A polynomial that is a statistical prism

2003 ◽  
Vol 87 (508) ◽  
pp. 76-85
Author(s):  
Mike Osborne ◽  
Mark Osborne

The roots of a polynomial can be represented as points in the complex plane. The time value of money (TVM) equation that is commonly used in finance is a polynomial equation. (See the appendix for a short description of the TVM equation and an example of its use in finance.) In [1] and [2] it is shown that concepts from financial mathematics can be obtained from the pattern of the roots of the TVM equation. The concepts are given in terms of distances between the roots and other salient points in the plane. This note shows that this particular polynomial, and the technique, can be applied more generally. When a series of data is fed into the coefficients of the polynomial, the mean and standard deviation of the data are seen in the complex plane as combinations of distances between the roots and other salient points. The results are aesthetically pleasing as well as mathematically interesting.

2006 ◽  
Vol 23 (1) ◽  
pp. 66-89
Author(s):  
Abu Umar Faruq Ahmad ◽  
M. Kabir Hassan

The time value of money is a basic investment concept and a basic element in the conventional theory of finance. The Shari`ah does not rule out this consideration, for it does not prohibit any increment in a loan given to cover the price of a commodity in any sale contract to be paid at a future date. What is prohibited, however, is making money’s time value an element of any lending relationship that considers it to have a predetermined value. Here, the Shari`ah requires that a loan be due in the same currency in which it was given. The value (i.e., purchasing power) of paper currencies varies due to changes in many variables over which the two parties of a loan contract usually have no control. This study examines possible modus operandi of time valuation according to the Shari`ah’s precepts vis-à-vis the concept of money, and whether any value can be attributed to time while considering money’s value. For this purpose, it investigates the juristic views on such relevant issues as the permissibility of difference between a commodity’s cash and credit prices and an increase and reduction of the loan’s amount in return for early repayment.


2005 ◽  
Author(s):  
Sheldon R. Smith ◽  
Steve D. Johnson ◽  
Rick T. Henage

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