Excel Conundrum - Formula for break even year

Hi

I have the following scenario:

I have a large Excel spreadsheet that is part of a quotation system to our customers and this illustrates the financial outlay for a piece of equipment and the payback period that equipment gives to the customer. The customer receives an annual estimated payment which is index linked (rises with inflation) and after x years the system has paid for itself, with future years generating profits.

So far we have only illustrated to our customers a worst case scenario where all payments are flat without being index linked, as we cannot predict the future and did not want to over promise. But sales have had a few conversations now when customers have seen quotes from other companies with much shorter payback periods, nearly losing the deal as the competitors showing this with inflation rises included.

So we now want to show both. For example:

Equipment cost (C) is £15,000 and the annual payment (p) is £1,500 the break even is C/p or 10 years.

Now with inflation (i) the payment is p+(p*i)=p1; p1+(p1*i)=p2 etc.

I am displaying this in a table showing a 20 year projection for payments and a graph to illustrate this from a starting point of -£15,000.

My issue is that the payments are ever increasing up to a point in time when the total payment is equal to the capital cost. As this is a curve simple calculations for C divided by p don't work...and I need to show:

Break even based on 0% inflation = x.x years
Break even based on 4% inflation = y.y years

So as I need to show the break-even year on a capital investment where payments towards this are index linked, how do I get the exact figure when there is no simple method to calculate it?

thanks much
capt.