The Doctrine of DECIMAL ARITHMETICK Simple Interest c. AS ALSO Of Compound Interest AND ANNUITIES Generally performed for any time of Payment or Rate of Interest by help of a particular Table of Forbearance of 1 l. Principal with Inlarged Rules Formerly abridged for portability in a Letter Case By John Collins Accomptant Philomath And since his Death both made Publick by J. D. LONDON Printed by R. Holt for Nath. Ponder at the Peacock in the Poultry near the Stocks-Market 1685. THE EPISTLE TO THE READER Courteous Reader IT is the accustomed way to Dedicate Books to some Honourable Person that thereby the Book might have the greater Esteem This Book needs no such Dedication for the Name of the Author which will never dye Ingenious Mr. John ted at the end of the Book whereby the Reader may see it no ways derogates from the Old Copy and thereby may see how full and plain the New Rules are in comparison to the Old This Book is a fit Companion for all Gentlemen Merchants Scriveners and other Trades-men that deal much in lending of Money upon Interest Mortgages buying of Estates either in Fee Copy or Lease holding Annuities Rent Charges Forbearance of Money Discompt or any other way concerning Interest c. When any Person does perfectly understand the large Rules he may if he pleases lay by the Book and only use the Compendium with the Tables to be carried about in a Letter Case and I hope in perusing this small Treatise the Reader will find that which will give him Satisfaction both as to the Rules and Tables Yours J. D. Decimal Arithmetick A Decimal Fraction is such a one whose Denominator is understood and not expressed and is an Unit with as many Cyphers following it as there are Figures and Cyphers in the Numerator Corollary Wherefore the annexing of Cyphers towards the right hand of a Decimal alters not its value A Decimal Fraction of Coin may be easily valued without the help of Tables For each Unit in the first place is in value 2 s. 5 in the second place 1 s. and the rest Farthings but if they exceed 25 48 there must be two farthings abated Example So ,854 is in value 17 s. 1 d. ,418 8. 4½ Addition and Substraction in Decimals is the same as in whole Numbers keeping the place of Units just under each other Multiplication in Decimals is the same as in Common Arithmetick saving as many Decimal Parts as are in both Multipliers so many must be cut off from the Product which if it have not so many places the Defect is to be supplied with Cyphers towards the left hand Division is the same as in whole Numbers without regard to Decimals till the Work is done and then use the Converse of the Rule for Multiplication viz. so many Decimals as are in the Dividend so many there must be in the Divisor and Quote and if there be not so many the Quotient must be supplied with Cyphers towards the left hand Simple Interest PROP. 1. TO compute the Interest for a day 6 365 is the Interest of 100 l. for a Day the 1 100 whereof is the Interest of 1 l. for a Day viz. 6 36500 Or 6 with Cyphers put on at pleasure divided by 36500 is 000164383 the Interest of 1 l. for a Day Prop. 2. The Decimals of Days in the Table at the end will serve to find the amount of 1 l. Simple Interest of any Rate for any time under 365 Days or a Year If you take the Decimal for one day or more and multiply that by 06. 7. 8. c. per Cent. or any other Rate the Product will give the Interest of one pound for a Day or more under 366 Days at Simple Interest Example 1. The Decimal for a day is ,002739726   ,06 The Interest of 1 l. for a day ,00016438356 Example 2. The Decimal of 121 days is ,331506849  ,06 The Interest of 1 l. for 121 days ,01989041094 ,002739726 Decimal for a day ,07 per Cent. ,00019178082 The Interest of 1 l. for a day at 7 l. per Cent. And so of any other rate of Interest Prop. 2. Forbearance of Money at Simple Interest The Interest of 1 l. for any Number of days at what rate of Interest you please be first found by the first Proposition that Product multiplied by the Sum propounded gives the Interest thereof for the time required Example To know the Amount of 140 l. for 121 days at 6 l. per Cent. Simple Interest The Decimal of 1 l. for 121 days 1,019890410 Multiplied by 140 Which is 142 l. 15 s. 8 d. 40795616400  1,019890410  142,784657400 Prop. 3. Rebate or the Present worth of Money due hereafter Find the Interest of 1 l. for the time given as in Prop. 1. And thereto add an Unit by it Divide any other Sum propounded and the Quote is its present Worth Example If 142 l. 15 s. 8 d. be due at the end of 121 days what is it worth in ready Money Worth in ready Money 140 l. at 6 l. per Cent. Simple Interest and may be done for any other rate of Interest working by the first Proportion and this former Rule Prop. 4. Equation of Payments By Prop. 3. compute all the Present Worths and then by Proportion If all those Present Worths amounted to the Total of all those Payments what did one pound amount to in the said time From the result substract an Unit the Remainder is the Interest of 1 l. for the time sought which divide by the Interest of 1 l. for a day the Quote is the Number of days sought If you are to Aequate an Annuity at Simple Interest I presume a Compendium may be found in Mengolus his Arithmetical Quadratures a Book I never saw who it 's probable by a Compendium gets the fact of an Arithmetical Progression and adds Fractions that have a constant Numerator and an Arithmetical Progression for their Denominators So much for Simple Interest my Design being more for the Explanation of the Tables for Compound Interest and Annuities Of Compound Interest THe Original thereof is Derived from Simple Interest for if it be Lawful to take Interest at all then it is as Lawful to put out the Interest-Money to Use as the Principal For ease in Calculating Questions that concern Compound Interest Arithmeticians do usually frame Tables in store to shew what 1 l. Principal forborn at any Rate for any determinate time shall amount unto the Construction whereof is by the Golden Rule as followeth As 100 l. Principal is to the amount thereof at the years end So is an Unit. To its amount to wit So is 1. 1 06. If 6 be the rate of Interest then it will hold again for the next year As 1. 1 06 so 1 06 to 1 1236 the principal and Interest at the second year Now because an Unit is in the first place which doth not divide it followeth that the second