Help / ideas with fixed income analysis problem

Hello everybody,

Although the context of my problem isn't important, it has to do with
the accretion of original issue discount for fixed income securities. 
I have been given the following iterative procedure by the
business/tax experts to calculate a particular point on a curve:

(I)Y - C = p1 (delta first period)
(I+p1)Y - C = p2 (delta second period)
(I+p1+p2)Y - C = p3 (delta third period)

Given these equations, one can draw a curve from point(I) to
point(I+p1) to point(I+p1+p2) etc.  However, in order to find
point(I+p1+p2+...+pn), one must iteratively solve n equations and then
take their sum.

I would like to know if there is any way to create a "closed" equation
to describe this function?  Something along the lines of "y =
nIY^(n-1) - nC", where n = number of periods (this is a totally
fabricated solution, I'm just worried that my terminology isn't clear,
so I'm trying to give an example of what I'm looking for).

It seems to me that I have a curve, therefore I have a continuous
function.  And if I have a continuous function, I should be able to
find an equation to represent it.  However, all the financial analysis
textbooks point to the iterative solution.

Can anyone help me?

Thank you!

Anthony