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

.

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

Compound Interest

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