple Interest, from 1 to 12 per Cent. 8.
  • The Golden Table of Trigonal Progression, of admirable Vse in all Calculations of the Amount or Present Worth of Annuities, &c. 9
  • The Number of Days from the beginning of any Month to the end of any other, throughout the Year, 13
  • [Page] The Amount of One Pound forborn any Number of Years under 32, at 6 per Cent. Simple Inte­rest, Page 16
  • The Amount of One Pound forborn any Number of equal Months under 25, at 6 per Cent. Simple Interest, 17
  • The Amount of One Pound forborn any Number of Days under 366, at 6 per Cent. Simple In­terest, 18
  • The Present Worth of One Pound due after any Number of Years to come, not exceeding 32, at 6 per Cent. Simple Interest, 27
  • The Present Worth of One Pound due after the expiration of any Number of Months under 25, at 6 per Cent. Simple Interest. 29
  • The Present Worth of One Pound due after the expiration of any Number of Days under 366, at 6 per Cent. Simple Interest, 31
  • The Reduction of Pence and Farthings into Deci­mal Fractions, to the Hundredth part of a Farthing, 41
  • The Use of the foregoing Tables, 46
  • A Comparison between these and Mr. Clavel's Tables, wherein it is proved, that the former are less troublesome, and more exact than the latter, 52
  • Of Annuities, 59
  • The Multiplication of any Rates of Interest what­soever belonging to each Year, for a forborn Annuity, to 100 Years, 60
  • [Page] To find the Amount of any Annuity for any given time, at any Rate of Simple Interest, Page 64
  • This kind of Interest for Annuities useless and ridiculous, 65
  • The Errors of the ordinary Rules and Tables for Rebate relating to Annuities, ibid.
  • Mr. Kersey and Dr. Newton both mistaken, 66
  • Diophantus Alexandrinus his third Proposition concerning Poligonal Numbers considered, 73
  • A second Reflection on Mr. Kersey's and Dr. New­ton's mistake, 87
  • Equation of Payments rectified, 93
  • The Amount and Present Worth of an Annuity of 100 l. for 5 Years, at 1, 2, 3, 4, 5, 6, and 10 per Cent. Simple Interest, Page 95, &c.
  • Observations on these Tables, 102
  • Equation of Vnequal Payments at times not equi­distant, 123
The CONTENTS of the Second Book.
  • COmpound Interest explained, Page 129
  • A Reflection upon Geometrical Progression, 131
  • The Amount of One Pound put out to Interest, and forborn any Number of Years under 32, or Quarters under 125, at 6 per Cent. Compound Interest, 141
  • [Page] The Amount of One Pound put out to Interest for any Number of Months under 25, at 6 per Cent. Compound Interest, Page 146
  • The Amount of One Pound put out to Interest for any Number of Days under 366, at 6 per Cent. Compound Interest, 147
  • The Present Worth of One Pound due after any Number of Years under 32, or Quarters under 125, at 6 per Cent. Compound Interest, 157
  • The Present Worth of One Pound due after the expi­ration of any Number of Months under 25, at 6 per Cent. Compound Interest, 162
  • The Present Worth of One Pound due after the expi­ration of any Number of Days under 366, at 6 per Cent. Compound Interest, 163
  • The Present Worth of One Pound Annuity, to con­tinue any Number of Years under 32, and pay­able by yearly Payments, at 5, 6, 7, 8, 9, and 10 per Cent. Compound Interest, 173
  • What Annuity to continue any Number of Years under 32, and payable by yearly Payments, One Pound will Purchase, at 5, 6, 7, 8, 9, and 10 per Cent. Compound Interest, 179
  • The Present Worth of any Lease or Annuity, for 21, 31, 41, 51, 61, 71, 81, or 91 Years; as likewise the Present Worth of the Fee-Simple, at 5, 6, 8, and 10 per Cent. Compound Interest, 184
  • The several Vses of the foregoing Tables, 186

THE DOCTRINE OF SIMPLE INTEREST EXPLAINED By a New and Exact Method, And the Errors of the Ordinary Rules and Tables of Rebate discovered and rectified.

CHAP. I.

INterest is either Simple, or Com­pound.

1. Simple Interest, is the Increase which arises from the Principal only, at 4, 5, 6, 7, &c. per Cent.

2. Compound Interest, is the Increase which arises from the Principal, and also from the Interest thereof.

[Page 2] Thus, if 100 l. be lent at Simple Interest for Two Years, at 6 per Cent. the In­crease thereof is 12 l. But if at Compound Interest, it gives 6 l. for the first Year, and 6 l. for the second Year, toge­ther with the Interest of the first 6 l. for the second Year. That is to say: [...] To which adding the Principal (viz. 100 l.) the Amount of both Principal and Compound Interest, for Two years, is 112.36 l. which by the Table of Reduction in the following Page is 112 l. 7 s. 2 d. 1 q. more by .000626 parts of a Pound.

The Doctrine of Simple Interest is plainly and clearly set forth in the fol­lowing Propositions.

But that the Practitioner may meet with no difficulty in the respective Ope­rations, he will here find made ready to his hand Seven short (but very significant) Tables.

[Page 3]

TABLE I. Reduction of Shillings, Pence, and Farthings, into Decimal Fractions.
Shil­lings.Deci­mals. Pence.Decimals.
   11.0458333
19.95 10.0416666
18.9 9.0375
17.85 8.03 [...]3333
16.8 7.0291666
15.75 6.025
14.7 5.0208333
13.65 4.0166666
12.6 3.0125
11.55 2.0083333
10.5 1.0041666
9.45   
8.4 Farth.Decimals.
7.35   
6.3 3.003125
5.25 2.0020833
4.2 1.0010416
3.15 ½.0005208
2.1 ¼.0002604
1.05 1/8.0001302

[Page 4]

TABLE II. The INTEREST of One Pound for One Year. From 1 to 12 per Cent.
Rates per Cent.Interest.
1.01
2.02
3.03
4.04
5.05
6.06
7.07
8.08
9.09
10.10
11.11
12.12

[Page 5]

TABLE III. The INTEREST of One Pound for One Half-Year. From 1 to 12 per Cent.
Rates per Cent.Interest.
1.005
2.01
3.015
4.02
5.025
6.03
7.035
8.04
9.045
10.05
11.055
12.06

[Page 6]

TABLE IV. The INTEREST of One Pound for One Quarter. From 1 to 12 per Cent.
Rates per Cent.Interest.
1.0025
2.005
3.0075
4.01
5.0125
6.015
7.0175
8.02
9.0225
10.025
11.0275
12.03

[Page 7]

TABLE V. The INTEREST of One Pound for One Month. From 1 to 12 per Cent.
Rates per Cent.Interest.
1.0008333
2.0016666
3.0025
4.00333
5.00416
6.005
7.00583
8.00666
9.0075
10.08333
11.09166
12.1

[Page 8]

TABLE VI. The INTEREST of One Pound for One Day. From 1 to 12 per Cent.
Rates per Cent.Interest.
1.00002739726
2.00005479452
3.00008219178
4.00010958904
5.00013698630
6.00016438356
7.00019178082
8.00021917808
9.00024657534
10.00027397260
11.00030136986
12.00032876712

[Page 9]

TABLE VII. THE GOLDEN TABLE OF Trigonal Progression. Of excellent use, in all Calcula­tions of the Amount or present Worth of Annuities, &c.
Arith. Prog.Trigonal Prog.
11
23
36
410
515
621
728
836
945
1055
1166
1278
1391
14105
15120
16136
17153
18171
[Page 10]Arith. Prog.Trigonal Prog.
19190
20210
21231
22253
23276
24300
25325
26351
27378
28406
29435
30465
31496
32528
33561
34595
35630
36666
37703
38741
39780
40820
41861
42903
43946
44990
451035
461081
471128
481176
491225
501275
511326
521378
531431
541485
551540
561596
571653
581711
591770
601830
[Page 11]Arith. Prog.Trigonal Prog.
611891
621953
632016
642080
652145
662211
672278
682346
692415
702485
712556
722628
732701
742775
752850
762926
773003
783081
793160
803240
813321
823403
833486
843570
853655
863741
873828
883916
894005
904095
914186
924278
934371
944465
954560
964656
974753
984851
994950
1005050
1015151
1025253
[Page 12]Arith. Prog.Trigonal Prog.
1035356
1045460
1055565
1065671
1075778
1085886
1095995
1106105
1116216
1126328
1136441
1146555
1156670
1166786
1176903
1187021
1197140
1207260
1217381
1227503
1237626
1247750

[Page 13]

TABLE VIII. A TABLE SHEWING The Number of Days from the Begin­ning of any Month to the End of any other.
  • JAnuary, 31. February, 59. March, 90. April, 120. May, 151. June, 181. July, 212. August, 243. September, 273. October, 304. November, 334. Decem­ber, 365.
  • February, 28. March, 59. April, 89. May, 120. June, 150. July, 181. August, 212. September, 242. October, 273. Novemb. 303. Decemb. 334. Jan. 365.
  • March, 31. April, 61. May, 92. June, 122. July, 153. August, 184. Sep­tember, 214. Octob. 245. Novemb. 275. Decemb. 306. Jan. 337. Febr. 365.
  • [Page 14] April, 30. May, 61. June, 91. July, 122. August, 153. September, 183. Octo­ber, 214. November, 244. December, 275. January, 306. February 334. March, 365.
  • May, 31. June, 61. July, 92. August, 123. September, 153. October, 184. No­vember, 214. December, 245. Jan. 276. February, 304. March, 335. April, 365.
  • June, 30. July, 61. August, 92. Sep­tember, 122. October, 153. Novemb. 183. December, 214. January, 245. Febr. 273. March, 304. April, 334. May, 365.
  • July, 31. August, 62. September, 92. October, 123. Novemb. 153. Decemb. 184. January, 215. February, 243. March, 274. April, 304. May, 335. June, 365.
  • August, 31. September, 61. Octob. 92. November, 122. December, 153. Janua­ry, 184. February, 212. March, 243. April, 273. May, 304. June, 334. July, 365.
  • [Page 15] September, 30. October, 61. No­vember, 91. December, 122. January, 153. February, 181. March, 212. April, 242. May, 273. June, 303. July, 334. Aug. 365.
  • October, 31. November, 61. Decemb. 92. January, 123. February, 151. March, 182. April, 212. May, 243. June, 273. July, 304. August, 335. September, 365.
  • November, 30. December, 61. Janu­ary, 92. February, 120. March, 151. April, 181. May, 212. June, 242. July, 273. Aug. 304. Sept. 334. Octob. 365.
  • December, 31. January, 62. Februa­ry, 90. March, 121. April, 151. May, 182. June, 212. July, 243. August, 274. Sep­tember, 304. October, 335. Novemb. 365.

Note, That in every Leap-year, Fe­bruary has 29 Days, and then you must allow a Day more than is here compu­ted for that Month.

[Page 16]

TABLE IX. The Amount of One Pound, put out to Interest, and forborn any Number of Years under 32. At the Rate of 6 per Cent. Simple Interest; And that Interest payable Yearly.
Years.Amount.
11.06
21.12
31.18
41.24
51.30
61.36
71.42
81.48
91.54
101.60
111.66
121.72
131.78
141.84
151.90
161.96
172.02
182.08
192.14
202.20
212.26
222.32
232.38
242.44
252.50
262.56
272.62
282.68
292.74
302.80
312.86

[Page 17]

TABLE X. The AMOUNT of One Pound, for any Number of equal Months under 25. At the Rate of 6 per Cent. Simple Interest.
Months.Amount.
11.005
21.010
31.015
41.020
51.025
61.030
71.035
81.040
91.045
101.050
111.055
121.060
131.065
141 070
151.075
161.080
171.085
181.090
191.095
201.100
211.105
221.110
231.115
241.120

[Page 18]

TABLE XI. The AMOUNT of One Pound, for any Number of Days under 366. At the Rate of 6 per Cent. Simple Interest.
Days.Amount.
11.000164383
21.000328767
31.000493150
41.000657534
51.000821917
61.000986301
71.001150684
81.001315068
91.001479452
101.001643835
111.001808219
121.001972602
131.002136986
141.002301369
151.002465753
161.002630136
171.002794520
181.002958904
191.003123287
201.003287671
211.003452054
221.003616438
231.003780821
241.003945205
251.004109589
261.004273972
271.004438356
281.004602739
291.004767123
301.004931506
311.005095890
321.005260273
[Page 19]Days.Amount.
331.005424657
341.005589041
351.005753424
361.005917808
371.006082191
381.006246575
391.006410958
401.006575342
411.006739725
421.006904109
431.007068493
441.007232876
451.007397260
461.007561643
471.007726027
481.007890410
491.008054794
501.008219178
511.008383561
521.008547945
531.008712328
541.008876712
551.009041095
561.009205479
571.009369862
581.009534246
591.009698630
601.009863013
611.010027397
621.010191780
631.010356164
641.010520547
651.010684931
661.010849314
671.011013698
681.011178082
691.011342465
701.011506849
711.011671232
721.011835616
731.011999999
741.012164383
751.012328767
761.012493150
[Page 20]Days.Amount.
771.012657534
781.012821917
791.012986301
801.013150684
811.013315068
821.013479451
831.013643835
841.013808219
851.013972602
861.014136986
871.014301369
881.014465753
891.014630136
901.014794520
911.014958903
921.015123287
931.015287671
941.015452054
951.015616438
961.015780821
971.015945205
981.016109588
991.016273972
1001.016438356
1011.016602739
1021.016767123
1031.016931506
1041.017095890
1051.017260273
1061.017424657
1071.017589040
1081.017753424
1091.017917808
1101.018082191
1111.018246575
1121.018410958
1131.018575342
1141.018739725
1151.018904109
1161.019068492
1171.019232876
1181.019397260
1191.019561643
1201.019726027
[Page 21]Day.Amount.
1211.019890410
1221.020054794
1231.020219177
1241.020383561
1251.020547945
1261.020712328
1271.020876712
1281.021041095
1291.021205479
1301.021369862
1311.021534246
1321.021698629
1331.021863013
1341.022027397
1351.022191780
1361.022356164
1371.022520547
1381.022684931
1391.022849314
1401.023013698
1411.023178081
1421.023342465
1431.023506849
1441.023671232
1451.023835616
1461.023999999
1471.024164383
1481.024328766
1491.024493150
1501.024657534
1511.024821917
1521.024986301
1531.025150684
1541.025315068
1551.025479451
1561.025643835
1571.025808218
1581.025972602
1591.026136986
1601.026301369
1611.026465753
1621.026630136
1631.026794520
1641.026958903
[Page 22]Day.Amount.
1651.027123287
1661.027287670
1671.027452054
1681.027616438
1691.027780821
1701.027945205
1711.028109588
1721.028273972
1731.028438355
1741.028602739
1751.028767123
1761.028931506
1771.029095890
1781.029260273
1791.029424657
1801.029589040
1811.029753424
1821.029917807
1831.030082191
1841.030246575
1851.030410958
1861.030575342
1871.030739725
1881.030904109
1891.031068492
1901.031232876
1911.031397259
1921.031561643
1931.031726027
1941.031890410
1951.032054794
1961.032219177
1971.032383561
1981.032547944
1991.032712328
2001.032876712
2011.033041095
2021.033205479
2031.033369862
2041.033534246
2051.033698629
2061.033863013
2071.034027396
2081.034191780
[Page 23]Day.Amount.
2091.034356164
2101.034520547
2111.034684931
2121.034849314
2131.035013698
2141.035178081
2151.035342465
2161.035506848
2171.035671232
2181.035835616
2191.036000000
2201.036164383
2211.036328766
2221.036493150
2231.036657533
2241.036821917
2251.036986301
2261.037150684
2271.037315068
2281.037479451
2291.037643835
2301.037808218
2311.037972602
2321.038136985
2331.038301369
2341.038465753
2351.038630136
2361.038794520
2371.038958903
2381.039123287
2391.039287670
2401.039452054
2411.039616437
2421.039780821
2431.039945205
2441.040109588
2451.040273972
2461.040438355
2471.040602739
2481.040767122
2491.040931506
2501.041095890
2511.041260273
2521.041424657
[Page 24]Day.Amount.
2531.041589040
2541.041753424
2551.041917807
2561.042082191
2571.042246574
2581.042410958
2591.042575342
2601.042739725
2611.042904109
2621.043068492
2631.043232876
2641.043397259
2651.043561643
2661.043726026
2671.043890410
2681.044054794
2691.044219177
2701.044383561
2711.044547944
2721.044712328
2731.044876711
2741.045041095
2751.045205479
2761.045369862
2771.045534246
2781.045698629
2791.045863013
2801.046027396
2811.046191780
2821.046356163
2831.046520547
2841.046684931
2851.046849314
2861.047013698
2871.047178081
2881.047342465
2891.047506848
2901.047671232
2911.047835615
2921.048000000
2931.048164383
2941.048328766
2951.048493150
2961.048657533
[Page 25]Day.Amount.
2971.048821917
2981.048986300
2991.049150684
3001.049315068
3011.049479451
3021.049643835
3031.049808218
3041.049972602
3051.050136985
3061.050301369
3071.050465752
3081.050630136
3091.050794520
3101.050958903
3111.051123287
3121.051287670
3131.051452054
3141.051616437
3151.051780821
3161.051945204
3171.052109588
3181.052273972
3191.052438355
3201.052602739
3211.052767122
3221.052931506
3231.053095889
3241.053260273
3251.053424657
3261.053589040
3271.053753424
3281.053917807
3291.054082191
3301.054246574
3311.054410958
3321.054575341
3331.054739725
3341.054904109
3351.055068492
3361.055232876
3371.055397259
3381.055561643
3391.055726026
3401.0558 [...]41 [...]
[Page 26]Day.Amount.
3411.056054793
3421.056219177
3431.056383561
3441.056547944
3451.056712328
3461.056876711
3471.057041095
3481.057205478
3491.057369862
3501.057534246
3511.057698629
3521.057863013
3531.058027396
3541.058191780
3551.058356163
3561.058520547
3571.058684930
3581.058849314
3591.059013698
3601.059178081
3611.059342465
3621.059506848
3631.059671232
3641.059835615
3651.060000000

[Page 27]

TABLE XII. The PRESENT WORTH of One Pound, due after any Number of Years to come, under 32. At the Rate of 6 per Cent. Simple Interest.
Years to come.Present Worth.
1.94339622
2.89285714
3.84745762
4.80645161
5.76923076
6.73529411
7.70422535
8.67567567
9.64935064
10.62500000
11.60240963
12.58139534
[Page 28]Years to come.Present Worth.
13.56179775
14.54347826
15.52631578
16.51020408
17.49504950
18.48076923
19.46728971
20.45454545
21.44247787
22.43103448
23.42016806
24.40983606
25.40000000
26.39062500
27.38167939
28.37313432
29.36496350
30.35714285
31.34965034

[Page 29]

TABLE XIII. The PRESENT WORTH of Due Pound, due after the expira­tion of any Number of Months under 25. At the Rate of 6 per Cent. Simple Interest.
Months to come.Present Worth.
1.99502487
2.99009900
3.98522167
4.98039215
5.97560975
6.97087378
7.96618357
8.96153846
9.95693779
10.95238095
11.94786729
12.94339622
[Page 30]Months to come.Present Worth.
13.93896713
14.93457943
15.93023255
16.92594444
17.92165898
18.91743119
19.91324200
20.90909090
21.90497737
22.90090090
23.89686098
24.89285714

[Page 31]

TABLE XIV. The PRESENT WORTH of One Pound, due after the expira­tion of any Number of Days under 366. At the Rate of 6 per Cent. Simple Interest.
Days to come.Present Worth.
1.99983564
2.99967134
3.99950709
4.99934290
5.99917876
6.99901467
7.99885064
8.99868666
9.99852273
10.99835886
11.99819504
12.99803128
13.99786757
14.99770391
15.99754031
16.99737676
17.99721326
18.99704982
19.99688643
20.99672310
[Page 32]Days to come.Present Worth.
21.99655982
22.99639659
23.99623341
24.99607029
25.99590723
26.99574421
27.99558125
28.99541835
29.99525549
30.99509269
31.99492994
32.99476725
33.99460460
34.99444201
35.99427948
36.99411700
37.993954 [...]7
38.99379220
39.99362987
40.99346761
41.99330539
42.99314323
43.99298112
44.99281906
45.99265706
46.99249511
47.99233321
48.99217136
49.99200957
50.99184782
51.99168614
52.99152450
53.99136292
54.99120139
55.99103991
56.99087848
57.99071711
58.99055579
[Page 33]Days to come.Present Worth.
59.99039453
60.99023331
61.99007215
62.98991104
63.98975000
64.98958899
65.98942804
66.98926714
67.98910629
68.98894549
69.98878475
70.98862406
71.98846341
72.98830283
73.98814230
74.98798181
75.98782138
76.98766100
77.98750067
78.98734040
79.98718018
80.98702001
81.98685989
82.98669983
83.98653980
84.98637984
85.98621993
86.98606008
87.98590027
88.98574052
89.98558081
90.98542116
91.98526156
92.98510202
93.98494253
94.98478309
95.98462369
96.98446435
[Page 34]Days to come.Present Worth.
97.98430506
98.98414582
99.98398663
100.98382749
101.98366841
102.98350937
103.98335039
104.98319146
105.98303258
106.98287376
107.98271498
108.98255626
109.98239758
110.98223896
111.98208039
112.98192188
113.98176340
114.98160498
115.98144662
116.98128830
117.98113004
118.98097183
119.98081367
120.98065556
121.98049750
122.98033949
123.98018152
124.98002361
125.97986576
126.97970795
127.97955020
128.97939250
129.97923485
130.97907725
131.97891970
132.97876221
133.97860473
134.97844734
[Page 35]Days to come.Present Worth.
135.97828999
136.97813269
137.97797545
138.97781825
139.97766111
140.97750401
141.97734697
142.97718997
143.97703304
144.97687614
145.97671930
146.97656250
147.97640576
148.97624906
149.97609242
150.97593583
151.97577928
152.97562279
153.97546635
154.97530996
155.97515362
156.97499732
157.97484108
158.97468489
159.97452875
160.97437266
161.97421662
162.97406063
163.97390470
164.97374880
165.97359296
166.97343717
167.97328143
168.97312574
169.97297009
170.97281450
171.97265896
172.97250346
[Page 36]Days to come.Present Worth.
173.97234803
174.97219263
175.97203729
176.97188199
177.97172675
178.97157155
179.97141640
180.97126131
181.97110626
182.97095127
183.97079631
184.97064141
185.97048656
186.97033177
187.97017702
188.97002232
189.96986767
190.96971307
191.96955852
192.96940401
193.96924959
194.96909518
195.96894083
196.96878652
197.96863227
198.96847806
199.96832387
200.96816976
201.96801570
202.96786169
203.96770773
204.96755382
205.96739995
206.96724614
207.96709237
208.96693865
209.96678498
210.96663136
[Page 37]Days to come.Present Worth.
211.96647778
212.96632426
213.96617079
214.96601737
215.96586399
216.96571066
217.96555738
218.96540415
219.96525096
220.96509783
221.96494475
222.96479171
223.96463871
224.96448578
225.96433289
226.96418004
227.96402725
228.96387451
229.96372181
230.96356916
231.96341656
232.96326401
233.96311151
234.96295906
235.96280665
236.96265429
237.96250198
238.96234972
239.96219750
240.96204533
241.96189322
242.96174114
243.96158912
244.96143715
245.96128522
246.96113334
247.96098151
248.96082973
[Page 38]Days to come.Present Worth.
249.96067800
250.96052631
251.96037467
252.96022309
253.96007154
254.95992004
255.95976860
256.95961720
257.95946585
258.95931454
259.95916329
260.95901208
261.95886092
262.95870981
263.95855875
264.95840773
265.95825676
266.95810584
267.95795497
268.95780414
269.95765335
270.95750262
271.95735194
272.95720130
273.95705071
274.95690016
275.95674967
276.95659922
277.95644882
278.95629847
279.95614816
280.95599790
281.95584769
282.95569753
283.95554742
284.95539735
285.95524732
286.95509735
[Page 39]Days to come.Present Worth.
287.95494742
288.95479753
289.95464770
290.95449791
291.95434817
292.95419847
293.95404882
294.95389923
295.95374967
296.95360016
297.95345070
298.95330129
299.95315192
300.95300261
301.95285334
302.95270411
303.95255493
304.95240580
305.95225672
306.95210768
307.95195869
308.95180974
309.95166084
310.95151199
311.95136318
312.95121442
313.95106573
314.95091706
315.95076844
316.95061986
317.95047134
318.95032285
319.95017442
320.95002603
321.94987769
322.94972939
323.94958114
324.94943204
[Page 40]Days to come.Present Worth.
325.94928478
326.94913667
327.94898861
328.94884059
329.94869262
330.94854470
331.94839682
332.94824898
333.9481 [...]120
334.94795346
335.94780576
336.94765811
337.94751051
338.94736295
339.94721544
340.94706798
341.94692056
342.94677319
343.94662587
344.94647858
345.94633135
346.94618416
347.94603701
348.94588991
349.94574286
350.94559585
351.94544889
352.94530198
353.94515512
354.94500829
355.94486151
356.94471478
357.94456809
358.94442145
359.94427485
360.94412830
361.94398179
362.94383533
363.94368897
364.94354254
365.94339622

[Page 41]

TABLE XV. A most useful TABLE for Reduction of Pence and Far­things into DECIMAL FRACTIONS, to the Hun­dredth part of a Farthing.
Far­things.Dectmal Fractions.
1.0010416
2.0020833
3.0031250

Pence & Far­things.Decimal Fractions.
(1).0041666
1.0052083
2.0062500
3.0072916
(2).0083333
1.0093750
2.0104166
3.0114583
(3).0125000
1.0135416
2.0145833
3.0156250
[Page 42]Pence & Far­things.Decimal Fractions.
(4).0166666
1.0177708
2.0187500
3.0197916
(5).0208333
1.0218750
2.0229166
3.0239583
(6).0250000
1.0260416
2.0270833
3.0281250
(7).0291666
1.0302083
2.0312500
3.0322916
(8).0333333
1.0343750
2.0354166
3.0364583
(9).0375000
1.0385416
2.0395833
3.0406250
(10).0416666
1.0427082
2.0437500
3.0447916
(11).0458333
1.0468750
2.0479166
3.0489583

[Page 43]

DECIMAL FRACTIONS for every Hundredth part of a Farthing.
Hun­dred Parts.Decimal Fractions.
1.000010416
2.000020833
3.000031249
4.000041666
5.000052083
6.000062499
7.000072916
8.000083333
9.000093749
10.000104166
11.000114583
12.000124999
13.000135416
14.000145833
15.000156249
16.000166666
17.000177083
18.000187499
19.000197916
20.000208333
21.000218749
22.000229166
23.000239583
24.000249999
25.000260416
26.000270833
27.000281249
28.000291666
29.000302083
30.000312499
[Page 44]Hun­dred Parts.Decimal Fractions.
31.000322916
32.000333333
33.000343749
34.000354166
35.000364583
36.000374999
37.000385416
38.000395833
39.000406249
40.000416666
41.000427083
42.000437499
43.000447916
44.000458333
45.000468749
46.000479166
47.000489583
48.000499999
49.000510416
50.000520833
51.000531249
52.000541666
53.000552083
54.000562499
55.000572916
56.000583333
57.000593749
58.000604166
59.000614583
60.000624999
61.000635416
62.000645833
63.000656249
64.000666666
65.000677083
66.000687499
67.000697916
68.000708333
[Page 45]Hun­dred Parts.Decimal Fractions.
69.000718749
70.000729166
71.000739583
72.000749999
73.000760416
74.000770833
75.000781249
76.000791666
77.000802083
78.000812499
79.000822916
80.000833333
81.000843749
82.000854166
83.000864583
84.000874999
85.000885416
86.000895833
87.000906249
88.000916666
89.000927083
90.000937499
91.000947916
92.000958333
93.000968749
94.000979166
95.000989583
96.000999999
97.001010416
98.001020833
99.001031249

The Use of the foregoing TABLES.

BEcause the usual Rate of Interest is 6 per Cent. there are Tables calcu­lated for the more ready dispatch of Questions relating either to the Amount, or Present Worth of any Sum; but for any other Rate from (1) to (12) the method will be very plain and practica­ble. I shall begin with some Examples at 6 per Cent.

Example 1. What is the Amount of 540 l. in seven Years, at 6 per Cent. Simple Interest?
Rule.

See for 7 years in the Margin of Table IX. and against it you find 1.42, the Amount of 1 l. in 7 years; multiply [Page 47] 540 by 1.42, and the Product is the Answer.

[...]

Example 2. What is the Amount of 540 l. in fifteen Months, at 6 per Cent. Simple Interest?
Rule.

Find 15 Months in the Margin of Table X. and against it is 1.075; by that multiply 540, and the Product is the Answer.

[Page 48] [...]

Example 3. What is the Amount of 540 l. in 279 Days, at 6 per Cent. Simple Interest?
Rule.

Find 279 Days in the Margin of Table XI. and against it is 1.0458, (you may take more or less of the Fraction, according as you desire to be more or less exact;) then multiply 1.0458 by 540, and the Product is the Answer.

[Page 49] [...]

Example 4. What is the Present Worth of 766.8 l. at the end of 7 Years, at 6 për Cent. Simple Interest?
Rule.

Find 7 Years in Table XII. and against it is .704225; then multiply that by the given Number 766.8, and the Product is the Answer.

[Page 50] [...]

Which is within 26 Hundred Parts of a Farthing of the truth, and is a suffi­cient Proof of the first Example.

Example 5. What is the present Worth of 580.5 l. due after 15 Months, at 6 per Cent. Simple Interest?
[Page 51] Rule.

Find 15 Months in Table XIII. and against it is .93023, &c. this being multiplied by 580.5, is an Answer.

[...]

Which is within one Farthing of the truth, and may be made within one Hundredth part of a Farthing of the truth, and is a clear Proof of the second Example.

[Page 52] And after this manner may any Question of this kind be easily and ex­actly resolved, and where the Sums are very great, the Operation will not be so tedious as that of working by Mr. Cla­vel's Tables. For a Proof of which, I shall here insert two Examples, one of the Amount, and the other of the pre­sent Worth of a considerable Sum.

Example 6. Suppose the King borrows of some Bankers 259879 l. 17s. 9d. 3q. for a year and 349 Days; what will be the Amount of Principal and Interest at the expiration of a Year and 349 Days, allowing them 6 per Cent?
The Operation by Mr. Clavel's Tables.

In Mr. Clavel's Tables I can find no more of this Sum at one time than 10000 l. therefore I seek the Interest of that, and find the Interest of 10000 l.

[Page 53] [...]

The odd Money I reduce into Deci­mal Parts of a Pound, by the Decimal Table in Mr. Russel's Appendix to Mr.Cla­vel, thus, [...]

Then because 200000 is twenty times 10000, I must multiply this Fraction and whole Number by 20, to find the Interest of 200000 l. for a Year, and 349 Days: and also multiply the said whole Number and Fraction by 5, for the In­terest of 50000, (there being five times 10000 contained in it) for the like time.

Example.

[...]

The Interest of the remaining part of the aforesaid Sum, viz. 9879 l. 17 s. (omitting the 9 d. 3 q.) is to be found in this manner: [...]

[Page 55] [...]

Reduce the Decimal Fractions of the Interest of 200000, and 50000, into Shillings and Pence, and then is the [Page 56] [...]

The Answer (without considering the Interest of 9 d. 3 q. which is not to be found by Mr. Clavel's Tables) is 290381 l. 19 s. 2 d. 3 q. very near.

The Operation according to the Rules of this little Book is performed by Sim­ple Addition, thus;

The given Sum redu­ced by Table I. is 259879.890625

The Amount of 1. l. for 365 and 349 Days, viz. 714 Days, is 1.1173698

[Page 57]

Tariffa for the Multiplicand.
1259879890625
2519759781250
3779639671875
41039519562500
51299399453125
61559279343750
71819159234375
82079039125000
92338919015625

The Multiplication contracted, as is directed in the Introduction to this little Book.

[...]

[Page] This Product, viz. 290381 l. 18 s. 9 d. 3 q. more by 86/100 of a Farthing, is the Answer.

Example 7.

Suppose there will be due after 349 Days, upon the several Branches of the King's Revenue, the Sum of 290381.94139 l. (or 18 s. 9 d. 3 q. more by 36/100 of a Farthing;) and His Majesty have occasion to convert this into ready Money, allow­ing the Advancers 6 per Cent. what is the present Worth of that Sum? or what must those persons advance in ready Money for the Premises?

Though it be the truest, and most exact way of all other, to Calculate either the Amount or present Worth of Money by Days, yet there is no help at all by Mr. Clavel's Tables to answer this Question.

[Page 58] But by this little Book, The Rule is,

l.

Multiply the given sum 290381.94139 by the Present Worth of 1 l. due at the end of 349 Days (which you will find in Table XIV.) .94574, and the Product is an Answer to the Question.

Tariffa for the Multiplicand.
129038194139
258076388278
387114582417
4116152776556
5145190970695
6174229164834
7203267358973
8232305553112
9261343747251

[Page] The Multiplication contracted, as in the Introduction is directed.

[...]

After the same manner are resolved any Questions, concerning either the Amount, or present Worth of any Sum, either for Years, Months, or Days. The next thing I shall Treat of is Annuities at Simple Interest, which shall be the Sub­ject of the following Chapter.

CHAP. II.
Of Annuities at Simple Interest.

THe increase of Annuities is by Mul­tiplication of the respective Rates of Interest, according to a Trigonal Progression, which may be better seen by comparing the Golden Table of Trigonal Progression in Chap. 1. with the following Table of Trigonal Increase, or Addition of (6) the Rate of Interest per Cent. and after it short Rules, which will hold for finding the Amount, or Present Worth of any Annuity, for any number of years, at any Rate of Simple Interest whatsoever.

[Page]

TABLE. The Multiplication of any Rates of Interest whatsoever belong­ing to each Year, for a For­born Annuity to 100 Years. This Table is Composed from the Golden Trigonal Table.
Years.A Trigonal Increase, or Addition of Rates of Interest.
10
21
33
46
510
615
721
828
936
1045
1155
1266
1378
1491
15105
16120
[Page 60]Years.A Trigonal Increase, or Addition of Rates of Interest.
17136
18153
19171
20190
21210
22231
23253
24276
25300
26325
27351
28378
29406
30435
31465
32496
33528
34561
35595
36630
37666
38703
39741
40780
41820
42861
43903
44946
45990
461035
471081
481128
491176
501225
[Page]Years.A Trigonal Increase, or Addition of Rates of Interest.
511275
521326
531378
541431
551485
561540
571596
581653
591711
601770
611830
621891
631953
642016
652080
662145
672211
682278
692346
702415
712485
722556
732628
742701
752775
762850
772926
783003
793081
803160
813240
823321
833403
843486
[Page 61]Years.A Trigonal Increase, or Addition of Rates of Interest.
853570
863655
873741
883828
893916
904005
914095
924186
934278
944371
954465
964560
974656
984753
994851
1004950

PROP. I.
To find the Amount of any Annuity, for any given time, and at any Rate of Simple Interest.

General Rule.

TO the Sum of the Annual, half-yearly, Quarterly, or Monthly Payments, add the Product of the Annual, Half-Yearly, Quarterly, of Monthly Rate, multiplied by the Num­ber in the foregoing Table, answering to the Number of Years, Half-Years, Quarters, or Months, in the Margin, that the Annuity is to continue; and the Total Sum is the true Amount of that Annuity.

Example 1.

What is the true Amount of an Annuity of 100 l. in five Years?

[Page 62] The Number in the foregoing Table answering to 5 in the Margin, is— 10

[...] That multiplied by 6 (the Annual Interest of 100 l.) makes— 60

To which add the five Annual Pay­ments, viz.— 500

The whole Amount is— 560

Example 2.

What is the Amount of an Annuity of 62 l. in four Years?

The Number in the foregoing Table answering to 4 in the Margin, is— 6

That multiplied by 3.72 (the Annual Interest of 62l. makes 22.32

To which adding the 4 Annual Payments, viz. 4 times 62 l.— 248.00

The whole Amount is— 270.32

PROP. II.
To know the Present Worth of any Annuity for any given Time, at any Rate, accompting Simple Interest.

FOr as much as the Present Worth of an Annuity is in effect, and must be imagined, a Principal, and the whole Amount of the Annuity as the Amount of the said Principal or Present Worth, in so long a time as the Annuity is continued,

The Proportion is, As the Amount of 1 l. for any time, Is to 1 l. So is the Amount of an Annuity, To the Present Worth.

Therefore the Rule is, Divide the Amount of the Annuity by the Amount of 1 l. in the given Time, and the Quotient is an Answer.

Example 1.

What is the Present Worth of an Annuity of 62 l. for four Years?

The Amount of 62 l. per Annum for four years by the foregoing Rules is found to be 270.32, and the Amount of 1 l. forborn four years, by Table IX. is found to be 1.24; wherefore I divide 270.32 by 1.24, thus: [...]

The Quotient 218 l. is the Answer.

Example 2.

What is the Present Worth of an Annuity of 100 l. to continue 100 Years?

[Page] The Amount of 100 l. Annuity for 100 years is 39700 l. the Amount of 1 l. put out to Interest for 100 years is 7 l. wherefore divide 39700 by 7, and the Quotient is the Answer.

[...]

For Proof of this, let 5671.4 be put out to Interest for 100 years, at 6 per Cent.

[...]

[Page 64]Wherefore the Operation is exact and just, though at the same time it is a cer­tain Argument, that the said Annuity to continue 100 years at Simple Interest, would be valued at above 56 years Pur­chase; for dividing 5671 by 100 (that is to say, cutting off the two last Figures) the remaining Figures shew it to be 56 years Purchase, over and above the Fraction of .71.

After the same Method,

The Amount of 100l. Annuity in 50 years is 12350l. the Amount of 1 l. put out to Interest at 6 per Cent. for 50 years is 4 l. wherefore dividing the said Amount by (4),

4) 12350 (3087.5

[Page] The Quotient, or Present Worth is 3087.5, which is above 30 years Pur­chase. From whence it is clear and manifest, that all Calculations of Annui­ties at Simple Interest are absolutely useless and ridiculous: For the truth is, all Pre­sent Worths or Purchases, either of Annui­ties, or Principal Sums, due at any time hereafter, ought to be considered in a Geometrical Proportion, from a Purchase for ever, (or to the end of the World) ac­cording to the several and respective Rates of Compound Interest. And if this be a truth as to Present Worths, it will be also a truth as to the Amounts, (as has been sufficiently explained in the Introduction to this Book.) And consequently, all Calculations, accor­ding to Simple Interest, ought wholly to be laid aside as erroneous and use­less.

CHAP. III.
The ERRORS of the ordinary Rules and Tables of Rebate, relating to Annuities, according to the Rate of Simple Interest, discovered and rectified.

ALthough all Tables of Rebate for Annuities at Simple Interest, ought to be wholly rejected as most ridiculous and useless, for the Reasons laid down in the foregoing Chapter, yet I do think it here seasonable, and indeed necessary▪ to animadvert upon the ordinary Rules relating to the present worth of such Annuities, which have been Composed by the respective Authors upon great mistakes, and for want of due reflection upon Arithmetical and Geometrical Pro­gressions.

I shall mention only two Examples.

The first is a Rule laid down by Mr. John Kersey, in his Appendix, bound [Page 66] up with Mr. Wingate's Arithmetick, Chap. 5. Pag. 378. Printed 1678. which is the very same with that made use of by Dr. Newton, in his Scale of Interest, pag. 20.

When it is required to find the present worth of an Annuity, by Rebating or Discompting at a given Rate of Simple Interest, the Operation will be as in the following Example, viz.

How much present Money is equivalent to an Annuity of 100 l. per Annum, to continue 5 Years, Rebate being made at the rate of 6 per Cent?

Answer 425 l. 18s. 9d. 2q. very near: Thus,

[...]

[Page 67]

For, saith he, it is manifest that there must be computed the present worth of 100 l. due at the first Years end. Also the present worth of 100 l. due at the second Years end, and in like manner for the third, fourth, and fifth Years. All which present Worths being added together, the Aggregate or Sum will be the total present worth of the Annuity, that is, 425 l. 18s. 9d. 2q. very near.

I must confess I cannot but wonder how such gross mistakes should pass through the hands of so many Learned and Ingenious Artists. For this very Example I find Published by the same Mr. Kersey, in the year 1650. and since that time, owned and made use of by several others.

But for the right understanding of the truth of this, and all other Questions of this kind. It is necessary to request the Reader to contemplate with me a few things.

[Page 68] 1. What is due of an Annuity that is not paid, at the end of the first, second, third, fourth, and fifth years, at Sim­ple Interest.

1. At the first years end.
 l.
At the first years end there is due the just sum of100
II. At the second years end. At the second years end, there is due,
 l.
1. For the first year100
2. For the second year100
Sum200

And besides this, For the Interest of the 100 l. due at the first years end, and detained during the whole second year— 6 l.

III. At the third years end. At the third years end, there is due,
 l.
1. For the first year100
2. For the second year100
3. For the third year100
Sum300

Besides this, there is due,

 l.
1. For the Interest of the first 100 l. for the second year6
2. For the Interest of the first 100 l. for the third year6
3. For the Interest of the second 100 l. for the third year6
Sum18

[Page 70]

IV. At the fourth years end.
 l.
1. For the first year100
2. For the second year100
3. For the third year100
4. For the fourth year100
Sum400

Besides this,

 l.
1. For the Interest of the first 100l. for the second year6
2. The Interest of the first 100l. for the third year6
3. The Interest of the first 100l. for the fourth year6
4. The Interest of the second 100l. for the third year6
5. The Interest of the second 100l. for the fourth year6
6. The Interest of the third 100l. for the fourth year6
Sum36

[Page 71]

V. At the fifth years end.
 l.
1. For the first year100
2. For the second year100
3. For the third year100
4. For the fourth year100
5. For the fifth year100
Sum500

Besides this,

 l.
1. For the Interest of the first 100l. for the second year6
2. For the Interest of the first 100l. for the third year6
3. For the Interest of the first 100l. for the fourth year6
4. For the Interest of the first 100l. for the fifth year6
 24
5. For the Interest of the second 100l. for the third year6
6. For the Interest of the second 100l. for the fourth year6
7. For the Interest of the second 100l. for the fifth year6
8. For the Interest of the third 100l. for the fourth year6
9. For the Interest of the third 100l. for the fifth year6
10. For the Interest of the fourth 100l. for the fifth year6
 36
 24
Sum Total of the Interest for the five years60
To which adding the five Annual payments, viz.500
The whole Amount of the Annuity of 100l. forborn five years, is560

In the next place, I desire the Ingeni­ous Reader to consider well the third Prop. of Diophantus Alexandrinus, con­cerning Peligonal Numbers.

ΔΙΟΦΑΝΤΟΥ ΑΛΕΞΑΝΔΡΕΩΣ ΠΕΡΙ ΠΟΛΙΤΟΝΩΝ ΑΡΙΘΜΩΝ.
PROP. III.

[...] &c. It Numbers (how many soever they be) exceed one another by an equal Internal, then the Internal between the greatest and the least, is Multipler of that equal Internal, according to the multitude of Numbers propounded, less by one.

For Example.

Let there be five given Terms, A, B, C, D, E, and let G be the common Interval or Difference.

[Page 74] To apply which, let

  • A=100
  • G=6
Number of Terms.Then is,  
1A=A1A=100
2B=A+G2B=100+6
3C=A+G+G3100+6+6
4D=A+G+G+G4D=100+6+6+6
5E=A+G+G+G+G5E=100+6+6+6+6

That is to say, the greatest Term is equal to the least, and as many Differences as there are more Terms besides the least. So here E is equal to 100, and 4 Differences, or 4 times 6. And the Sums of those Numbers are the true Amount of an Annuity at Simple Interest; thus,

The Annual Rents, toge­ther with the Annual Inte­restsThe Sums of Annual Rents, & Annual Inte­rests, for there­spective Years.The Number of An­nual Interests, or Differences, that are contained in every re­spective Sum, besides the Annual Rents.
11001100 
2100+62206=1
3100+6+63318=3
4100+6+6+64436=6
5100+6+6+6+65560=10

Therefore the true Amount of an Annuity of 100l. is as follows.

Year. Amounts
1100100
2100+100+6206
3100+100+100+6+6+6318
4100+100+100+100+6+6+6+6+6+6436
5100+100+100+100+100+6+6+6+6+6+6+6+6+6+6560

[Page 76] Consequently the Proportion is not as Mr. Kersey makes it, save only for the first year.

But the true proportion holds thus, viz.

   Amounts.Present worths.
At the1years endAs 106 to 100∷ So 100 to94.33962
2As 112 to 100∷ So 206 to183.92856
3As 118 to 100∷ So 318 to269.49152
4As 124 to 100∷ So 436 to351.61290
5As 130 to 100∷ So 560 to430.76923

Now therefore to perfect the Demonstration,

1. The present worth of the first year is94.33962
[Page 77] 2. Because 183.92856 is the present worth of the two first years, therefore if the present worth of the first year (Viz. 94.33962) be deducted out of it, it must needs leave the present worth of the second year, viz.89.58894
3. Because 269.49152 is the present worth of the three first years, therefore deducting out of it 183.92856, (viz. the present worth of the two first years) it leaves the present worth of the third year, viz.85.56296
4. So deducting 269.49152 out of 351.61290, there remains the present worth of the fourth year82.12138
5. And 430.76923 less by 351.61290, is the present worth of the last year, viz.79.15633
Total Sum of all the present worths430.76923

[Page 78] To conclude, it is evident from the two last Calculations, and that by clear Demonstration, That,

 l.
1. The Amount of the first year is100
2. The Amount of the two first years is206
3. The Amount of the three first years is318
4. The Amount of the four first years is436
5. The Amount of all five years is560

As likewise, That the present Worth,

1. Of the first year is94.33962
2. Of the two first years is183.92856
3. Of the three first years is269.49152
4. Of the four first years is351.61290
5. Of all five years is 430.76923

[Page 79] And lastly, it is evident and plain, That the present Worth,

1. Of the first year is94.33962
2. Of the second year is89.58894
3. Of the third year is85.56296
4. Of the fourth year is82.12138
5. Of the fifth year is79.15633
Total Sum of the present worths430.76923

Whereas Mr. Kersey makes the Total of the present worths but 425.93933, which is a very great mistake; as are all his particular present worths, (the first only excepted) which he could not well Calculate amiss.

Besides, if 425.93933 be put out for five years, it will amount to no more than 553.714109. Whereas 430.76923 in five years, at 6 per Cent. amounts to 560 l. which is the true Amount of 100 l. per Annum for five years, as has been sufficiently Demonstrated, and agrees [Page 80] exactly with the foregoing Rule: So that Mr. Kersey in this Example falls short of the truth, as to the present worth, no less than 4.8353, that is, 4l. 16 s. 8 d. 1 q. more by 96/100 of a Farthing. Which Error, if it be so considerable in an An­nuity of 100 l. per Annum, what would it be in an Annuity of 100000 paid per Annum? No less than 4835 l. 6 s.

2 Example.

A second Example I have borrowed from Mr. Dary, who has truly detected the Error of it, although he has not sufficiently explained the Reason of the Error; and therefore the Reader will find it here more strictly examined and refuted by a plain Demonstration obvi­ous to the meanest capacity.

The Example is this: What is the present worth of an Annual Rent of 62 l. to be enjoyed four Years to come, allowing the Purchaser 6 per Cent. Simple Interest?

[Page 81] The usual Method, says Mr. Dary, is thus: [...]

Now let the Error of this Operation be traced from the beginning.

1. The Annual Interest of 62 l. per Annum, is 3.72; where­fore by the foregoing Prop. of Diophantus Alexandrinus, pag. 73.

[Page 82] The Amount of [...]

Therefore the true Amount of an Annuity of 62 l. at each years end, is as follows.

At the end of the [...]

[Page 83] Wherefore the true Calculation of the present Worths is as follows, viz.

At the end of the [...]

[Page 84] Now therefore,

1. The present worth of the first year is—58.490
2. The present worth of the two first years less by the present worth of the first, that is, from 114.035 deducting 58.490, the present worth of the second year is—55.545
3. The present worth of the three first years (the present worth of the two first being deducted) that is, from 167.084 deducting 114.035, the remainder of the present worth of the third year is—53.049
4. Deducting from 218 the present worth of all four years, 167.084 the present worth of the first three years, the remainder (viz. 50.916) is the present worth of the fourth year—50.916

[Page 85] So then, The present worth, [...]

Whereas the usual way of Rebate makes it not above 216.390, which is less than the truth by 1.610, which is [...] l. 12 s. 2 d. 2 q. ferè.

[Page 86] And if 216.390 be put out at Interest at 6 per Cent. for four years, it will amount to no more than 268.3236, which is less than the true Amount of 218 l. viz. 270.32 by 1.9964, which being reduced, is 1 l. 19 s. 11 d. more by 11/100 parts of a Farthing.

All which may serve as a sufficient caution against such erroneous Tables and Calculations.

A second Reflection upon that Example of Mr. John Kersey.

I Must confess that the present Worth of 100 l. payable a year hence is 94.33962; and that the present worth of a single 100 l. payable two years hence, is as he has put it 89.28571; and the present worth of another bare 100 l. payable three years hence is 84.74576; and so to the end. And the Total of those present worths is as he has put it, viz.

[...]

[Page 88] And this is part of that very Table which I have calculated (being the twelfth Table of the first Chapter of this first Book) for The present worth of One Pound after any Number of Years under 32.

But reason tells me, that in this Cal­culation there is no consideration had of the Forbearance of Interest; for certain it is, if the first 100 l. had been paid at the first years end, it might have been put out to Interest, and at the five years end would have given an increase of four times 6 l. or 24 l. at Simple Interest; and so the second 100 l. would have in­creased in the three last years three times 6 l. or 18l.

That is to say,

 l.
The first 100 l. would increase in the four last years24
The second 100 l. would increase in the three last years18
The third 100 l. would increase in the two last years12
The fourth 100 l. would increase in the last year6
The whole increase60

[Page 89] Therefore there would be due, if all were forborn,

 l.
1. At the first years end100
2. At the second years end100+06
3. At the third years end100+12
4. At the fourth years end100+18
5. At the fifth years end100+24
 500+60

Now to Calculate the present worth of any, or all of these Sums, let it be considered by what proportion the Cal­culation ought to be made.

For Example.

Suppose the Annuity to be forborn only two years, and it be required to give the present worth of the two first years.

Whatsoever the Answer is, all will agree, that the Sum which is given in to be the present worth of those two years, being put out to interest, must amount to [...] at the end of two years.

[Page 90] Therefore I say, As 112 to 100∷ So 206 to 183.92856.

If this be a true Answer, then that Sum, viz. 183.92856, being put out to Interest at 6 per Cent. for two years, must amount to 206.

By the former Rules.

[...]

Now this Total Sum wants but [...]/100000 of 206.

[Page 91] For, [...]

But now take the Sum of Mr. Kersey's two years present Worths, viz.

[...]

Let therefore this Sum be put out to Interest for two years.

Wherefore as before, [...] [Page 92] [...]

Which is less than 206 (the true Amount of an Annuity of 100 l. for two years) by .3396304; which though it be but 6 s. 8 d. and somewhat more in two years time, yet were the Sum greater, or the time longer, it would prove a very considerable Error.

Wherefore I conclude, that Mr. Kersey's Calculations are erroneous as to Annui­ties, and mine exact: And there needs no further Illustrations or Demonstrati­ons about it.

The next thing to be Treated of in course, is touching the Equation of several Payments, and reducing them into one entire Payment at a certain time, so as there may be no loss either to Creditor or Debtor.

CHAP. IV.
Equation of Payments Rectified, and made Practicable for all Merchants, and others.

EQuation of Payments is by all agreed to be the reducing of seve­ral Payments into one entire Payment, at such a time, as neither Creditor or Debtor may be a loser by it, they being both agreed, the one to pay, and the other to receive, the said entire Payment at the appointed time.

Now of the Books that I have met with, and the Men I have discoursed with, about Equation of Payments at Simple Interest, some have adventured to give Rules for it, others have endeavoured to shew that such Rules are erroneous, and some of the most Learned of them have concluded the thing to be absolutely impracticable and impossible; and so [Page 94] left the poor Merchants to agree as they please about it.

The truth is, they have been, and are all of them, mistaken about the pre­sent Worths of Annuities at Simple Inte­rest, and that mistake has begot many others.

The method that I shall therefore take, shall be, First, to expose to the Readers view both the true Amount and present Worth of an Annuity of 100 l. for five years, at several Rates of Interest. And from thence frame, and give a gene­ral Rule for the reducing of several equal Payments due at equi-distant times, to one entire Payment. And after that, another Rule for reducing of unequal Payments at several times not equi­distant, to one entire Payment at a cer­tain time, so as neither he who pays, nor he who receives it, shall be any loser by it.

The Tables of the Amounts and pre­sent Worths of an Annuity of 100 l. for five years (at different Rates of Interest) do here follow in their order.

[Page 95]

TABLE I. At (1) per Cent. Simple Interest.
Years.The Amount of 100 l. [...] 1, 2, 3, 4, or 5 Years.Amount of Annual Payments at the end of 1, 2, 3, 4 or 5 Years.The present Worth of the first year, the first two years, the first three years, the first four years, or all the five years.The particular pre­sent Worths of the first, second, third, fourth, or fifth yearThe Amount of the Total present Worth of all the five Pay­ments, at the end of the first, second, third, fourth, or fifth year.
110110099.0099099.00990490.57142
2102201197.0588298.04892495.42856
3103303294.1747597.11593500.28570
4104406390.3846196.20986505.14285
5105510485.7142895.32967509.99999
    485.71428 

[Page 96]

TABLE II. At (2) per Cent. Simple Interest.
Years.The Amount of 100 l. in 1, 2, 3, 4, or 5 Years.Amount of Annual Payments, at the end of 1, 2, 3, 4 or 5 Years.The present Works of the first two years, the first three years, the first four years, or all the five years.The particular pre­sent Works of the first, second, third fourth, or fifth yearThe Amount of the Total present Worth of all the five Pay­ments, at the end of the first, second, third, fourth, or fifth year.
110210098.0392198.03921482.18181
2104202194.2307696.19155491.63635
3106306288.6792494.44848501.09089
4108412381.4814892.80224510.54543
5110520472.7272791.24579519.99999
    472.72727

[Page 97]

TABLE III. At (3) per Cent. Simple Interest.
Years.The Amount of 100 l. in 1, 2, 3, 4, or 5 Years.Amount of Annual Payments, at the end of 1, 2, 3, 4 or 5 Years.The present Worth of the first year, the first two years, the first three years, the first four years, or all the five years.The particular pre­sent Worths of the first, second, third, fourth, or fifth year.The Amount of the Total present Worth of all the five Pay­ments, at the end of the first, second, third, fourth, or fifth Year.
1103100. 97.0873797.08737474.69564
2106203191.5094394.42206488.52173
3109309283.4862391.97680502.34782
4112418373.2142889.72805516.17390
5115530460.8695687.65528529.99999
    460.86956 

[Page 98]

TABLE IV. At (4) per Cent. Simple Interest.
Years.The Amount of 100 l. in 1, 2, 3, 4, or 5 Years.Amount of Annual Payments, at the end of 1, 2, 3, 4 or 5 Years.The present Worth of the first year, the first two years, the first three years, the first four years, or all the five years.The particular pre­sent Worths of the first, second, third, fourth, or fifth year.The Amount of the Total present Worth of all the five Pay­ments, at the end of the first, second, third, fourth, or fifth year.
110410096.1538496.15384468.00000
2108204188.8888892.73504486.00000
3112312278.5714289.68254504.00000
4116424365.5172486.94582522.00000
5120540450.0000084.48276540.00000
    450.00000 

[Page 99]

TABLE V. At (5) per Cent. Simple Interest.
Years.The Amount of 100 l. in 1, 2, 3, 4, or 5 Years.Amount of Annual Payments, at the end of 1, 2, 3, 4 or 5 Years.The present Worth of the first year, the first two years, the first three years, the first four years, or all the five years.The particular pre­sent Worths of the first, second, third, fourth, or fifth year.The Amount of the Total present Worth of all the five Pay­ments, at the end of the first, second, third, fourth, or fifth year.
110510095.2380995.23809461.99999
2110205186.3636391.12554483.99999
3115315273.9130487.54941505.99999
4120430358.3333384.42029527.99999
5125550439.9999981.66666549.99999
    439.99999 

[Page 100]

TABLE VI. At (6) per Cent. Simple Interest.
Years.The Amount of 100 l. in 1, 2, 3, 4, or 5 Years.Amount of Annual Payments, at the end of 1, 2, 3, 4, or 5 Years.The present worth of the first year, the first two years, the first three years, the first four years, or all the five years.The particular pre­sent Worths of the first, second, third, fourth, or fifth year.The Amount of the Total present Worth of all the five Pay­ments, at the end of the first, second, third, fourth, or fifth year.
110610094.3396294.33962456.61538
2112206183.9285689.58894482.46153
3118318269.4915285.56296508.30769
4124436351.6129082.12138534.15384
5130560430.7692379.15633559.99999
    430.76923 

TABLE VII. At (10) per Cent. Simple Interest.
Years.The Amount of 100 l. in 1, 2, 3, 4, or 5 Years.Amount of Annual Payments, at the end of 1, 2, 3, 4, or 5 Years.The present worth of the first year, the first two years, the first three years, the first four years, or all the five years.The particular pre­sent Worths of the first, second, third, fourth, or fifth year.The Amount of the Total present Worth of all the five Pay­ments, at the end of the first, second, third, fourth, or fifth year.
111010090.9090990.90909440.00000
2120210175.0000084.09090480.00000
3130330253.8461578.84615520.00000
4140460328.5714274.72527560.00000
5150600400.0000071.42858600.00000
    399.99999 

Observations upon the foregoing Tables.

1. IT is observable, That as the Rate of Interest increases, the present Worth decreases; that is to say,

For the present Worth of an Annuity of 100 l. for five years,

At1per Cent. is485.71428
2472.72727
3460.86956
4450.00000
5439.99999 &c.
6430.76923
10399.99999 &c.

2. It is no less observable, That an Annuity of 100l. increases by a Trigo­nal Progression of the respective Rates. But the Present Worth increases by an Unitarian Addition of the Rate to the Principal for each year respectively. And these two ways are very different the one [Page 103] from the other, as may be seen by com­paring them together, as follows in the Example of an Annunity of 100l. at 6 perCent. Simple Interest.

   Amount of the Annui­ty for each of the five years.Amount of the present Worth of the Amuity for each of the five years.
At the1years end100456.61538
2206482.46153
3318508.30769
4436534.15384
5560559.99999 &c.

And yet how different soever they are at their first setting out, and by the way, yet the further they go, the nearer they come together, and at last agree to an insensible difference, and such as may be diminished in insinitum, either to the Hundredth, or Theirsandth, or any less part of a Farthing whatsoever can be desired.

3. As a consequence of the foregoing Observation:

[Page 104] If A. be to pay B. 100l. per Annum for five years, and they agree that the 500l. shall be paid at one entire Pay­ment, they must be sure to pitch upon such a time, as that the said 500l. being put out to Interest from that time to the end of five years, may be equal to the whole Amount of those five Annual Payments.

For Example.

Let the Rate of Interest be 6 per Cent. per Annum, and the Time of paying the said 500l. be at the end of three years, and so there are two years to come.

If the said 500l. for two years, at 6 per Cent. will amount to 560l. (which is the whole Amount of the Annuity at the five years end) the Time is right, if not, it is a false Time.

But the Annual Interest of 500l. is 30l. therefore in two years it is 60l. and that added to 500, makes 560l. And therefore it was a just time to pay the said 500l. at one entire Payment. For so B. has at the five years end, the whole [Page 105] effect of his Annuity improved to the utmost, at 6 per Cent. Simple Interest.

And B. having paid nothing before of the Annuity, and being obliged to pay nothing of it afterwards; but having enjoyed it for three years (which is the best part of it) already, and being to enjoy it two years more; the 500l. he now pays, is only as a Purchase of the Amount of the whole Annuity, which will be due at the five years end, viz. 560 l. and so gives the Present Worth of 560 l. from the three years end to the 5 years end; and so he pays not a Farthing more than the true worth of it. And for that true worth of it, to the end of the 5 years he has enjoyed, and must enjoy the said Annuity it self to the end of the said five years. And so neither A. nor B. have the least wrong or loss, neither the one by paying, nor the other by recei­ving, this one entire Payment of 500 l. at the three years end; and if either or both should sell their concerns, it would be the same thing.

[Page 106] 4. It is observable that the present Worth of the said Annuity, at any Rate of Interest, does at the three years end ex­ceed the Aggregate of the said five Sums, (or 500 l.)

For Example.

The present Worth of an Annuity of 100 l. per Annum to continue five years, does at the end of three years, Amount,

At1per Cent. to500.28570
2501.09089
3502.34782
4504.00000
5505.99999
6508.30769
10520.00000

5. It being as evident from this last Observation, That the present Worth of the whole Annuity being put out to Inte­rest for three years, will at any Rate of Interest, exceed the Aggregate of all [Page 107] the five Payments, and the greater the Rate of Interest is, the greater is that Excess.

For Example.

At (1) per Cent. the Excess is but . 28570; at (2) per Cent. the Excess is somewhat more, viz. 1.09089; at (3) per Cent. it is 2.34782; at (10) per Cent. it is 20l. and at (15) per Cent. it would be much more.

And it being likewise evident by all the foregoing Tables, whatever the Rate of Interest be, That 500l. more by the Interest of 500l. for two years, is equal to the whole Amount of the Annuity of 500l. for five years. That is to say,

The Interest of 500 l. for two years,

At (1) per Cent. is 10 l. which added to 500 l. makes the Amount510 l.
At (2) per Cent. is 20 l. which added to 500 l. makes the Amount520 l.

At (3) per Cent. is 30 l. which added to 500 l. makes the Amount530 l.
At (4) per Cent. is 40 l. which added to 500 l. makes the Amount540 l.
At (5) per Cent. is 50 l. which added to 500 l. makes the Amount550 l.
At (6) per Cent. is 60 l. which added to 500 l. makes the Amount560 l.

And lastly, it being sufficiently evi­dent by the third Observation, That if the 500 l. be paid at one entire Payment, at the end of three years, or, which is all one, two years before the Annuity be at an end; neither Creditor nor Debtor can have the least wrong, or suffer the least loss.

It may therefore be safely concluded, That it is practicable and possible to give a good and true Rule for Equation of seve­ral Payments; and likewise, that it is no way necessary (as some very Learned [Page 109] Artists would needs have perswaded me) to try that Rule by this Mark, viz. That the present Worth of the said 500 l. at the three Years end, must be the present Worth of the whole Amount of the said An­nuity. For by what has been already proved, the present Worth of the whole Annuity at any Rate of Interest, will at the three years end exceed the said 500 l.

Now therefore I shall proceed to give two General Rules.

The first, for Equation of several equal Payments at equi-distant times.

The second, for Equation of several unequal Payments at several times not equi-distant.

1. General Rule.
Rule.

For Equation of any given Number of equal Payments due at equi-distant Times.

Out of the whole Amount of the An­nuity, of Monthly Payment, deduct [Page 110] the Aggregate of the several Pay­ments, and the Remainder, if Annual, multiply by 365; if Monthly, by 30.416; then divide the Product by the Annual, or Monthly Interest of the said Aggre­gate, and the Quotient is the number of Days, before the end or Term of the Annuity, or Monthly Payment, when the said Aggregate may be paid with­out loss to either Creditor or Debtor.

1. Example.

Let the Annuity be 100 l.

The time it is to continue five years.

The whole Amount of the An­nuity560
The Aggregate of the several Payments500
The Annual Interest of the Ag­gregate (viz. 500)30

Now suppose A. be obliged to pay to B. 100 l. per Annum for five years, but they both agree that A. shall pay to B. the Aggregate 500 l. at one entire Pay­ment.

[Page 111] And then the Question is, at what time the said 500 l. is to be paid?

Therefore as the Rule directs, [...] That divided by 30, gives a Quotient, which is the true number of Days before the end of the said Annuity, when the said 500 l. is to be paid, viz. 730

Those 730 Days divided by 365, gives a Quotient of two years.

So then the true time of paying the said Aggregate of several payments, (viz. 500 l.) is two years before the end of five years; that is at the end of the third year.

2. Example.

A. is to pay B. 62 l. per Annum for four years; but they agree that A. shall pay the Aggregate of the several Sums, (viz. 248) at one entire Payment.

If the Annual Payment be62.00
The Amount of that in four years, at 6 per Cent. will be270.32
The Aggregate of the several Payments, or four times 62, is248.00
The Annual Interest of the said Aggregate14.88

Wherefore, [...]

This 22.32 is first to be multiplied by 365, which is 8146.80.

[Page 113] That Product 8146.80 being divided by the Annual Interest of the Aggregate 248, viz. 14.88, gives a Quotient of 547.5 Days.

This Quotient 547 Days and [...]/10, or a half, is a true Answer to the Question; that is to say, 547 Days and a half, or one Year, and 172 Days and a half, be­fore the end of four years, is the just time to pay the said Aggregate, or 248, at one entire Payment; so as neither he who pays it, nor he who receives it, may be a loser.

But that all things may be exposed clearly to the Readers view, I shall here repeat the thing, and set down the whole Operation.

1. The Annual Payment for four years is62.00 l.
2. The whole Amount of this in four years is270.32 l.
3. The Aggregate, or four years Payments, that is, four times 62l. is248.00 l.
4. The Annual Interest of the said Aggregate is14.88 l.

[Page 114] Now the Question is, what is the true time for paying the said Aggregate, or 248, at one entire Payment?

To Answer this, I proceed according to the aforesaid Rule. [...]

2. I multiply this Remainder by 365, thus, [...]

3. This Product I divide by the Annual Interest of the Aggregate, viz. 14.88.

[Page 115]

Tariffa for the Divisor.
11488
22976
34464
45952
57440
68928
710416
811904
913392
1014880

[...]

And the Quotient 547.5, is an An­swer to the Question.

That is to say, (as before) one year, and 172 days, and a half, before the end of four years.

Or, which is the same thing, two years, and 192 days and a half, after the Agreement, must the 248 l. be paid at one entire Payment; and for the Reasons aforesaid, there is no loss to either A. or B. [Page 116] For Proof of this,

Let 248 l. be put out to Interest at 6 per Cent. for one year, and 172 days and a half, that is, 547.5 days (which is the Quotient, or the time given from the Payment thereof to the end of the Annuity) and if it make up the whole Amount of the Annuity, viz. 270.32, the Operation is right.

Tariffa for the Mul­tiplicand.
100016438356
200032876712
300049315068
400065753424
500082191780
600098630136
700115068492
800131506848
900147945204
1000164383560

For Example.

[...]

Then I make the following Tariffa, and proceed to multiply the foregoing Pro­duct by 248.

Tariffa for the Multiplicand.
1089999999100
2179999998200
3269999997300
4359999996400
5449999995500
6539999994600
7629999993700
8719999992800
9809999991900

[Page 118] [...]

Wanting but 1/10000 (which is not the Hundredth part of a Farthing) of the true Amount of the whole Annuity, viz. 270.32, and therefore the Opera­tion is just.

And thus may any Question of this nature be resolved, to a Day, and parts of a Day; for if both these last Questions had been made for Months, the same Rule must have been observed.

For Example.

If A. is to pay to B. 100 l. per Month for five Months, when may he pay the 500 l. at one entire Payment, at the Rate of 6 per Cent?

[Page 119] The Payments being Monthly, [...]

Therefore, [...]

In pursuance of the aforesaid General Rule. [...]

[Page 120] Let therefore 5 be multiplied by 30.416, or the true number of Days that are in one equal Month. [...]

And let that (152.080) be divided by 2.500, or the Monthly Interest of 500 l. at 6 per Cent.

Tariffa for the Divisor.
125
250
375
4100
5125
6150
7175
8200
9225

[...]

The Quotient (60.832) is a true Answer in Days.

[Page 121] That is to say, 60 Days and 832/1000 of a Day, (which makes two equal Months) before the end of five Months; or (which is all one) three Months after the agreement, or after the first day, when the said Debt was growing due, is the just time of paying the 500 l. at one entire Payment.

For Proof of this.

If 500 l. be put out to Interest at 6 per Cent. for two equal Months, or 60.832 Days, and does give 5 l. it makes the 500 l. become 505 l. which is the full Amount of those five Months Pay­ments, and is a just Answer to the Que­stion.

But, [...]

And the Operation is exact.

[Page 122] And this I take to be sufficient for the Resolution of any Question of this nature.

I shall proceed in the next place to Discourse about unequal Payments, at times not equi-distant.

A brief Discourse concerning the Equation of unequal Payments at Times not equi-distant.

For Example.

A Merchant owes 500 l. to be paid at three several unequal Payments, viz. at the end of four Months 300 l. at the end of six Months 100 l. and at the end of twelve Months 100 l. but the Debtor agrees with the Creditor to dis­charge the Debt (viz. 500 l.) at one entire Payment.

The Question is, at what time this 500 l. may be paid, without damage or prejudice to either Creditor or Debtor?

The General Rule is this.

First find the true Amount of each of the Sums, from the first day of the A­greement, to the last day of Payment, as supposing them to be forborn to the last. Then out of that deduct the Aggregate [Page 124] of the respective Payments, and multi­ply the Remainder, if Annual, by 365; if Monthly, by 30.4166; and the Pro­duct divide by the Annual or Monthly Interest of the said Aggregate, and the Quotient is the Number of Days from the last Day of Payment, ac­compting backwards.

The Operation is as follows.

First, the length of Time from the day of the Agreement, to the last day of Payment, is just twelve Months.

So then,

1. In the first place, 300 l. pay­able after 4 Months, and be­ing forborn to the end of 12 Months, has 8 Months Inte­rest to accompt for, viz.12.000
2. In the second place, 100 l. payable after 6 Months, and being forborn to the end of 12 Months, has 6 Months Interest to accompt for, viz.3.000
3. To these Sums adding the500.000
The whole Amount is515.000

[Page 125] Then, [...]

And the Proportion is this.

If 2.5 be the Interest of 500 l. for one Month, how many Months Interest will 15 make?

Wherefore divide 15 by 2.5, and the Quotient is the Answer to the Question.

Tariffa for the Divisor.
125
250
375
4100
5125
6150
7175
8200
9225

The Operation is this. [...]

That is to say, if the said 500 l. be paid six Months before the end of twelve Months or (which is all one) at the end of [Page 126] six Months, there will be no loss or damage either to Creditor or Debtor.

For Proof of this,

1. In the first place, 300l. was due at 4 Months end, and being con­tinued 2 Months longer, the In­terest thereof for 2 Months is 3 l. the whole Amount is303 l.
2. In the next place, 100 l. paid at 6 Months end, is the time it was due100 l.
3. In the last place, the other 100 l. paid 6 Months before the time, there must be an abatement made of 3 l.97 l.
Total Sum500 l.

So that in the first Sum there is an increase of 3 l. and in the last there is a decrease of 3 l. which are to be set one against the other; and the whole Amount is the Aggregate of the respe­ctive Sums, and being paid at the end of 6 Months makes the Equation just 500 l.

[Page 127] After this manner may any Number of unequal Sums payable at any Number of Times not equi-distant, be Equated, and a time set for the Payment of the Aggregate; and not only so, but if the Debtor A. owe to B. 100l. per Annum, or per Month, for any Number of Years or Months, and A. and B. agreeing toge­ther that it shall be in the power of A. to pay to B. the true value of his Preten­sions at the end of any of the Years or Months, it is very Practicable, for the present Worth of the whole Amount at the end of any of the Years or Months resolves the doubt, and is an Answer the Question.

For Example.

A. owes to B. 100 l. per Annum for five years, and they agree that A. shall buy it off at the end of any of the four years, for at the end of 5 years nothing less than the whole 560 l. will pay the Dein.

1. The present worth of 560 l. (or the whole Amount) at the first years end, is451.6129

[Page 128]

2. The present worth of 560 l. at the second years end, is474.5762
3. The present worth of 560 l. at the third years end, is500, 0000
4. The present worth of 560 l. at the fourth years end, is528.3018
5. The present worth of 560 l. at the fifth years end, is560, 0000

Thus I have as briefly as the nature of the thing would permit, explained the Doctrine of Simple Interest, as likewise that of Annuities, and Equation of several Pay­ments at Simple Interest, which is of ex­cellent use for 6 12, or 18 Months, because the difference between Simple and Com­pound Interest is not material in so short a time.

But for as much as the business of An­ [...]uities, or Purchases, for any considerable Number of years, does most properly and truly belong to the Doctrine of Com­pound Interest, I shall make that the Sub­ject of the following Book.

THE DOCTRINE OF COMPOUND INTEREST.
LIB. II.

CHAP. I.
The Doctrine of Compound Interest explained.

Compound Interest, or Interest upon Interest, increases not only from the Principal, but also from the Interest, in the man­ner hereafter exprest.

That is to say,

If 100l. be put out to Interest at 6 per Cent.

1. The first year there will be due106.0000
2. The second year that (106l.) is made a Princi­pal, and being put out for a year, becomes112.3600
3. The third year that (112.360) is made a Prin­cipal, and being put out to Interest, amounts to119.1016

And so in infinitum.

So that the respective Amounts for each respective year, are so many Geome­trical Proportional Numbers.

For, As 100 to 106, for the first year ∷ So 106 to 112.36, for the second year.

[Page 131] Again, As 106 to 112.36 ∷ So 112.36 to 119.1016, for the third year.

Item, As 112.36 to 119.1016 ∷ So 119.1016 to 126.247016, for the fourth year. &c.

But to the end, that the Ingenious Practitioner may have entire satisfaction in the business of Interest upon Interest, it will be necessary to make some Re­flection upon Geometrical Proportion and Progression.

Reflection upon Geometrical Progression.

If Numbers (how many soever they be) contain the one the other by an equal Ratio, then the greatest of those Num­bers is Multipler of the Powers of the Denomination of that equal Ratio mul­tiplied by the least, according to the mul­titude of the given Numbers less by one.

[Page 132] Let the given Numbers be 2, 6, 18, 54.

Then by the Hypothesis, the first multiplied by (3) is equal to the second; and the second multiplied by (3) is equal to the third; and so in infinitum.

That is to say,
FirstTerm2=2 ———— 2
Second6=2 into 3 ——— 6
Third18=2 into 3 into 3 —— 18
Fourth54=2 into 3 into 3 into 3 — 54

That is to say in a Symbolical way,

[Page 133] Let there be any Number of Proportionals, A, B, C, D, E, F, G, and the Ratio R.

FirstTermA=A
SecondB=A into R
ThirdC=A into R into R
FourthD=A into R into R into R
FifthE=A into R into R into R into R
SixthF=A into R into R into R into R into R
SeventhG=A into R into R into R into R into R into R

[Page 134] To apply this to the present purpose, let the first Geometrical Term be (1.) the Ratio (. 06)

 First Power.Second Power.Third Power.Fourth Power.Fifth Power.Sixth Power.Geometri­cal Propor­tional Numbers.
A=100      100.000
B=100into1.06     106.000
C=100into1.06into1.06    112.360
D=100into1.06into1.06into1.06   119.101
E=100 into1.06 into1.06 into1.06 into1.06  126.247
F=100 into1.06 into1.06 into1.06 into1.06 into1.06 133.823
G=100 into1.06 into1.06 into1.06 into1.06 into1.06 into1.06141.851

The Geometrical Numbers at length are these that follow, though there is no necessity of making use of them all, the difference being indiscernable.

[Page 135]

Years.Amount at 6 per Cent. Compound Interest.
11.06
21.1236
31.191016
41.26247696
51.3382255776
61.418519112256
71.50363025899136
81.5938480745308416
91.689478959002692096
101.79084769654285362176

[Page 136] NOw for as much as these Geometri­cal Proportional Numbers swell into a great Number of places, and the Mul­tiplications become tedious, it has been look'd upon as impracticable to find them out by any way, but by the help of the Logarithms. But I shall endeavour to shew a way how it may be very practi­cable to find out any of these Numbers, for any year under 32, without much trouble or difficulty.

For Example.

Let it be demanded to give the Amount of I l. in eight years, at 6 per Cent. Compound Interest, not having any help of a Table.

The Operation is thus.

First, I Square 1.06, which is 1.1236, and the Product is the Amount in two years.

[Page 137] Secondly, I Square 1.1236, and that gives me the Proportional Number an­swering to (4) in the Margin, viz. 1.26247, &c.

Thirdly, I Square 1.26247, and that gives me the Proportional Number answer­ing to (8) in the Margin, which was the thing proposed, viz. 1.59384, &c.

Now if it had been demanded to find the Proportional Number answering to (16) in the Margin, it is the Square of 1.59384, &c.

And the Square of 1.59384 gives the Proportional Number answering to (32) in the Margin.

Thus far the Method is clear for all even Numbers; but for the odd Num­bers,

The Rule is this:

Having found the Proportional Number answering to the greater half of the given Number in the Margin, Square it, and divide it by the least and [Page 138] first Proportional Number, and the Quotient is the Number desired.

For Example.

Let it be demanded to find the Propor­tional Number answering to (3) in the Margin, and let (1.06) be the least Pro­portional Number.

Having found 1.1236 to be the Proportional Number answering to (2) in the Margin, which (2) is the greater half of (3), I Square 1.1236, and it gives 1.26247, which I divide by 1.06, and the Quotient (1.1910, &c.) is the Proportional Number desired.

Again,

Let it be demanded to find the Propor­tional Number answering to (5) in the Margin.

[Page 139] Having found the Proportional Number answering to (3) in the Margin, (which 3 is the greater half of 5) viz. 1.1910; the Square thereof, viz. 1.4185, being divided by 1.06, the Quotient is the Number desired, viz. 1.3382.

Thus (9) is the greater half of (17), and therefore the Proportional Number answering to (9) in the Margin being Squared, and that Square divided by 1.06, gives 3.700, for the Proportional Number answering to (17) in the Mar­gin. And so may the Proportional Num­ber of any odd Number in the Margin be found out, without the help of Lo­garithms.

But for as much as exact Tables truly Calculated are most ready for use, I have with no small Pains and Charge (not Transcribed other Mens Tables and Errors, but) carefully and exactly Cal­culated several Tables of my own; by the help of which, may easily and rea­dily be found out either the Amount, or Present Worth of any Sum, at any Rate of Compound Interest, and the like for [Page 140] Annuities and Purchases, after the same manner, and in the same method as I have done in the first Book of this small Treatise, for the Amount and Present Worth of either Principal Sums, or Annuities, at Simple Interest.

TABLE I. The AMOUNT of One Pound put out to Interest, and forborn any Number of Years under 32, or Quarters under 125. At the Rate of 6 per Cent. Compound Interest.
Years and Quar­ters.Amount.
(0)1.000000
11.014674
21.029563
31.044670
(1)1.060000
11.075554
21.091336
31.107351
(2)1.123600
11.140087
21.156817
31.173792
(3)1.191016
11.208493
21.226226
31.244219
[Page 142](4)1.262477
11.281002
21.299799
31.318872
(5)1.338225
11.357862
21.377787
31.398005
(6)1.418519
11.439334
21.460455
31.481885
(7)1.503630
11.525694
21.548082
31.570798
(8)1.593848
11.617236
21.640967
31.665046
(9)1.689479
11.714270
21.739425
31.764949
(10)1.790847
11.817126
21.843790
31.870846
(11)1.898298
11.926154
21.954418
31.983096
[Page 143](12)2.012196
12.041723
22.071683
32.102082
(13)2.132928
12.164226
22.195984
32.228207
(14)2.260904
12.294080
22.327743
32.361900
(15)2.396558
12.431725
22.467407
32.503614
(16)2.540351
12.577628
22.615452
32.653831
(17)2.692773
12.732286
22.772379
32.813061
(18)2.854339
12.896223
22.938722
32.981844
(19)3.025599
13.069996
23.115045
33.160755
[Page 144](20)3.207135
13.254196
23.301948
33.350400
(21)3.399564
13.449448
23.500065
33.551424
(22)3.603537
13.656415
23.710069
33.764509
(23)3.819749
13.875800
23.932673
33.990380
(24)4.048934
14.108348
24.168633
34.229803
(25)4.291870
14.354849
24.418751
34.483591
(26)4.549383
14.616139
24.683876
34.752607
(27)4.822346
14.893108
24.964909
35.037763
[Page 145](28)5.111686
15.186695
25.262803
35.340029
(29)5.418388
15.497896
25.578571
35.660431
(30)5.743491
15.827770
25.913284
36.000054
(31)6.088101

[Page 146]

TABLE II. The AMOUNT of Due Pound, put out to Interest for any Number of Months un­der 25. At the Rate of 6 per Cent. Compound Interest.
Months.Amount.
11.004867
21.009758
31.014673
41.019612
51.024575
61.029562
71.034574
81.039610
91.044670
101.049755
111.054865
121.060000
131.065159
141.070344
151.075554
161.080789
171.086050
181.091337
191.096649
201.101987
211.107351
221.112741
231.118158
241.123600

[Page 147]

TABLE III. The AMOUNT of Due Pound, put out to Interest for any Number of Days under 366. At the Rate of 6 per Cent. Compound Interest.
Days.Amount.
11.000160
21.000319
31.000479
41.000639
51.000798
61.000958
71.001118
81.001278
91.001438
101.001598
111.001757
121.001917
131.002077
141.002237
151.002397
161.002557
171.002717
181.002878
191.003038
201.003198
211.003358
221.003518
231.003678
241.003839
[Page 148]251.003998
261.004159
271.004320
281.004480
291.004640
301.004801
311.004961
321.005121
331.005282
341.005442
351.005603
361.005764
371.005924
381.006085
391.006245
401.006406
411.006567
421.006727
431.006888
441.007049
451.007209
461.007370
471.007531
481.007692
491.007853
501.008014
511.008175
521.008336
531.008497
541.008658
551.008818
561.008980
571.009141
581.009302
591.009463
601.009624
611.009786
621.009947
631.010108
641.010269
651.010431
661.010592
[Page 149]671.010753
681.010915
691.011076
701.011237
711.011398
721.011560
731.011722
741.011883
751.012045
761.012207
771.012368
781.012530
791.012691
801.012853
811.013015
821.013177
831.013338
841.013500
851.013662
861.013824
871.013986
881.014147
891.014309
901.014471
911.014633
921.014795
931.014957
941.015119
951.015281
961.015443
971.015605
981.015768
991.015930
1001.016093
1011.016254
1031.016417
1031.016579
1041.016741
1051.016903
1061.017066
1071.017228
1081.017391
[Page 150]1091.017553
1101.017715
1111.017878
1121.018040
1131.018203
1141.018365
1151.018528
1161.018691
1171.018853
1181.019016
1191.019179
1201.019341
1211.019504
1221.019667
1231.019830
1241.019992
1251.020155
1261.020318
1271.020481
1281.020644
1291.020807
1301.020970
1311.021133
1321.021296
1331.021459
1341.021622
1351.021785
1361.021948
1371.022112
1381.022275
1391.022438
1401.022601
1411.022765
1421.022928
1431.023091
1441.023254
1451.023418
1461.023581
1471.023745
1481.023908
1491.024072
1501.024235
[Page 151]1511.024399
1521.024562
1531.024726
1541.024889
1551.025053
1561.025217
1571.025380
1581.025544
1591.025708
1601.025871
1611.026035
1621.026199
1631.026363
1641.026527
1651.026691
1661.026855
1671.027018
1681.027182
1691.027346
1701.027510
1711.027675
1721.027839
1731.028003
1741.028167
1751.028331
1761.028495
1771.028659
1781.028824
1791.028988
1801.029152
1811.029316
1821.029481
1831.029645
1841.029809
1851.029974
1861.030138
1871.030302
1881.030467
1891.030632
1901.030796
1911.030961
1921.031126
[Page 152]1931.031290
1941.031455
1951.031619
1961.031784
1971.031949
1981.032114
1991.032278
2001.032443
2011.032608
2021.032773
2031.032938
2041.033103
2051.033268
2061.033433
2071.033598
2081.033763
2091.033928
2101.034098
2111.034258
2121.034423
2131.034588
2141.034753
2151.034919
2161.035084
2171.035249
2181.035414
2191.035580
2201.035745
2211.035910
2221.036076
2231.036241
2241.036407
2251.036572
2261.036737
2271.036903
2281.037069
2291.037234
2301.037400
2311.037565
2321.037731
2331.037897
2341.038062
[Page 153]2351.038228
2361.038394
2371.038560
2381.038725
2391.038891
2401.039057
2411.039223
2421.039389
2431.039555
2441.039721
2451.039887
2461.040053
2471.040219
2481.040385
2491.040551
2501.040717
2511.040883
2521.041050
2531.041216
2541.041382
2551.041548
2561.041715
2571.041881
2581.042047
2591.042214
2601.042380
2611.042546
2621.042713
2631.042879
2641.043046
2651.043212
2661.043379
2671.043545
2681.043712
2691.043879
2701.044045
2711.044212
2721.044379
2731.044545
2741.044712
2751.044879
2761.045046
[Page 154]2771.045213
2781.045380
2791.045546
2801.045713
2811.045880
2821.046047
2831.046214
2841.046381
2851.046548
2861.046715
2871.046883
2881.047050
2891.047217
2901.047384
2911.047551
2921.047719
2931.047886
2941.048053
2951.048220
2961.048388
2971.048555
2981.048723
2991.048890
3001.049057
3011.049225
3021.049393
3031.049560
3041.049728
3051.049895
3061.050063
3071.050230
3081.050398
3091.050566
3101.050734
3111.050901
3121.051069
3131.051237
3141.051405
3151.051573
3161.051741
3171.051908
3181.053076
[Page 155]3191.052244
3201.052412
3211.052580
3221.052748
3231.052916
3241.053084
3251.053253
3261.053421
3271.053589
3281.053757
3291.053925
3301.054094
3311.054262
3321.054430
3331.054599
3341.054767
3351.054935
3361.055104
3371.055272
3381.055441
3391.055609
3401.055778
3411.055946
3421.056115
3431.056284
3441.056452
3451.056621
3461.056790
3471.056958
3481.057127
3491.057296
3501.057465
3511.057633
3521.057802
3531.057971
3541.058140
3551.058309
3561.058478
3571.058647
3581.058816
3591.058985
3601.059154
[Page 156]Days.Amount.
3611.059323
3621.059492
3631.059661
3641.059830
3651.060000

[Page 157]

TABLE IV. The PRESENT WORTH of Due Pound, due after any Number of Years under 32, or Num­ters under 125. At the Rate of 6 per Cent. Compound Interest.
Years and Quar­ters.Present Worth.
(0).0000000
1.9855383
2.9712858
3.9572394
(1).9433962
1.9297531
2.9163074
3.9030560
(2).8899964
1.8771256
2.8644409
3.8519397
(3).8396193
1.8274770
2.8155103
3.8037167
[Page 158](4).7920936
1.7806387
2.7693493
3.7582233
(5).7472581
1.7364516
2.7258013
3.7153050
(6).7049605
1.6947656
2.6847182
3.6748160
(7).6650571
1.6554393
2.6459606
3.6366189
(8).6274123
1.6183389
2.6093967
3.6005839
(9).5918984
1.5833386
2.5749026
3.5665885
(10).5583947
1.5503194
2.5423609
3.5345175
(11).5267875
1.5191693
2.5116612
3.5042618
[Page 159](12).4969693
1.4897823
2.4826993
3.4757187
(13).4688390
1.4620588
2.4553767
3.4487912
(14).4423009
1.4359045
2.4296006
3.4233879
(15).4172650
1.4112307
2.4052836
3.3994226
(16).3936463
1.3879535
2.3823430
3.3768137
(17).3713644
1.3659939
2.3607010
3.3554847
(18).3503438
1.3452772
2.3402839
3.3353629
(19).3305130
1.3257332
2.3210226
3.3163801
[Page 160](20).3118047
1.3072955
2.3028515
3.2984718
(21).2941554
1.2899014
2.2857089
3.2815771
(22).2775051
1.2734919
2.2695367
3.2656388
(23).2617972
1.2580112
2.2542799
3.2506026
(24).2469785
1.2434068
2.2398867
3.2364176
(25).2329986
1.2296291
2.2263082
3.2230355
(26).2198100
1.2166312
2.2134983
3.2104108
(27).2073679
1.2043690
2.2014135
3.1985008
[Page 161](28).1956301
1.1928010
2.1900128
3.1872648
(29).1845567
1.1818877
2.1792573
3.1766649
(30).1741101
1.1715924
2.1691113
3.1666663
(31).1642569

[Page 162]

TABLE V. The PRESENT WORTH of One Pound, due after the expiration of any Number of Months under 25. At the Rate of 6 per Cent. Compound Interest.
Months.Present worth.
1.9951560
2.9903355
3.9855383
4.9807644
5.9760136
6.9712858
7.9665810
8.9618988
9.9572394
10.9526026
11.9479884
12.9433962
13.9388264
14.9342788
15.9297531
16.9252494
17.9207676
18.9163074
19.9118689
20.9074518
21.9030561
22.8986817
23.8943285
24.8899964

[Page 163]

TABLE VI. The PRESENT WORTH of One Pound, due after the expiration of any Number of Days under 366. At the Rate of 6 per Cent. Compound Interest.
Days.Present Worth.
1.9998404
2.9996808
3.9995212
4.9993616
5.9992021
6.9990426
7.9988831
8.9987237
9.9985643
10.9984048
11.9982455
12.9980861
13.9979268
14.9977675
15.9976083
16.9974490
17.9972898
18.9971306
19.9969714
20.9968123
21.9966532
22.9964941
23.9963350
24.9961759
[Page 164]25.9960169
26.9958579
27.9956990
28.9955400
29.9953810
30.9952222
31.9950633
32.9949045
33.9947457
34.9945869
35.9944282
36.9942694
37.9941107
38.9939520
39.9937934
40.9936347
41.9934760
42.9933175
43.9931590
44.9930004
45.9928419
46.9926834
47.9925250
48.9924665
49.9923081
50.9921497
51.9919914
52.9917330
53.9915747
54.9914165
55.9912582
56.9911000
57.9909418
58.9907836
59.9906254
60.9904673
61.9903092
62.9901511
63.9899930
64.9898350
[Page 165]65.9896769
66.9895190
67.9893611
68.9892031
69.9890452
70.9888874
71.9887297
72.9885718
73.9884139
74.9882561
75.9880983
76.9879406
77.9877829
78.9876252
79.9874676
80.9873100
81.9871523
82.9869948
83.9868372
84.9866797
85.9865222
86.9863647
87.9862073
88.9860498
89.9858924
90.9857350
91.9855777
92.9854204
93.9852631
94.9851058
95.9849486
96.9847913
97.9846341
98.9844770
99.9843198
100.9841627
101.9840056
103.9838485
103.9836914
104.9835344
[Page 166]105.9833774
106.9832204
107.9830635
108.9829066
109.9827497
110.9825928
111.9824359
112.9822791
113.9821223
114.9819656
115.9818088
116.9816521
117.9814954
118.9813387
119.9811821
120.9810254
121.9808688
122.9807123
123.9805557
124.9803992
125.9802427
126.9800862
127.9799298
128.9797733
129.9796169
130.9794606
131.9793042
132.9791479
133.9789916
134.9788353
135.9786791
136.9785228
137.9783666
138.9782105
139.9780543
140.9778982
141.9777421
142.9775860
143.9774300
144.9772739
[Page 167]145.9771179
146.9769620
147.9768060
148.9766500
149.9764942
150.9763383
151.9761824
152.9760266
153.9758708
154.9757150
155.9755593
156.9754036
157.9752479
158.9750922
159.9749366
160.9747809
161.9746253
162.9744697
163.9743142
164.9741587
165.9730032
166.9738477
167.9736922
168.9735368
169.9733814
170.9732260
171.9730707
172.9729154
173.9727600
174.9726047
175.9724495
176.9722942
177.9721390
178.9719839
179.9718287
180.9716736
181.9715185
182.9713634
183.9712084
184.9710534
[Page 168]185.9708983
186.9707433
187.9705884
188.9704334
189.9702785
190.9701236
191.9699688
192.9698140
193.9696591
194.9695044
195.9693496
196.9691949
197.9690400
198.9688954
199.9687308
200.9685762
201.9684216
202.9682670
203.9681124
204.9679579
205.9678033
206.9676489
207.9674944
208.9673400
209.9671855
210.9670311
211.9668768
212.9667224
213.9665681
214.9664138
215.9662596
216.9661053
217.9659511
218.9657969
219.9656428
220.9654886
221.9653345
222.9651804
223.9650263
224.9648723
[Page 169]225.9647183
226.9645643
227.9644103
228.9642563
229.9641024
230.9639485
231.9637946
232.9636408
233.9634870
234.9633332
235.9631794
236.9630256
237.9628719
238.9627182
239.9625645
240.9624109
241.9622573
242.9621037
243.9619500
244.9617965
245.9616430
246.9614895
247.9613360
248.9611825
249.9610291
250.9608757
251.9607223
252.9605690
253.9604157
254.9602623
255.9601091
256.9599558
257.9598026
258.9596494
259.9594962
260.9593430
261.9591799
262.9590369
263.9588837
264.9587306
[Page 170]265.9585775
266.9584245
267.9582715
268.9581185
269.9579656
270.9578127
271.9576598
272.9575069
273.9573541
274.9572013
275.9570485
276.9568957
277.9567430
278.9565902
279.9564375
280.9562849
281.9561322
282.9559796
283.9558270
284.9556744
285.9555219
286.9553693
287.9552168
288.9550644
289.9549119
290.9547595
291.9546071
292.9544547
293.9543023
294.9541500
295.9539977
296.9538454
297.9536932
298.9535409
299.9533887
300.9532365
301.9530843
302.9529322
303.9527800
304.9526280
[Page 171]305.9524759
306.9523239
307.9521719
308.9520199
309.9518679
310.9517160
311.9515640
312.9514121
313.9512603
314.9511084
315.9509566
316.9508048
317.9506530
318.9505013
319.9503495
320.9501978
321.9500462
322.9498945
323.9497429
324.9495913
325.9494397
326.9492881
327.9491366
328.9489851
329.9488336
330.9486822
331.9485307
332.9483793
333.9482279
334.9480766
335.9479251
336.9477739
337.9476226
338.9474713
339.9473201
340.9471689
341.9470177
342.9468665
343.9467154
344.9465642
[Page 172]345.9464131
346.9462621
347.9461110
348.9459600
349.9458090
350.9456580
351.9455071
352.9453561
353.9452052
354.9450543
355.9449035
356.9447526
357.9446018
358.9444511
359.9443003
360.9441495
361.9439988
362.9438481
363.9436975
364.9435468
365.9433962

[Page 173]

TABLE VII. The PRESENT WORTH of One Pound Annuity, to continue any Number of Years under 32, and payable by Yearly Payments, at 5, 6, 7, 8, 9, and 10 per Cent. Compound Interest. [Page 174] The PRESENT WORTH of One Pound Annuity, Comp. Int. At
Years.5 per Cent.6 per Cent.7 per Cent.
10.952380.943390.93457
21.859411.833391.80801
32.723242.673012.62431
43.545953.465103.38721
54.329474.212364.10019
65.075694.917324.76653
75.786375.582385.38928
86.463216.209795.97129
97.107826.801696.51523
107.721737.360087.02358
118.306417.886877.49867
128.863258.383847.94268
139.393578.852688.35765
149.898649.294988.74546
1510.379659.712249.10791
1610.8377610.105899.44664
[Page 176]1711.2740610.477259.76322
1811.6895810.8276010.05908
1912.0853211.1581110.33559
2012.4622011.4699210.59401
2112.8211511.7640710.83552
2213.1630012.0415811.06124
2313.4885712.3033711.27218
2413.7986412.5503511.46933
2514.0939412.7833511.65358
2614.3751813.0031611.82577
2714.6430313.2105311.98671
2814.8981213.4061612.13711
2915.1410713.5907212.27767
3015.3724513.7648312.40904
3115.5928313.9290812.53187
[Page 175]Years.8 per Cent.9 per Cent.10 per Cent.
10.925920.917430.90909
21.783261.759111.73553
32.577092.531292.48685
43.312123.239713.16986
53.992703.889653.79078
64.622874.485914.35526
75.206365.032954.86841
85.746635.534815.33492
96.246885.995245.75902
106.710086.417656.14456
117.138966.805196.49506
127.536077.160726.81369
137.903777.486907.10335
148.244237.786147.36668
158.559478.060687.60608
168.851368.312557.82371
[Page 177]179.121638.543638.02155
189.371888.755628.20141
199.603598.950118.36492
209.818149.128548.51356
2110.016809.292248.64869
2210.200749.442428.77154
2310.371059.580208.88322
2410.528759.706618.98474
2510.674779.822589.07704
2610.809979.928979.16094
2710.9351610.026589.237 [...]
2811.0510710.116139.30656
2911.1584010.198289.36960
3011.2577810.273659.42691
3111.3498110.342849.47901

[Page]

TABLE VIII. Shewing what Annuity, to con­tinue any Number of Years under 32, and payable by Yearly Payments, One Pound will Purchase, at the Rate of 5, 6, 7, 8, 9, and 10 per Cent. Compound Interest. [Page 180] A TABLE shewing what Annuity One Pound will Purchase, at several Rates of Comp. Int.
Years.5 per Cent.6 per Cent.7 per Cent.
11.050001.060001.07000
2.53780.54543.55309
3.36720.37411.38105
4.28209.28859.29519
5.23097.23739.24389
6.19701.20336.20979
7.17281.17913.18555
8.15472.16103.16746
9.14069.14702.15348
10.12950.13586.14237
11.12038.12679.13335
12.11282.11927.12590
13.10645.11296.11965
14.10102.10758.11434
15.09634.10296.10979
16.09226.09895.10585
[Page 182]17.08869.09544.10242
18.08554.09235.09941
19.08274.08962.09675
20.08024.08718.09439
21.07799.08500.09228
22.07597.08304.09040
23.07413.08127.08871
24.07247.07967.08718
25.07095.07822.08581
26.06956.07690.08456
27.06829.07569.08342
28.06712.07459.08239
29.06604.07357.08144
30.06506.07264.08058
31.06418.07181.07983
[Page 181]Years.8 per Cent.9 per Cent.10 per Cent.
11.080001.090001.10000
2.56076.56846.57619
3.38803.39505.40211
4.30192.30866.31547
5.25045.25709.26379
6.21631.22291.22960
7.19207.19869.20545
8.17401.18067.18744
9.16007.16679.17364
10.14902.15582.16274
11.14007.14694.15396
12.13269.13965.14676
13.12652.13356.14077
14.12129.12843.13574
15.11682.12405.13147
16.11298.12029.12781
[Page 183]17.10962.11704.12466
18.10670.11421.12192
19.10412.11173.11954
20.10184.10954.11745
21.09983.10761.11562
22.09803.10590.11400
23.09642.10438.11257
24.09497.10302.11126
25.09367.10180.11016
26.09250.10071.10915
27.09144.09973.10825
28.09048.09885.10745
29.08961.09805.10672
30.08882.09733.10607
31.08814.09670.10550

[Page 184]

TABLE IX. The PRESENT WORTH of any Lease, or Annuity, for 21, 31, 41, 51, 61, 71, 81, or 91 Years; as likewise the PRESENT WORTH of the see Simple. At 5, 6, 8, and 10 per Cent. Compound Interest.
Years to be Pur­chased.At 5 per Cent. The Purchase of Freehold Land.At 6 Per Cent. The Purchase of Copyhold Land, or Leases of Land.
 Years.Qua.Mo.Years.Qua.Mo.
2112311130
3115311332
4117011501
5118101530
6118321620
7119111612
8119211620
9119301620
Fee Sim­ple.20001622
Years to be Pur­chased.At 8 per Cent. The Purchase of very good Houses.At 10 per Cent. The Purchase of Leases of ordi­nary Houses.
 Years.Qua.Mo.Years.Qua.Mo.
211000832
311111930
411132932
511210932
6112111000
7112121000
8112201000
9112201000
Fee Sim­ple.12201000

CHAP. II.
The Use of the preceding TABLES of Compound Interest.

HAving with all imaginable care framed and calculated divers Tables relating to Compound Interest, it will be needful to apply the same to Use and Practice.

The Use of the first TABLE, shown in Two Examples.

Example I.

Suppose it be demanded to give the Amount of 136l. 15s. 6d. being for­born 20 years, at 6 per Cent. Compound Interest.

[Page 187] Direction.

The given Sum must first be reduced by the first Table of the first Book, and made 136.775, and then multiplied by the Number in the first Table answering to (20), in the Margin of pag. 144, viz. 3.20713.

Tariffa for the Mul­tiplicand.
1136775
2273550
3410325
4547100
5683875
6820650
7957425
81094200
91230975

[Page 188] The Operation may be contracted, according to the Rule in the Intro­duction.

[...]

The Product 438.6552 is the true Answer, and being reduced by the fifteenth Table of the first Book, makes 438l. 13 s. 1 d. 1 q.

Example 2.

Suppose it be demanded to give the Amount of the aforesaid Sum in 20 Years and 3 Quarters.

[Page 189] Direction.

Multiply the aforesaid Sum of 136.775, by the Number which answers to 20 Years and 3 Quarters, viz. 3.35040.

The Operation may be contracted as before. [...]

The Product 458.2509 is the Answer to the Question, and being reduced by the fifteenth Table of the first Book, makes 458l. 5s. more by 22/100 (or Ninety Two Hundred parts) of a Farthing.

The use of the second TABLE.

Suppose it be desired to know the Amount of 42 l. in 7 Months, at 6 per Cent. Compound Interest.

Direction.

Seek the Number in Table II. an­swering to (7) in the Margin, viz. 1.034574, and multiply it by 42, and the Product is the Answer. [...]

Which Product being reduced is 43 l. 9 s. 2 q. more by 2/100 (or Two Hundred parts) of a Farthing.

The use of the third TABLE.

Suppose it be demanded to find the Amount of 42 l. in 104 Days.

Direction.

Find the Number in Table III. an­swering to (104) in the Margin, viz. 1.016741, and multiply that by 42, and the Product is the Answer. [...]

Which Product being reduced, makes 42 l. 14 s. 2 q. more by 99/100 (or Ninety Nine Hundred parts) of a Farthing.

The use of the fourth TABLE.

Let it be demanded to find the Pre­sent Worth of 438 l. 13 s. 1 d. 1q. due and payable after the expiration of 20 Years, at 6 per Cent. Compound Interest.

Direction.

The given Sum being converted into a Decimal Number is 438.65520, then find the Number in Table IV. answering to (20) in the Margin, viz. .3118047, and multiplying one by another, the Product is the Answer.

Tariffa for the Multiplicand.
14386552
28773104
313159656
417546208
521932760
626319312
730705864
835092416
939478968

[Page 193] And the Operation may be contracted thus to seven places, by the Rule in the Introduction. [...]

The Product 136.7747 is a manifest Proof of the truth of the Operation in the first Example of the use of the first Table, pag. 186. there being not so much as the Hundredth part of a Farthing dif­ference.

[Page 194] The Use of the fifth TABLE.

Let the Present Worth of 43.452108 l. due after the expiration of 7 Months, be sought, according to the Rate of 6 per Cent. Compound Interest.

Tariffa for the Mul­tiplicand.
143452108
286904216
3130356324
4173808432
5217260540
6260712648
7304164756
8347616864
9391068972

[Page 195] The Operation contracted by the Rule in the Introduction. [...]

Which Product 41.99997 is a clear and manifest Proof of the truth of the Operation in the use of the second Table, pag. 190.

The Use of the sixth TABLE.

Let it be required to find the Present Worth of 42.703122 l. after the end of 104 Days, at the Rate of 6 per Cent. Compound Interest.

[Page 196]

Tariffa for the Multiplicand.
142703122
285406244
3128109366
4170812488
5213515610
6256218732
7298921854
8341624976
9384328098

The Operation contracted by the Rule in the Introduction. [...]

[Page 197] Which Product 41.99997, is a clear and manifest Proof of the truth of the Operation in the Example, calculated to shew the use of the third Table, pag. 191.

The Use of the seventh and ninth TABLES.

Let it be required to find the Present Worth of an Annuity of 56 l. to continue 21 years, and payable by yearly pay­ments, at the Rate of 6 per Cent. Com­pound Interest.

Direction.

First find the Number in Table VII. answering to (21) in the Margin, which is 11.76407; then multiply it by 56, without a Tariffa, because there are but two places in the Multiplicator, and the Product is the Answer.

[Page 198] [...]

Which Product being reduced by the fifteenth Table of the first Book, makes 657 l. 15 s. 9 d. more by 40/100 (or Forty Hundred parts) of a Farthing, which agrees with Mr. Kersey's Exam­ple, in his Appendix to Mr. Wingate's Arithmetick, pag. 412. only this Calcu­lation is more exact than his, and some­what nearer to the truth.

The Use of the eighth TABLE.

Let it be demanded what Annuity, to continue 14 years, and payable by yearly payments, will 320 l. buy, allowing 6 per Cent. Compound Interest.

[Page 199] Direction.

Seek in the Margin of Table VIII. the Number (14), and the Number answering to it, under the Title of 6 per Cent. viz. .10758; which mul­tiply by 320, and the Product is the Answer. [...]

Which Product 34.42560, being reduced by the fifteenth Table of the first Book, makes 34 l. 8 s. 6 d. more by 57/100 (or Fifty Seven Hundred parts) of a Farthing.

A farther Use of the seventh TABLE.

To convert a present Sum or Fine into an Annual Rent; or on the contrary, to bring down an Annual Rent by a present Sum or Fine.

Example 1.

A Landlord Lets a Lease of a House and Land for 21 years, and is to have 100 l. for that Lease, and a yearly pay­ment of 30 l. what Fine or present Money must the Tenant give, to bring down the Rent from 30 l. to 10 l. per Annum, allowing 6 per Cent. Compound Interest?

Direction.

First find the difference of 10 l. and 30 l. which is 20 l. then find by Table VII. pag. 176. what an Annuity of 1 l. to continue 21 years, is worth in present Money, which is 11.76407 l. then multiply 11.76407 by 20, and the [Page 201] Product gives the Present Worth of 20 l. per Annum for 21 years.

The Operation. [...]

Which Product 235.28140 being re­duced, is 235 l. 5 s. 7 d. 2 q. more by 14/100 (or Fourteen Hundred parts) of a Farthing.

Example 2.

A Landlord demands a Fine, or pre­sent Sum, for a Lease of 127 l. per Annum, to continue 7 years; what is the Sum, allowing 6 per Cent. Com­pound Interest?

Direction.

Find by Table VII. the Present Worth of 1 l. Annuity for 7 years, at 6 per Cent. viz. 5.58238, which multiply by 127, and the Product is the Answer.

[Page 202] The Operation. [...]

Which Product 708.96226 being re­duced by the fifteenth Table of the first Book, makes the just Sum of 708 l. 19 s. 2 d. 3 q. more by 77/100 (or Seventy Seven Hundred parts) of a Farthing.

And here the Reader is desired to take notice of a printed Sheet sold in Westmin­ster-Hall, Entituled, “A President for Purchasers, &c. Or Anatocisme (commonly called Compound Interest) made easie, &c. Computedly W. Leybourn. The principal Table in this Sheet is printed from a Copper Plate, but so full of gross Errors and mistakes, that it is not sit to be used: For

[Page 203] In this last Example, that Table makes tho Sum but 706 l. 16 s. 6 d. which the Table of this Book makes 708 l. 19 s. 2 d. 3 q. and more, (which Sum agrees with Mr. Clavel's Tables). But in very many places there is no less than 4, 5, 6, and 10 Pound mistaken, which must needs deceive all those, who do in the least rely upon, or give any cre­dit to it.

So that the AUTHOR of this little Book hopes, That the manifold Errors in the Calculations of other Writers, will occasion a more kind acceptance of his more than ordinary care and diligence in all the foregoing Tables; if not,

—Redit Labor actus in Orbem.

[...].

FINIS.

ADVERTISEMENT.

THere is newly Printed a Vade Mecum, or Necessary Com­panion; containing, 1. Sir Samuel Morland's Perpetual Almanack, in Copper Plates, with many useful Tables proper thereto. 2. The Computation of Years, comparing the Years of each King's Reign from the Conquest with the Years of Christ. 3. Reduction of Weights and Measures. 4. The ready Casting up any Number of Farthings, Half-pence, Pence, Shillings, Nobles and Marks; with Sir Samuel Morland's New Table for Guinneys. 5. The Interest and Rebate of Money, the Forbearance, Discompt, and Purchase of Annuities, at 6 per Cent. 6. The Rates of Post-Letters, both Inland and Outland, with the Times for sending or receiving them; also the Post-Stages, shewing the Length of each Stage, and the Distance of each Post-Town from London. 7. The Rates or Fares of Coach-men, Carr-men, and Water-men. And are sold by R. Northcot, Bookseller, either next St. Peter's Alley in Cornhill, or at the Anchor and Mariner on Fish-Street-Hill; by John Playford, Printer, near the Blew-Anchor Inn in Little Britain; and by Charles Blount, Bookseller, at the Black-Raven in the Strand, near the Savoy.

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