Growth factor (math)

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The growth factor is the constant quotient of two successive terms of a geometric sequence . The term is mainly used when the episode describes a real exponential growth process. When it comes to the interest on capital or debt, one also speaks of the interest factor . A growth factor of is colloquially referred to as "growth". In financial mathematics , one speaks of the compounding or discounting factor . Growth to mean a growth factor , that is a growth on twice; growth by means of a growth factor , thus a growth of three times, etc. With growth factor is present, however, "negative growth". In financial mathematics then one speaks of discounting - or discounting . The term “growth factor” is not used for geometric sequences with negative .

calculation

The growth factor can be calculated from two consecutive terms and a geometric sequence using the following equation:

For example, the growth factor of the sequence , , , ... calculated, for example with the members and through .

The following equation can be used to calculate from any two terms and with the distance :

If and, on the other hand, are members of an error-prone sequence with exponential growth, then this equation is used to determine the geometric mean of the growth factor between members to . Examples: The growth factor of the sequence , , , ... calculated, for example with the members and through . The average growth factor of the faulty sequence , , , is calculated with the members and through .

If the growth rate is known, the growth factor can be calculated with:

With the same equation, the growth factor can also be calculated from the percentage growth if you divide its value by 100 beforehand. Example: The growth factor of a geometric sequence with a growth rate of or a growth of is calculated by or .

Negative growth

For between 0 and 1 there is a "negative growth", i.e. a decrease, because it must be negative. From a financial mathematical point of view , the discounting or discounting factor at the rate of interest is then usually designated with

.

Example: With a "negative growth" of is and the interest rate . The discount factor and the discount factor then belong to this interest rate .

Individual evidence

  1. ^ IN Bronštejn, KA Semendjajew, G. Musiol, H. Mühlig: Taschenbuch der Mathematik . 6th edition. Harri Deutsch, Frankfurt am Main 2005, ISBN 978-3-8171-2006-2 .