Arithmetic gradient P/G calculator

Discount a sequence increasing by a fixed increment, starting with zero gradient in year one.

P = \frac{G \times \left[\left(1 + i\right)^{n} - i \times n - 1\right]}{i^{2} \times \left(1 + i\right)^{n}}

Calculator

Enter the values you know and leave one box empty. Calculate finds the empty one, the result or any input.

Given

P = \frac{100 \times \left[\left(1 + 0.08\right)^{10} - 0.08 \times 10 - 1\right]}{{0.08}^{2} \times \left(1 + 0.08\right)^{10}} \approx 2{,}598

Symbol	Meaning	Unit
$P$	present worth of the gradient	$
$G$	increase per successive payment	$/period
$i$	discount rate per period	decimal
$n$	number of periods	periods

Results are estimates for study and screening. Check the inputs, units and assumptions before you use them for design, billing or contract decisions.