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A51383 The doctrine of interest, both simple & compound explained in a more exact and satisfactory method then [sic] 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, discomps, and purchase of annulites : as likewise, equation of payments made practicable and useful for all merchants and others : together with divers other useful reflections / ... Sir S. Morland. Morland, Samuel, Sir, 1625-1695. 1679 (1679) Wing M2778; ESTC R13339 38,468 270

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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 100 l. 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 10 7.93 7.35 20 14.27 11.46 30 20.03 13.76 40 25.52 15.01 50 30.87 15.72 60 36.13 16.16 70 41.32 16.38 80 46.48 16.50 90 51.60 16.57 100 56.71 16.61 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 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 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 30 s. a Quarter for 100 l. let out to him at 6 per Cent. because if 100 l. be put out to Interest and the Interest come to 1 l. 10 s. the first Quarter that 101 l. 10 s. by the end of the next Quarter keeping to Geometrical Proportion will become 103 l. 5 d. 1 q. more by 6● 100 of a Farthing that is to say 100 l. after this manner would amount in a years time to 106 l. 2 s. 8 d. 2 q. 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 1000000 l. and it were agreed to pay at the Rate of 30 s. for each 100 l. the first Quarter and it were not paid 'till the Twelve Months end the Amount would be as follows Which at the years end amounts to 60000 l. which ought to be the Total Sum of the Interest for 12 Months at 6 per Cent. and over and above the said 60000 l. there is 1363 l. 11 s. 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 6 l. 2 s. 8 d. 2 q. 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 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 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. 15 9 6 1 39 8 3 0 48 7 2 1 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 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. 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 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