math lessons - 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 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:

$a (0) = 1.$
It is an increasing function, in most cases, because interest are rarely negative.

Common accumulation functions

The accumulation function for the two common types of interest:

$a(t)=1+t \cdot i.$

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