You and I are going to run a little risk here: I run the risk of dealing with this applied-maths
problem whereas I'm definitey more pure-maths oriented, and you run the risk
that what I do here is trash:
I think that what you want to know is what discount must you offer (and what formula
to produce) to your clients if your contract is terminated after some fraction of the
original one year, so it is simply a rule of three (or whatever this is called in engish):
if by the whole work (1) you give 40% discount, then for a proportion of r (r < 1) of this
work, you must give discount...
Thus, if your work is terminated after a portion r of that 1 year, you must charge
, where x = the original price for
the whole one year work without discount.