# The History of Business and Financial Mathematics

Work provided to Mathematics Only by
Prof. Jean Piton-Gonçalves

I-) Introduction

The concept of interest is very old and has been widely disseminated and used throughout history. This concept arose naturally when man realized that there is a close relationship between money and time. Processes of capital accumulation and currency devaluation would normally carry the idea of ​​interest, as they were basically due to the time value of money.

The older boards show a high degree of computational skill and make it clear that the positional sexagesimal system was long established. There are many early texts dealing with the distribution of agricultural products and arithmetic calculations based on these transactions. The tables show that the ancient Sumerians were familiar with all sorts of customary legal contracts, such as invoices, receipts, promissory notes, credit, simple and compound interest, mortgages, deeds of sale, and endorsements.

There are boards that are commercial company documents and others that deal with weight and measurement systems. Many arithmetic processes were carried out with the help of several tables. Of the 400 mathematical tables about half were mathematical tables. The latter involve multiplication tables, multiplicative inverse tables, square and cube tables, and even exponential tables. For these, they were probably used, along with the challenge, in compound interest problems. Inverse boards were used to reduce division to multiplication.

II-) Interest and Taxes

Interest and taxes have been around since the earliest records of civilizations on earth. One of the first indications appeared in Babylon already in the year 2000 BC. In earlier quotations, interest was paid for the use of seeds or other borrowed conveniences; interest was paid in the form of seeds or other goods. Many of the existing practices originated in the old ways of borrowing and returning seeds and other agricultural products.

History also reveals that the idea had become so well established that there was already an international banker firm in 575 BC with its central offices in Babylon. His income came from the high interest rates charged for using his money to finance international trade. Interest is not only one of our earliest applications of financial mathematics and economics, but its uses have undergone little change over time.

As with all instructions that have existed for thousands of years, some of the interest rate practices have been modified to meet current requirements, but some of the old customs still persist so that their use today still involves some cumbersome procedures. . However, we must remember that all the old practices that still persist were entirely logical at the time of their origin. For example, when seeds were loaned for sowing in a certain area, it was logical to expect payment at the next harvest - within a year. Thus, the calculation of interest on an annual basis was more reasonable; as well as the establishment of compound interest to finance the old business trips, which could not be completed in a year. According to the necessity of each epoch, new ways of working with the time-interest relation (semiannual, bimonthly interest) , diary, etc).

There are boards in the Berlirn, Yale, and Louvre collections that contain compound interest problems, and there are some boards in Istanbul that seem to have originally been boards from a 'to n from 1 to 10 and to a = 9, 16, 100. and 225. With these tables one can solve exponential equations of type a '= b. On a Louvre table, circa 1700 BC, there is the following problem: How long should a certain sum of money be applied to compound annual interest of 20 percent to double it?

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