ARITHMETIC GRADIENT.

It frequently happens that the cash flow series is not of constant amount A. Instead, there is a uniformly increasing series as shown:

Cash flows of this form may be resolved into two components:

Note that by resolving the problem in this manner, the first cash flow in the arithmetic gradient series becomes zero. This is done so that G is the change from period to period, and because the gradient (G) series normally is used along with a uniformseries (A). We already have an equation for P', and we need to derive an equation for P". In this way, we will be able to write