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Encyclopedia > Accumulation function

The accumulation function a(t) is a function defined in terms of time t expressing the time value of money. It is used in interest theory. The time value of money (TVM) or the present discounted value is one of the basic concepts of finance, developed by Leonardo Fibonacci in 1202. ...


The accumulation function assumes the initial investment to be 1. To obtain value of money where the initial investment is k, simply have

A(t) = k cdot a(t).

The accumulation function has the following two properties:

In mathematics, functions between ordered sets are monotonic (or monotone) if they preserve the given order. ...

Common accumulation functions

The accumulation function for the two common types of interest:


Simple interest

a(t)=1+t cdot i.

Compound interest

a(t) = (1 + i)t.

  Results from FactBites:
 
Accumulation function - definition of Accumulation function in Encyclopedia (110 words)
The accumulation function a(t) is a function defined in terms of time t expressing the time value of money.
The accumulation function assumes the initial investment to be 1.
It is an increasing function, in most cases, because interest are rarely negative.
Interest - Wikipedia, the free encyclopedia (1277 words)
The amount function for compound interest is an exponential function in terms of time.
In mathematics, the accumulation function are often expressed in terms of e, the base of the natural logarithm.
One should consult definitions of the exponential function for the mathematical proof of this limit.
  More results at FactBites »


 

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