M. Porcius Cato Posted February 13, 2007 Author Report Share Posted February 13, 2007 Re compounding periods. On a two year loan, the compunding period may be annual, semi-annual or monthly, etc. Think of a 0% bond. It is the compounding periods that are critical in determining the sum returned. Yes, of course. But if we vary the compounding period over an infinite hypothetical space, is there any value which returns an algorithm for calculating financial losses on one's fingers? Quote Link to comment Share on other sites More sharing options...
Gaius Octavius Posted February 13, 2007 Report Share Posted February 13, 2007 (edited) Yes, of course. But if we vary the compounding period over an infinite hypothetical space, is there any value which returns an algorithm for calculating financial losses on one's fingers? This entire statement is beyond my 'cognitive methods'. Edited February 13, 2007 by Gaius Octavius Quote Link to comment Share on other sites More sharing options...
Ruthe Posted February 14, 2007 Report Share Posted February 14, 2007 (edited) Phew - gents! Well, all I know is that Atticus' fingers must have been a lot better than mine. :whistling:/>/> But more seriously, did Cicero mean to imply that Atticus would count on his fingers, or was he referring to Atticus' speedy fingers on an abacus? Just a thought that struck me. You may find a previous thread also titled "Roman Mathematics" currently at the bottom of page 3 of Romana Humanitas can provide some guidance on Roman interest calculations and the use of 'finger' and abacuses (I am informed that abacus is not a Roman word and so the plural is NOT 'abacii'). My post of August 14 2006 at 02:19Am in that thread and some of the following posts describe the use of a Roman Pocket Calculator (which was a form of abacus but streamlined for portability). It includes the following link to the site of Prof. Dr. J Edited December 2, 2012 by Ruthe Quote Link to comment Share on other sites More sharing options...
M. Porcius Cato Posted February 14, 2007 Author Report Share Posted February 14, 2007 (edited) It is not hard to see why the Romans set their standard rate of interest at 12% and its multiples and factors given their use of duodecimal fractions. But they were also known to charge interest at rates other than 12% and its multiples and factors. We have Latin terms for: Asses usurae, or one as per month for the use of one hundred = 12 per cent Deunces usurae 11 per cent Dextantes usurae 10 per cent Dodrantes usurae 9 per cent Besses usurae 8 per cent Septunces usurae 7 per cent Semisses usurae 6 per cent Quincunces usurae 5 per cent Trientes usurae 4 per cent Quadrantes usurae 3 per cent Sextantes usurae 2 per cent Unciae usurae 1 per cent Edited February 14, 2007 by M. Porcius Cato Quote Link to comment Share on other sites More sharing options...
Ruthe Posted February 14, 2007 Report Share Posted February 14, 2007 It is not hard to see why the Romans set their standard rate of interest at 12% and its multiples and factors given their use of duodecimal fractions. But they were also known to charge interest at rates other than 12% and its multiples and factors. We have Latin terms for: Asses usurae, or one as per month for the use of one hundred = 12 per cent Deunces usurae 11 per cent Dextantes usurae 10 per cent Dodrantes usurae 9 per cent Besses usurae 8 per cent Septunces usurae 7 per cent Semisses usurae 6 per cent Quincunces usurae 5 per cent Trientes usurae 4 per cent Quadrantes usurae 3 per cent Sextantes usurae 2 per cent Unciae usurae 1 per cent I did not imply that other rates were not used, only that the standard was 12%. As for all the other rates, these were all elements of the duodecimal fractions used by the Romans. The first group below were used for both weights and lengths and a subset were used for fractional parts of capacities but with different names. ............................As=1........Uncia=1 As......................12/12.............12 Deunx................11/12.............11 Dextans..............10/12..(5/6)...10 Dodrans................9/12.(3/4).....9 Bes.......................8/12.(2/3).....8 Septunx.................7/12.............7 Semis....................6/12.(.1/2)....6 Quincunx...............5/12..............5 Triens....................4/12.(1/3).....4 Quadrans...............3/12.(1/4).....3 Sextans.................2/12.(1/6).....2 Sesuncia................1/8............1 1/2 Uncia.....................1/12.............1 In addition, there were also the following fractions. Semuncia].............1/24............1/2 Duella]...................1/36...........1/3 Sicilicus]................1/48............1/4 Sextula]................1/72............1/6 Drachma]..............1/96............1/8 Dimidio sextula]....1/144...........1/12 Tremissis]............1/216...........1/18 Scrupulus]............1/288...........1/24 Obulus]................1/576...........1/48 Bissiliqua]............1/864...........1/72 Cerates]..............1/1152..........1/96 Siliqua]................1/1728..........1/144 Calcus]................1/2304..........1/192 What I intended was to illustrate the Roman use of duodecimal fractions as part of the argument that they were far more capable practical mathematicians then previously portrayed. Simply because of their unusual and unwieldy written numeral system, it has been implied that they were incapable of performing complex calculations. This is an argument to refute that impression. Quote Link to comment Share on other sites More sharing options...
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