Before I post the problem I should check that this is being posted in the right forum. Not being a mathematician myself I am not even certain of the area of maths I should be posting the question. Some say the solution would be solved with a complex polynomial and others say it is a variation on a geometric series). Apologies if this is in the wrong forum and would you kindly point me to the right one.

In non mathematical terms here is the problem. I have clients who ask me to calculate a return on their investment from existing pension portfolios. The inputs I usually receive are the dates of lump sums invested and amounts and the dates of regular monthly sums invested, their respective dates and amounts. Then I look up the current value and want to try to figure out what the return or ever something resembling a best estimate of a return would be.

example case

a) Lump sum invested in December Jan 2011 of £55,186 plus

b) Regular monthly contributions made since Jan 2011 amounting to £64,220. Monthly contribution amounts have varied between £1394 per month and £1878 per month.

c) Total value of contributions is a+b (£120,036) however b has been invested over a period of time.

d) Value today is £149,000

I would be happy taking average value of monthly contributions as a guide if that would make the problem easier to solve.

Any help would be appreciated.