Your question needs better clarification.

sorry for this.

So I have 4 real estate projects, for each of them there is a lease in
place, where a tenant pays a rent.
The problem is that this rent might change at any date, within the
year. In the example above, for the project A, tenant pays 1800m from
1/11/2011 to 31/10/2012. This means that in 2012 tenant pays for the
first 10 months= (1800/12)*10. Then for the last 2 months of 2012 rent
steps up to (2200/12) per month (second row in the example above).
And so on.
Rent might change/step up without any fixed rule. I need a formula
which gives me the total paid for each project in a specific year. So
the formula would check how many months for the year in question
tenant pays a specific bracket (in the example above, for 2012 tenant
pays first bracket for 10 months, and second bracket for 2 months) and
sum the result. I believe is a sort of Sumproduct IF the bracket falls
within the year I am summing up, or something like this.

Hope this is clearer now
thanks a lot in advance
cheers