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:

Simple interest

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

Compound interest

$a(t)=(1+i)^{t}.$